Modelling spatial and spectral systematic noise patterns on CHRIS/PROBA hyperspectral data Luis G´omez-Chova*a , Luis Alonsob , Luis Guanterb , Gustavo Camps-Vallsa , Javier Calpea , and Jos´e Morenob a GPDS,
b LEO,
Electronics Engineering Department, University of Valencia, Earth Sciences and Thermodynamics Department, University of Valencia, Doctor Moliner 50, 46100, Burjasot (Valencia), Spain. ABSTRACT
In addition to typical random noise, remote sensing hyperspectral images are generally affected by non-periodic partially deterministic disturbance patterns due to the image formation process and characterized by a high degree of spatial and spectral coherence. This paper presents a new technique that faces the problem of removing the spatial coherent noise known as vertical stripping (VS) usually found in images acquired by push-broom sensors, in particular for the Compact High Resolution Imaging Spectrometer (CHRIS). The correction is based on the hypothesis that the vertical disturbance presents higher spatial frequencies than the surface radiance. The proposed method introduces a way to exclude the contribution of the spatial high frequencies of the surface from the destripping process that is based on the information contained in the spectral domain. Performance of the proposed algorithm is tested on sites of different nature, several acquisition modes (different spatial and spectral resolutions) and covering the full range of possible sensor temperatures. In addition, synthetic realistic scenes have been created, adding modeled noise for validation purposes. Results show an excellent rejection of the noise pattern with respect to the original CHRIS images. The analysis shows that high frequency VS is successfully removed, although some low frequency components remain. In addition, the dependency of the noise patterns with the sensor temperature has been found to agree with the theoretical one, which confirms the robustness of the presented approach. The approach has proven to be robust, stable in VS removal, and a tool for noise modeling. The general nature of the procedure allows it to be applied for destripping images from other spectral sensors. Keywords: PROBA, CHRIS, hyperspectral images, noise reduction, vertical stripping, radiometric calibration.
1. INTRODUCTION Hyperspectral images acquired by remote sensing instruments are generally affected by two kinds of noise. The first one can be defined as standard random noise, which varies with time and determines the minimum image signal-to-noise ratio (SNR). In addition, hyperspectral images can present non-periodic partially deterministic disturbance patterns, which come from the image formation process and are characterized by high degree of spatial and spectral coherence1 . In this work, we focus on modeling and correcting the coherent spatial and spectral structures produced by these systematic disturbances. Most of the air or space-borne hyperspectral sensors are push-broom imaging spectrometers. Instruments operated in a push-broom mode consist of an optical system forming a line image of Earth onto the entrance slit of a spectrometer, and an area-array detector at the spectrometer focal plane. Usually, the detector is a Charge Coupled Device (CCD) two dimensional array whose rows are assigned to separate wavelengths, and columns to separate resolved points in the Earth image. Figure 1 shows the push-broom operation mode for the acquisition of spectral images. The optical system collects the light arriving from a long and narrow strip of the surface below by means of a thin slit. The system is oriented perpendicular to the direction of motion of the sensor and the sequential acquisition of lines as the platform moves forward generates the image. The image of the * corresponding author e-mail:
[email protected]; phone: +34 963544024; fax: +34 963544353
mn
age
X
lu Co
Spectral Wavelength λ
Im
High T: Narrow Slit Larger VS effect
Low T: Wide Slit Smaller VS effect
Telescope CCD
Diffraction Grid
Slit
Along-track Platform motion
λi
CCD Sensitivity
0,85
X ath Sw e ag Im Ground
0,80
Image Length Y
0,75
Image Column X
Figure 1. Design of a push-broom imaging spectrometer that shows its operation mode and the sources of the coherent spatial noise patterns (figure based on an original of Barducci et.al.).
strip of land is diffracted separating the different wavelengths and projected onto a CCD array properly aligned so the line is parallel to one of the axis (spatial) while the diffraction is produced along the perpendicular axis (spectral). Therefore, each pixel in a line of the image at a given wavelength has been acquired by a different element of the CCD; while every column of the image for that wavelength has been measured by the same element of the CCD. Would be the CCD and the slit ideally built then all the CCD elements would have the same sensitivity and response, producing even and noise-free images. But, in real devices, neighboring elements of the CCD show pixel-to-pixel variations. The same applies to the width of the slit along its length resulting in the intensity of an homogeneous area to be slightly different in each column of elements of the CCD array. The effect of these imperfections in the resulting image is a vertical pattern known as ”vertical stripping” (VS). Usually, the whole system is fully characterized after assembly, obