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Destriping MODIS Data Using Overlapping Field-of-View Method Maurizio di Bisceglie, Member, IEEE, Roberto Episcopo, Carmela Galdi, Member, IEEE, and Silvia Liberata Ullo, Member, IEEE
Abstract—Multispectral sensors using array of detectors are affected by striping, an artifact that appears as a series of horizontal bright or dark periodic lines in the remotely sensed images. Nonlinearities and memory effect of detectors are the main causes of the striping problem that is not effectively corrected in the onboard or postprocessing calibration phases. In order to clear striping from images, we consider a new procedure based on detector response equalization and apply it to Moderate Resolution Imaging Spectroradiometer data from Terra and Aqua satellites. After identification of the out-of-family detectors, a least squares equalization stage is considered for calibration by using the intrinsic data redundancy caused by the bow-tie effect, where multiple observations of the same field of view are available from different detectors. The main advantage of this method, with respect to others such as the histogram equalization, is due to the independence of the measurements on the scene statistics, which, otherwise, will cause an overestimation or underestimation of the detectors’ responses. The new procedure performance is validated using data received at the Mediterranean Agency for Remote Sensing and Environmental Control ground station facility in Benevento—Italy and data downloaded from NASA LAADS Web site. The main results are presented, by showing the effectiveness of the method and the stability of the correction coefficients, at least on one-orbit periods. Index Terms—Calibration, equalization, least squares (LS), Moderate Resolution Imaging Spectroradiometer (MODIS), striping.
I. I NTRODUCTION
T
HE MODERATE Resolution Imaging Spectroradiometer (MODIS), onboard Terra and Aqua satellites, is an imaging radiometer based on a cross-track dual-sided scan mirror and a set of linear array detectors with spectral interference filters located into four focal plane assemblies. MODIS provides multispectral observations in 36 spectral bands ranging from 0.4 to 14.5 μm with spatial resolutions from 250 m to 1 km. During the scan cycle, the sensor is pointed toward four onboard calibrators that are used to convert the instrument measurements to a radiometrically calibrated data product. Reflectance data come from the 20 reflective solar bands, calibrated through the Solar Diffuser biweekly (Terra) or triweekly
Manuscript received March 21, 2007; revised October 31, 2007 and February 20, 2008. Current version published January 28, 2009. M. di Bisceglie, C. Galdi, and S. L. Ullo are with the Facoltà di Ingegneria, Università degli Studi del Sannio, 82100 Benevento, Italy (e-mail:
[email protected];
[email protected];
[email protected]). R. Episcopo is with the BU Observation System and RADAR, Thales Alenia Space, 00131 Rome, Italy (e-mail:
[email protected]). Digital Object Identifier 10.1109/TGRS.2008.2004034
(Aqua). Radiance data come from the 16 thermal emissive bands, calibrated scan by scan through the Blackbody and the Space View [1]–[5]. Since its first acquisition in February 2000, it was clear that some additional efforts would have been necessary in order to reach the full potential from MODIS instrument. The MODIS Characterization Support Team has deeply investigated the optical crosstalk from band 31 into bands 32–36, the short-wave infrared thermal leaks, and the electronic crosstalk among bands 5–7 and 20–26. Other specific factors, as the nonuniform channel-to-channel response within a band and the gain changes, have been largely analyzed too [6], [7]. At the current stage of research, among the problems that remain not completely solved, striping is a well-known impairment that affects the radiometric measurement of MODIS and, more generally, represents a very common problem for all instruments based on a sensor array. A stripe is an artifact that appears as a series of horizontal bright or dark periodic lines in the remotely sensed images. In principle, striping could be removed by inverting the gain function of the individual detectors, and therefore, recent sensors have onboard calibrators to track the detectors’ response continually or, as for MODIS, periodically. However, some nonlinearities in the system characteristics cannot be easily captured, and some striping still affects the images even after the gain function inversion. Several methods have been proposed in the literature for destriping satellite images. Among statistical matching methods, a destriping algorithm for Landsat MSS images [8] has been implemented by Horn and Woodham. This algorithm is based on the assumption that the probability of observing a given radiance value is approximately the same for all detectors. At the first stage, the authors consider a linear correspondence between input and output of each sensor, where the offset and the gain are known in some way or are estimated using simple statistics drawn from the observations. In a first approximation, coefficients are computed using the mean and the standard deviation of the data, and this method is referred to as moment matching. Final results have demonstrated that the method is effective whenever the observations from the individual detectors have the same empirical cumulative distribution function (ECDF). Other works are based on a histogram evaluation procedure: Kautsky et al. [9] proposed a smoothed histogram modification and Weinreb destriped Geostationary Operational Environmental Satellite images by matching the ECDFs [10]. In 1990, Wegener designed an improved histogram-matching algorithm where ECDFs are made over homogeneous regions [11]. The histogram-matching approach has some interesting features, particularly for high- and medium-resolution sensors where the
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hypothesis of homogeneous ECDF is not so far from reality. More recently, in 2003, Gumley et al. [12] have adapted the histogram-matching technique to remove striping and banding in MODIS data, and in 2004, Xiaoxiang et al. [13] have applied the original algorithm to destripe SZ-3 Chinese MODIS data. After that, the destriping algorithm has been included in the International MODIS/AIRS Processing Package (IMAPP), but further modifications are necessary in order to reduce its sensitivity to nonhomogeneous areas. A different approach, based on spatial filtering, has been presented by Crippen [14]; in this paper, a low-pass filter has been used for removing the scan-line noise from Landsat Thematic Mapper data. The results, however, highlight that some information has been lost and that low-pass filtering leads to significant blurring in the image. To circumvent this problem, Chen et al. in 2003 [15] exploit the regularity of the stripes to identify and modify the frequency content only at the “striping” frequencies. The reconstruction of the scene information content at such frequencies, even if improved, is not a trivial operation, and some information is still lost. Very recently, the histogram-matching approach has been combined with an iterated weighted least squares facet filter [16]. The overall algorithm is able to reduce detector-to-detector stripes, mirror stripes, and noisy stripes. The last class of algorithms relies on radiometric equalization. Moving from the first algorithms, mainly based on the equalization of nonperiodic striping [17] and on image processing through histogram modification [8], [9], Corsini et al. in 2000 [18] successfully designed a striping removal procedure for Modular Optoelectronic Scanner B data. According to the proposed model, the signal recorded by the jth detector is the sum of the contributions from the Earth–atmosphere system in the field of view (FOV), from the striping term (that depends on the scene), and from the thermal noise. Starting from this model, the authors suggest to estimate the striping contribution by averaging a set of quasi-homogeneous adjacent rows. This operation leads to computing an estimate of the striping signal in a polynomial form whose unknown coefficients are suitably estimated. The limit of this method is due to homogeneity constraint on images to be destriped. Open literature and research are clearly moving toward the analysis of homogeneous spatial regions and toward the development of onboard calibration procedures. Along this way, the scope of this paper is the derivation of a calibration algorithm for MODIS detectors using the intrinsic redundancy in the sensor FOV. We focus on the thermal emissive bands, where two calibrators, the Blackbody and the Space-View, are used to adjust the calibration coefficients according to a predefined procedure, but residual time-varying nonlinearities, which are not compensated, still induce occasional striping. The acquisition geometry of the instrument [19] provides extra information through the bow-tie effect, a distortion in the geometry of the instantaneous FOV (IFOV) occurring at wide scan angles. Due to bow-tie, subsequent scans overlap at the outer edges of the swath, and multiple observations of the same FOV are produced. The basic idea, presented in [20] and exploited here in a more extensive way, is to provide side information for cross-calibration purposes. The implementation requires two fundamental steps: the identification
of the detectors that behave correctly (which we define in the sequel as the in-family (IF) detectors) and equalization of the detectors that produce the striping (which we call outof-family (OF) detectors). Other side questions that will be addressed are the identification of the overlapping FOVs, the evaluation of the overlap percentage, and the preequalization of the IF detectors. MODIS detectors will be classified as IF or OF based on suitable figures of performance. The first figure is the bow-tie-based detector distance (BTBDD), based on radiance values measured in the overlapping FOV; the second figure is a distance between distributions. The destriping of the OF detectors is based on a least squares (LS) formulation of the problem, aimed at equalizing the overall response of the detectors through a model for the striping signal that is linear in the parameters. Bands 24, 27, 28, and 30 of MODIS data have been used to validate the proposed algorithm. The data sets have been acquired at the Mediterranean Agency for Remote Sensing and Environmental Control (MARSec) ground station facility in Benevento, Italy, and processed using the University of Wisconsin IMAPP [12] and FRAPPE (FRAmework package for Pipeline Processing Experiment, a parallel version of IMAPP and NASA-DAAC processing software jointly implemented by MARSec and University of Wisconsin). Short-time variation of the equalization coefficients has also been considered using granules 20040721.0810 and 20040721.0945, relative to successive satellite passes. II. O VERLAPPING FOV M ETHOD The FOV overlap is due to the technical features of the MODIS instrument where a cross-track mirror scans a portion of the Earth surface whose dimensions are 2330 km across track times 10 km along track (AT) at nadir. Due to the geometry of the Earth footprint, which, at wide view angles (i.e., far from nadir), enlarges, taking the shape of a bow-tie, the observations from some contiguous detectors of the array overlap. The degree of overlap between two detectors is, essentially, a geometric problem depending on the instrument characteristics and on its orbit. Fig. 1 shows the reprojection on the Earth geoid, only for wide view angles, of three successive MODIS scans: It is clear that the IFOVs overlap, but this occurs between some specific detectors only. Geometric evaluations lead to Table I where the × mark indicates that the corresponding pairs of detectors overlap in two consecutive scan lines. Thus, detectors d1 −d5 are the first five detectors in the array, and they observe the upper region of the scene at the nth scan line, while detectors d6 −d10 , in the (n + 1)th scan line, have some FOVs overlapping with d1 , and so on. At a first look, it is not difficult to understand that the number of overlapping pairs is small if compared to the overall number of cells and that the range of available radiance values will be reduced after the selection of the overlapping FOVs. Moreover, it may happen that some detector overlaps with some OF detector only, and in this case, it cannot be correctly characterized and equalized using the bow-tie data. The destriping procedure is analyzed in the next sections that are structured as follows: A) identification of overlapping FOVs; B) detectors classification;
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TABLE II INITIAL BTBDD. NONOVERLAPPING PAIRS ARE MARKED AS NA. VALUES IN [W · m−2 · sr−1 · μm−1 ] × 10−3
Fig. 1. IFOVs of MODIS instrument, near the edge of the scan, reprojected on the Earth geoid. Different scans in green–red–black colors show the overlap at wide scan angles. TABLE I AVAILABLE OVERLAP IN TWO CONSECUTIVE SCAN LINES FROM SOME CONTIGUOUS DETECTORS
C) preequalization of IF detectors; D) destriping via LS minimization; E) performance indices. A. Identification of Overlapping FOVs This analysis is devoted to the identification of the useful FOVs and to the evaluation of their overlap percentages. A preliminary task is carried out through the geolocation data for finding the overlapping areas. A flat-Earth approximation is used with the understanding that, for small areas (few square kilometers), the error introduced with respect to the true shape of the geoid is negligible. The evaluation of the overlap percentages requires an acceptance threshold for declaring that the FOVs overlap and a weighting function accounting for a nonperfect overlap. The experimental analysis on MODIS data has demonstrated that a threshold value of 0.65 is a good compromise between accuracy of measurements and number of available samples. Instead, a further increase of the acceptance threshold reduces both the number of available points (sometimes dramatically) and the range of available radiance values and may compromise the effectiveness of the algorithm.
Fig. 2. ECDF for all the detectors computed on the original image.
for each pair of detectors on the overall scene. The BTBDD is a reliable measure, but its evaluation is possible on bow-tie data only, and this reduces the range of radiance values that is available for calibration. On the other hand, the SDD includes all the observable radiance values, but it is scene dependent and may be biased by the fine details of the image that are viewed by detector arrays, and for this reason, the SDD classification is used only in a validation phase. btb is the normalized weighted rootFormally, the BTBDD Dij mean-square (rms) error between bow-tie measurements by detectors di and dj , with the weights given by the overlap percentage, to limit the effects due to variable scenes when the overlap is only partial. The BTBDD is (Ri − Rj )T Wij (Ri − Rj ) btb (1) = Dij tr(Wij ) where Ri is the vector of radiance measurements from detector di taken from the Nij FOVs overlapping with dj , Rj is the corresponding set of values from dj , and Wij is a diagonal matrix whose entries are the overlap percentages between detectors. The SDD is defined as Dij =
N 1 Fi z(n) − Fj z(n) , N n=1
where Fi (·) is the ECDF evaluated on the observations of detector i [similarly for Fj (·)], z(n) is the nth ordered sample from the union of the observations of both detectors, and N is the number of all the observed radiance values [21]. The average SDD for detector di is then defined as
B. Detector Classification The identification of the OF detectors is made by observing two distances: the BTBDD, which is computed on the overlapping data, and the sample distributional distance (SDD), which is a measure of similarity between two distributions, computed
(2)
Di =
1 Dij |Mi |
(3)
j∈Mi
where Mi is a suitable set of detectors. At this point, the OF detectors are those showing a large (bow-tie based) detector
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distance and a large distributional distance. All the detectors showing metric values exceeding appropriate thresholds for the BTBDD and the SDD values, chosen according to the observed values, will be declared as OF. At the end of the procedure, the detectors that are not declared as OF detectors represent the set of IF detectors, DIF , having cardinality NIF . C. Preequalization of IF Detectors Starting from Table I, we define D as the set of the pairs of detectors (di , dj ) with di , i = 1, . . . , 5, belonging to the scan line n whose FOV has an overlap with detectors dj , j = 6, . . . , 10, at the scan (n + 1). We also define the set of indices from the pairs of IF detectors sharing the same FOV as Ibt = {(i, j) : (di , dj ) ∈ D, di , dj ∈ DIF }
(4)
whose cardinality is Nbt . The preequalization problem consists in the evaluation of a set of gains and offsets such that all responses from IF detectors are as close as possible to each other. The problem will be solved in two steps: First, the scatter plot between each pair of overlapping detectors is fitted with a straight line; then, a reference (fictitious) detector is found using a smallest perturbation technique. The first step requires solving the set of equations LS ai 1 + bi ri = aj 1 + bj rj ,
(i, j) ∈ Ibt
(5)
where (ri , rj ) are the pairs of vectors representing the radiance values sensed in the same FOV by the IF detectors di and dj , and LS indicates that we are looking for an LS solution. By defining uij = (ai − aj )/bj and vij = bi /bj , (i, j) ∈ Ibt , we may write (5) as
In addition, we require that the solution is of a smallest perturbation type, i.e., a = [a1 , . . . , aNbt ]T must be the closest to 0 and b = [b1 , . . . , bNbt ]T the closest to 1, with 0 and 1 being the zero and unit Nbt -dimensional vector, respectively. Indeed, given the solution θ LS and solving with respect to the original variables, we obtain the equalization coefficients ai = u∗ij bj + ∗ bj for all the pairs of IF detectors observing aj and bi = vij the same FOV. We note that, for each pair of detectors, it is possible to provide the relative calibration law but not the individual values of the coefficients. We may, however, define a reference (fictitious) detector dr whose behavior represents the smallest perturbation with respect to all the other detectors. Thus, we define the reference detector as the least perturbed by the equalization laws ∗ br , ai = u∗ij br + ar and bi = vij
(i, j) ∈ Ibt
(10)
in the sense that the sum norm Ω = (a2 + b − 12 ) is minimized. By using the optimum coefficients, we obtain 2 ∗ 2 u∗ij br + ar + vij . (11) Ω= br − 1 (i,j)∈Ibt
The minimum is reached when the two partial derivatives with respect to ar and br are simultaneously zero. The corresponding values of a∗r and b∗r are b∗r u∗ij a∗r = − b∗r =
(i,j)∈Ibt
Nbt
= −b∗r u∗ ∗ vij (i,j)∈Ibt
2 u∗ij
∗ 2 + vij − u∗ij u∗
(i,j)∈Ibt
LS uij 1 + vij ri = rj ,
(i, j) ∈ Ibt .
(6)
The LS solution is found by minimizing the quantity (y − Hθ)T (y − Hθ)
(7)
where θ is the vector of the parameters, organized in the pairs (uij , vij ), (i, j) ∈ Ibt , y is the vector of radiance values (r1 , r2 , . . . , rNbt ) such that rj corresponds to the second entry of the set of pairs Ibt , and the block diagonal matrix H is the observation matrix ⎤ ⎡ H1 0 · · · · · · 0 .. ⎥ .. ⎢ . 0 ⎢ 0 . ⎥ ⎢ . .. ⎥ ⎢ . (8) H=⎢ . 0 Hi 0 . ⎥ ⎥ ⎥ ⎢ . . . . ⎣ . . 0 0 ⎦ 0 · · · · · · 0 HNbt whose nonzero entries are Hi = [1, ri ] and ri corresponds to the first entry of the set of pairs Ibt . Note that the observation matrix has a number of rows equal to the overall number of observed radiance values from IF detectors sharing the same FOV and 2 × Nbt columns. Since the observation matrix H is full rank, the LS solution of (7) is known to be [22] θ LS = (HT H)−1 HT y.
(9)
=
v∗ (u∗ )2
+ (v ∗ )2 − (u∗ )2
(12)
where x denotes the sample mean. It is worth to point out that the inversion is not unique whenever the detector i overlaps with more than one detector j, and each result defines a correct equalization for di . A possible way for finding the best choice is to search for the best sum norm from those obtained by retaining one couple (i, j) and discarding all the others. D. Destriping via LS Minimization After preequalization of IF detectors, the next stage is the destriping procedure that is applied to all OF detectors. Let us define r as the vector of data from the equalized detectors and y as the vector of data from an OF detector. A preliminary inspection of the typical scatter plots of y versus r highlights the typical nonlinear behavior of the OF detectors that essentially occurs at the low radiance values where a lower response is shown with respect to the IF detectors. Experimental considerations and some consistency constraints have led us to adopt a piecewise linear law for the equalization of the OF detectors. To motivate our choice, we observe the following. 1) Data recorded on the bow-tie region do not span the whole range of radiance values, but the equalization curve
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TABLE III INITIAL SDD BETWEEN DETECTORS. VALUES ×10−3
should be meaningful also outside the fitting range; in this view, a linear response is what we expect. 2) Higher order polynomials result in a more accurate fitting even if, for noisy observations, this accuracy can lead one to describe also the noise part within the signal. Accordingly, let us consider a problem of LS minimization with a polynomial model described by two line pieces with different slopes and a consistency constraint for continuity in the breakpoint. We compute the quadratic error as the sum of two components 2L and 2U corresponding to the linear regression errors in the lower and upper regions, respectively, weighted through the FOV overlap percentage matrix W. To give a formal description to the minimization problem, let r and y be the vectors obtained by collecting the N radiance measurements from all the preequalized detectors overlapping with the OF detector y, and let 2x be the squared error given by (yx − Hx θ x )T Wx (yx − Hx θ x ) x ∈ {L, U }, where Hx = [1; rx ] is the N × 2 observation matrix and θ x is the vector of unknown parameters representing the intercept and the slope of the line. With obvious notations, we can give a more compact form to the overall error by letting WL HL 0 0 W= (13) H= 0 HU 0 WU T T T T T for matrices, and θ = [θ T L θ U ] and y = [yL yU ] for vectors. Indeed, the problem can be formalized as θ LS = arg min (y − Hθ)T W(y − Hθ) (14) R∗ ,θ with the constraint CT θ = 0 ∗ T ∗ T where C = [HT is the consistency conL (R ) − HU (R )] ∗ straint at the breakpoint R . The solution is found by introducing the Lagrange equation
J=
1 (y − Hθ)T W(y − Hθ) − (CT θ)T λ 2
(15)
and solving for θ to minimize the Lagrangian and to satisfy the constraint on λ. The solution turns out to be θ LS = (HT WH)−1 HT Wy − (HT WH)−1 Cλ where the expression of the multiplier is −1 T λ = CT (HT WH)−1 C C θ ULS
(16)
(17)
with θ ULS = (HT WH)−1 HT Wy being the unconstrained solution.
TABLE IV RELATIVE PERCENTAGE VARIATIONS OF THE BTBDD FOR IF DETECTORS AFTER THE PREEQUALIZATION STAGE. NONOVERLAPPING PAIRS ARE MARKED AS NA
E. Performance Indices In some cases, it may happen that one or more detectors cannot be considered in the equalization process since they do not overlap with any IF detector. In this case, the equalization of these detectors can be made in a second stage by using the equalized (previously OF) detectors. The risk is that some residual striping that is not compensated may affect the equalization process. A possible alternative is to resort to the histogram-matching method. The performance of the destriping procedure has been evaluated by adopting the performance indices used for the classification step, i.e., the bow-tie-based detector distance as the local measure of striping and the SDD as the global measure. Although the proposed method is aimed at minimizing the BTBDD, the result is that the SDD decreases as well. The converse is not true. We highlight, in fact, that the CDF distance brings some information on the scene in addition to that on the detector behavior. Therefore, a zero distance does not necessarily correspond to the ideal result for a scene without stripes, but a reduction of the SDD is likely tied to a reduction in the striping effect. Other performance figures are based on the analysis in the Fourier domain. We consider here two figures of merit: the noise reduction ratio (NRR) and the image distortion ratio (IDR). The NRR is the ratio between the energy at the striping frequency in the AT direction for the original signal and the same energy for the equalized signal. For MODIS data granules, the data size is 1354 × 10 × Nscan and the striping harmonics are at j × Nscan , where Nscan is the fundamental nonnormalized frequency. The NRR includes contributions from the noise and image. In particular, the latter contribution is affected by the natural variability of the scene. Thus, ideally (that is without striping contribution), the NRR remains bounded. The IDR instead is the ratio of the energy after and before destriping, where the summation is computed by discarding the striping frequencies. A unit value of IDR corresponds
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TABLE V RELATIVE PERCENTAGE VARIATIONS OF THE SDD AFTER THE PREEQUALIZATION STAGE
Fig. 3. Initial scatter-plot density of radiance values for detector 1 versus the equalized radiance values of IF detectors. Bisector in black, two lines fitting in light gray. The color bar shows the density of the scatter plot in log scale.
to the minimum image distortion condition. Formally, we define 10
NRR =
Fig. 4. Scatter-plot density of equalized radiance values for detector 1 versus the equalized radiance values of IF detectors. The color bar shows the density of the scatter plot in log scale. TABLE VI RELATIVE PERCENTAGE VARIATIONS OF BOW-TIE-BASED DETECTOR DISTANCES AFTER DESTRIPING OF DETECTORS d1 , d3 , AND d8
|R(0, jNscan )|2
j=1 10
|Req (0, jNscan )|2 j=1 |Req (0, i)|2 IDR =
i=jNscan
|R(0, i)|2
(18)
i=jNscan
where R(N1 , N2 ) denotes the 2-D discrete Fourier transform of the radiance data. III. E XPERIMENTAL R ESULTS The destriping procedure has been tested using a data set collected by MODIS/Terra on July 21, 2004 (09.45 UTC) at the MARSec ground station facility in Benevento (Italy). We have considered spectral radiance data, measured per unit wavelength in [W · m−2 · sr−1 · μm−1 ], from band 24, which show a marked striping and a heterogeneous environmental structure made by a combination of water, ground, and mountains. Data have been processed to level 1 using IMAPP software on a clus-
ter of ten processors running Rocks parallel environment. In the following sections, the steps of the algorithm and corresponding results will be carefully examined. A. Classification of Detectors and Preequalization Procedure After identification of the overlapping FOVs, detectors are classified following the rules of Section II-A. Initial values of the BTBDD are calculated and reported in Table II. The BTBDD values are compared to a suitably chosen threshold whose value is computed once and for all with the aim at keeping the striping under a noise floor. According to the observed values, a threshold equal to 3.8 · 10−3 is considered in this case to declare OF detectors. Detector d1 exhibits large distances from the other detectors. Thus, it is classified as an OF detector, and row 1 is removed. Detector d10 exhibits small
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TABLE VII RELATIVE PERCENTAGE VARIATIONS OF THE SDD AFTER DESTRIPING OF DETECTORS d1 AND d3
distances, except for the pair (d3 , d10 ), and can be considered as IF. Detectors d2 and d9 present small distance values and are also flagged as IF. Both d3 and d8 exhibit distance values larger than 3.8 · 10−3 with IF detectors; thus, they are considered OF. Detectors d4 , d7 , and d5 are IF, and detector d6 cannot be classified because it overlaps with an OF detector only. Classification based on the BTBDD is thus the following: DIF = {d2 , d4 , d5 , d7 , d9 , d10 }, DOF = {d1 , d3 , d8 }, and d6 is not classified. The classification procedure based on the SDD values, calculated from the ECDFs shown in Fig. 2 and reported in Table III, is not detailed here for shortness, but some comments are, nonetheless, useful for better understanding. By using SDD values, detectors d1 and d3 are classified as OF, but detector d8 is classified as IF. The final comparisons, after destriping, however, strongly suggest to declare d8 as OF, thus following the BTBDD method. Afterward, the preequalization stage is implemented by solving the LS problem in (7). After preequalization, the relative variations of the BTBDD and the SDD values are reported in Tables IV and V, respectively, where positive values denote a distance decrease. It is worth to note that the preequalization stage minimizes the global distance between the IF detectors and a reference detector, but the SDD between two IF detectors may not decrease as well. B. Destriping In this section, the constrained LS equalization procedure will be applied to the OF detectors. Moreover, some additional investigation will be implemented for determining if a piecewise linear or other nonlinear laws are the most appropriate for our modeling. To show, with more clear evidence, the performance of the equalization procedure, it is useful to deal with the density of scatter plot, where a color scale proportional to the number of observations in a given bin is used. Fig. 3 shows the spectral radiance recorded by detector 1 plotted versus the radiance from the equalized detectors overlapping with detector 1. This figure highlights that the expected linearity is well verified for radiance values greater than 0.15, while the behavior at lower radiance values is spread around a line with different slope. For readers’ ease, the bisector is also reported in the same figure as a black line. The results of fitting with two lines are reported in the same figure in light-gray color. The estimated threshold value is 0.1217, and the coefficients for the lower and upper lines are (−0.0345, 1.2432) and (−0.0036, 0.9898), respectively. The weighted rms error decreases from 7.21 · 10−3 to 3.50 · 10−3 after destriping. The resulting scatterplot density is shown in Fig. 4. The values of the BTBDD
Fig. 5. Power spectral densities (blue) before and (red) after destriping.
after destriping are shown in Table VI. Note that all values are lower than the initial values. The corresponding relative variations of SDD with respect to preequalized data are reported in Table VII. The results show that the SDD between detector d1 and other detectors is markedly decreased after destriping. On the other hand, not for every pair, the distance is definitively decreased. This emphasizes the difference between the SDD method and the BTBDD method, the last one giving more reliable results, as in the case of detector d8 . The justification may be its intrinsic independence on the scene statistics that makes this method more robust. From a larger bulk of simulations, we may derive some conclusions related to fitting with polynomial curves or with three-piecewise linear function. 1) Fitting with a parabolic function: The results show that fitting of data is better in the lower and midrange of values, but higher discrepancies are observed for highradiance values. 2) Fitting with three-piecewise linear function: The fitting is tight with the two line fitting for midrange and highradiance values. In the lower region of radiance values, the three-piecewise equalization is influenced by the noise floor. C. Equalization of the Nonoverlapping Detectors In this experiment, detector d6 is excluded from the equalization procedure since it overlaps only with an OF detector
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Fig. 6. (Left) Detail of the original image. (Center) Color scale for radiance values [W · m−2 · sr−1 · μm−1 ]. (Right) Detail of the image after the FOM processing.
(d1 ). Thus, we resort to the histogram-matching procedure for this case. Final results have shown that the BTBDD between detectors (1, 6) changes from 4.74 · 10−3 to 4.68 · 10−3 .
D. Remarks on Experimental Results We address here some final issues, sometimes based on other processing experiments that are not reported here for shortness.
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Fig. 7. Results for Terra MODIS data set MOD021KM.A2004260.0310. 005.2007261154550 (coast of northern China). Figures show (top) the original image, (middle) the destriped image, and (bottom) the normalized power spectral density for band 27.
Fig. 8. Results for Terra MODIS data set MOD021KM.A2004260.0310. 005.2007261154550 (coast of northern China). Figures show (top) the original image, (middle) the destriped image, and (bottom) the normalized power spectral density for band 28.
The analysis of performance indices indicates that the noise reduction factor is 7.9 dB, while the image distortion factor is −0.03 dB. The noise reduction is evident from the inspection of Fig. 5, where the power spectral densities evaluated as averaged periodograms AT are plotted before (in blue) and after destriping (in red). In the top-right corner of the figure, a detail of the first harmonic at νAT = 0.1 is shown by highlighting that, after destriping, the peak energy is decreased by approximately 20 dB. In some other experiments, results have been
investigated for different values of the minimum overlap percentage ηmin by showing that, for MODIS band 24, the value of 65% provides the best performances. This is reasonable if we observe that by increasing the minimum overlap percentage, the number of the available overlapping FOVs decreases as well, and for ηmin above 80%, d1 and d10 detectors do not overlap anymore. Some other comparative results are shown in Fig. 6 (corresponding to different radiance range of values) where on the
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Fig. 9. Results for Terra MODIS data set MOD021KM.A2004260.0310. 005.2007261154550 (coast of northern China). Figures show (top) the original image, (middle) the destriped image, and (bottom) the normalized power spectral density for band 30.
Fig. 10. Results for Terra MODIS data set MOD021KM.A2004203.0945. 005.2007022123816 (east–central Europe). Figures show the (top) original image, (middle) the destriped image, and (bottom) the normalized power spectral density for band 27.
left side, the original image subset is reported, and on the right side, the same subset is presented after the destriping with the FOV methodology (FOM). Particularly interesting is the subset showing the darker areas of the image: After processing, the stripes are still evident, and this indicates that in these areas, the presence of the noise has influenced the estimation of the fitting laws. Finally, the analysis for different bands and data sets has been carried out to evaluate the effectiveness of the algorithm
under other possible conditions, also showing the radiometric impact of the destriping processing on the MODIS radiances. Precisely, spectral radiances from bands 27, 28, and 30 have been chosen since they are usually affected by strong striping. Data sets MOD021KM.A2004260.0310.005.2007261154550, MOD021KM.A2004203.0945.005.2007022123816, retrieved from NASA LAADS archive, have been analyzed, the former representing a large portion of land and sea in the northern China, while the latter showing a cloudy land in the east–central
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Fig. 11. Results for Terra MODIS data set MOD021KM.A2004203.0945. 005.2007022123816 (east–central Europe). Figures show (top) the original image, (middle) the destriped image, and (bottom) the normalized power spectral density for band 28.
Fig. 12. Results for Terra MODIS data set MOD021KM.A2004203.0945. 005.2007022123816 (east–central Europe). Figures show (top) the original image, (middle) the destriped image, and (bottom) the normalized power spectral density for band 30.
Europe. The results reported in Figs. 7–12 show that the algorithm is able to significantly reduce the stripes that, however, remain visible in some regions. It should also be mentioned that, if compared with other techniques, as in [16], the results are less impressive. Nonetheless, we remark that the proposed technique preserves the fine details of the image since it does not apply any smoothing. This is clearly visible in the subfigure inside Fig. 5 where the reader can check the absolute closeness
of the PSD values before and after destriping but for the striping frequencies. To provide a precise assessment of the destriping effects on the spectral radiance values, the analysis of the difference between data, from each detector, before and after destriping, has been carried out, and four statistical parameters have been evaluated: 1) RMS of the difference rms ; 2) mean of the difference ¯;
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TABLE VIII STATISTICAL PARAMETERS OF THE DIFFERENCE BETWEEN SPECTRAL RADIANCES [W · m−2 · sr−1 · μm−1 ], BEFORE AND AFTER DESTRIPING, FOR DATA SET MOD021KM.A2004260.0310.005.2007261154550. OF DETECTORS ARE IN BOLD
TABLE IX STATISTICAL PARAMETERS OF THE DIFFERENCE BETWEEN SPECTRAL RADIANCES [W · m−2 · sr−1 · μm−1 ], BEFORE AND AFTER DESTRIPING, FOR DATA SET MOD021KM.A2004203.0945.005.2007022123816. OF DETECTORS ARE IN BOLD
3) maximum absolute difference max(||); 4) Kolmogorov-Smirnov statistic Dks , i.e., the maximum distance between the empirical cumulative distributions, for each detector, before and after destriping. The results reported in Tables VIII and IX deserve some specific comment. It is evident that, in general, the values of the statistical indices associated with the different detectors are different, in some case even significantly; this can be explained by observing that higher values pertain to OF detectors, while lower values pertain to IF detectors. Moreover, OF detectors undergo a more strong equalization process, whereas IF detectors undergo only a lighter preequalization stage. For an easier readability of the results in the tables, we reported in bold the columns of the OF detectors. Finally, a graphical comparison between ECDFs before and after destriping is reported for selected detectors and bands in both data sets, as shown in Figs. 13 and 14, where the two plots in the upper line refer to OF detectors and the two in the lower line refer to IF detectors. We finally underline that the IFOV overlap technique is intrinsically radiance preserving since the equalization is based on a distance measure evaluated on IFOVs observing the same scene. This is different from other techniques, like histogram equalization, and CDF matching, where the detectors are equalized through observations from adjacent different resolution cells.
IV. A NALYSIS B ASED ON D ATA S ET 20040721.0810 AND S HORT -T IME V ARIATIONS To evaluate the possible time-varying behavior of the estimated parameters, the following comparison is made: First, the data set 20040721.0810, collected by MODIS/Terra on July 21, 2004 (08.10 UTC), has been destriped through the FOM; then, the same data set has been equalized by using the parameters derived from the analysis of the 20040721.0945 data. The time interval between the two data sets is 95 min, which is approximately the time required by the platform to complete one orbit (these granules are two consecutive data sets acquired at MARSec ground station facility). This also gives us information about the short-term stability of the MODIS instrument and eventually represents the basis for monitoring the long-term variations of the detector’s response. Shown in Table X are the initial BTBD distances computed for the granule, while Tables XI and XII show the BTBDD variations after the destriping procedure using the 0810 and the 0945 coefficients, respectively. Some interesting considerations can be drawn from the tables. First, the behavior of the detectors is essentially the same on very short-term variations: Calibration is not recovered on one-orbit period. Second, the calibration coefficients are sufficiently accurate on short-time periods but give suboptimal results and cannot be used for several orbits. Third, some degradation of the performance should be, in any
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TABLE X DATA SET 08.10: BTBDD VALUES IN [W · m−2 · sr−1 · μm−1 ] × 10−3
TABLE XI DATA SET 08.10: RELATIVE PERCENTAGE VARIATIONS OF THE BTBDD A FTER FOM U SING 0810 C OEFFICIENTS
Fig. 13. Comparison between ECDFs before and after destriping for data set MOD021KM.A2004260.0310.005.2007261154550, band 27. (Top) OF detectors. (Bottom) IF detectors.
TABLE XII DATA SET 08.10: RELATIVE PERCENTAGE VARIATIONS OF THE BTBDD A FTER FOM U SING 0945 C OEFFICIENTS
residual stripes, in general, that are more evident in the images processed with unmatched coefficients. V. F INAL R EMARKS
Fig. 14. Comparison between ECDFs before and after destriping for data set MOD021KM.A2004203.0945.005.2007022123816, band 28. (Top) OF detectors. (Bottom) IF detectors.
case, accepted when unmatched coefficients are used in the equalization procedure. Results are confirmed by the analysis of the performance indices: the noise reduction and the image distortion. A degradation of about 1.6 dB in the NRR (from 7.94 to 6.28 dB) and a negligible reduction of IDR are the price to pay for using unmatched coefficients. By concluding the comparative analysis, three subsets of the original 0810 granule have been reported after destriping with 0810 coefficients (on the left of Fig. 15) and by using the 0945 coefficients (on the right of Fig. 15). The figure shows the results after destriping in three different radiance regions. There is some evidence of
The FOV overlap methodology, introduced and validated in this paper, can be considered a valid alternative to the histogram equalization when a precise detail-preserving processing is required. The main aspect of the algorithm is that the equalization is not biased by the fine details of the scene and can be considered as a final stage of calibration. The achieved results are generally good, as largely presented in this paper, but a possible application of the algorithm to the global MODIS data set requires a more extensive testing phase and many refinements to improve efficiency, data representation, and automatization. It must also be underlined that the estimation of the equalization parameters is a critical task and that even small residual errors may cause a visible striping. The issue of short/long-term stability of the equalization coefficients has also been investigated in this paper. Results demonstrated that the calibration terms should be reevaluated for each image, although the OF detectors may remain unchanged over more orbits. On very short time intervals (one orbit), the experimental analysis has shown that using unchanged parameters produces suboptimal but, anyway, acceptable results. Future research will be focused on the evaluation of the mirror-side dependence of the destriping coefficients. This is tied to the presence of a dual-sided scan mirror, where one half of the overlapping measurements is recorded using one face and the other half is recorded using the opposite mirror side. In this view, the set of overlapping detectors should be built by considering the detectors from the two sides of the mirror as different, and consequently, two sets of coefficients are defined for each detector, one for each mirror side.
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Fig. 15. (Left) Detail of the image 20040721.0810 after the FOM processing with 0810 coefficients. (Center) Color scale for radiance values [W · m−2 · sr−1 · μm−1 ]. (Right) Detail of the image 20040721.0810 after the FOM processing with 0945 coefficients.
R EFERENCES [1] MODIS Characterization Support Team, MODIS level 1b in-granule calibration code, Oct. 15, 2002. MCST Int. Memo. M1037. [2] R. Barbieri, H. Montgomery, S. Qiu, B. Barnes, D. Knowles, Jr., N. Che, and I. L. Goldberg, MODIS level 1b: algorithm theoreti-
cal basis documentation, Feb. 13, 1997. Version 2.0, MCM-ATBD-01U-DNCN. [3] W. L. Barnes, T. S. Pagano, and V. V. Salomonson, “Prelaunch characteristics of the Moderate Resolution Imaging Spectroradiometer (MODIS) on EOS-AM1,” IEEE Trans. Geosci. Remote Sens., vol. 36, no. 4, pp. 1088– 1100, Jul. 1998.
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[4] B. Guenther, G. D. Godden, X. Xiong, E. J. Knight, S. Y. Qiu, H. Montgomery, M. H. Hopkins, M. G. Khayat, and Z. Hao, “Prelaunch algorithm and data format for the level 1 calibration products for the EOSAM1 Moderate Resolution Imaging Spectroradiometer (MODIS),” IEEE Trans. Geosci. Remote Sens., vol. 36, no. 4, pp. 1142–1151, Jul. 1998. [5] J. Young, PFM MWIR/LWIR Radiometric Calibration I: Theory and Measurement Equations, 1997, Raytheon Santa Barbara Remote Sensing, Goleta, CA, SBRS Memo, PL3095-N06555. [6] X. Xiong, K. Chiang, J. Esposito, B. Guenther, and W. Barnes, “MODIS on-orbit calibration and characterization,” Metrologia, vol. 40, no. 1, pp. S89–S92, Feb. 2003. [7] X. Xiong, K. Chiang, B. Guenther, and W. Barnes, “MODIS thermal emissive bands calibration algorithm and on-orbit performance,” in Proc. SPIE Int. Soc. Opt. Eng., 2002, vol. 4891, pp. 95–104. [8] B. K. P. Horn and R. J. Woodham, “Destriping LANDSAT MSS images by histogram modification,” Comput. Graph. Image Process., vol. 10, no. 1, pp. 69–83, 1979. [9] J. Kautsky, N. I. Nichols, and D. L. B. Jupp, “Smoothed histogram modification for image processing,” Comput. Graph. Image Process., vol. 26, no. 3, pp. 271–291, 1984. [10] M. P. Weinreb, R. Xie, J. H. Lienesch, and D. S. Crosby, “Destriping GOES images by matching empirical distribution functions,” Remote Sens. Environ., vol. 29, no. 2, pp. 185–195, Aug. 1989. [11] M. Wegener, “Destriping multiple sensor imagery by improved histogram matching,” Int. J. Remote Sens., vol. 11, no. 5, pp. 859–875, 1990. [12] [Online]. Available: http://cimss.ssec.wisc.edu/gumley/IMAPP/IMAPP. html [13] Z. Xiaoxiang, F. Tianxi, and H. Qian, “Destripe multi-sensor imaging spectroradiometer data,” in Proc. CGMS XXXII, 2004. CMA-WP 07. [14] R. E. Crippen, “A simple spatial filtering routine for the cosmetic removal of scan-line noise from Landsat TM P-tape imagery,” Photogramm. Eng. Remote Sens., vol. 55, pp. 327–331, 1989. [15] J. Chen, Y. Shao, H. Guo, W. Wang, and B. Zhu, “Destriping CMODIS data by power filtering,” IEEE Trans. Geosci. Remote Sens., vol. 41, no. 9, pp. 2119–2124, Sep. 2003. [16] P. Rakwatin, W. Takeuchi, and Y. Yasuoka, “Stripe noise reduction in MODIS data by combining histogram matching with facet filter,” IEEE Trans. Geosci. Remote Sens., vol. 45 pt. 2, no. 6, pp. 1844–1845, Jun. 2007. [17] V. R. Algazi and G. E. Ford, “Radiometric equalization of non-periodic striping in satellite data,” Comput. Graph. Image Process., vol. 16, pp. 287–295, 1982. [18] G. Corsini, M. Diani, and T. Walzel, “Striping removal in MOS-B data,” IEEE Trans. Geosci. Remote Sens., vol. 38, no. 3, pp. 1439–1446, May 2000. [19] M. Nishihama, R. Wolfe, D. Solomon, F. Patt, J. Blanchette, A. Fleig, and E. Masuoka, MODIS level 1a earth location: Algorithm theoretical basis document, Aug. 26, 1997. Version 3.0, SDST-092. [20] P. Antonelli, M. Bisceglie, R. Episcopo, and C. Galdi, “Destriping MODIS data using IFOV overlapping,” in Proc. IGARSS, 2004, vol. 7, pp. 4568–4571. [21] R. B. D’Agostino and M. A. Stephens, Goodness-of-Fit Techniques. New York: Marcel Dekker, 1986. [22] L. L. Sharf, Statistical Signal Processing, Detection, Estimation, and Time Series Analysis. Reading, MA: Addison-Wesley, 1991.
Maurizio di Bisceglie (M’91) received the Dr.Eng. degree in electronic engineering and the Ph.D. degree in electronics and telecommunications from the Università degli Studi di Napoli, Napoli, Italy. In 1997, he was a Research Fellow with the University College of London, London, U.K. Since 1998, he has been with the Facoltà di Ingegneria, Università degli Studi del Sannio, Benevento, Italy, as a Professor of telecommunications. His research activities are in the field of statistical signal processing with applications to radar and remote sensing. He was a Cochair of the NASA Direct Readout Conference, in 2005, an organizer of the Italian phase of EAQUATE (European AQUA Thermodynamic Experiment) mission, and the Scientific Director of Mediterranean Agency for Remote Sensing and Environmental Control.
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Roberto Episcopo was born in Naples, Italy, on November 14, 1975. He received the Dr.Eng. degree (with honors) in telecommunication engineering from the University of Naples “Federico II,” Naples, in 2001 and the Ph.D. degree in information engineering from the University of Sannio, Benevento, Italy, in 2005. From 2005 to 2006, he was with a postdoc program of the Università degli Studi del Sannio, Benevento, Italy and Mediterranean Agency for Remote Sensing. His research activities were focused on MODIS data destriping and on change detection for very high resolution remotely sensed data. In 2006, he collaborated with the Space Science Engineering Center, University of Wisconsin, Madison, for designing a collocation algorithm of MODIS and AIRS instruments onboard the Aqua platform. Since November 2006, he has been with the BU Observation System and RADAR, Thales Alenia Space, Rome, Italy.
Carmela Galdi (M’01) received the Dr.Eng. and Ph.D. degrees in electronic engineering from the Università di Napoli “Federico II,” Naples, Italy. In 1993, she was a Software Engineer with Alcatel Italia, Salerno, Italy. From 1994 to 2000, she was with the Università di Napoli “Federico II.” In 1995, she spent a four-month period for study and research with the Signal Processing Division, University of Strathclyde, Glasgow, U.K. In 1997 and 1998, she spent some months with the University College London, London, U.K. and with the Defence, Evaluation and Research Agency, Malvern, U.K., where she was involved in a research project on optimum detection in non-Gaussian noise. Since 2000, she has been with the Facoltà di Ingegneria, Università degli Studi del Sannio, Benevento, Italy, where she is currently an Associate Professor of telecommunications. Her research interests are in the field of statistical signal processing, non-Gaussian models of radar backscattering, and remote sensing applications.
Silvia Liberata Ullo (M’07) was born in Palmanova, Udine, Italy, on August 5, 1964. She received the Doctor degree in electronic engineering (cum laude), with a thesis on telecommunications, from the University of Naples, Naples, Italy, in 1989 and the Master’s degree in business administration, with a thesis on manufacturing operations, from the Sloan School of MIT, Boston, in 1992. Since 2001, she has been a teacher with the Università degli Studi del Sannio, Benevento, Italy, where in 2004, she joined the Facoltà di Ingegneria as a Researcher in remote sensing and telecommunications. Her research interests are in the field of statistical processing with applications to radar and remote sensing.
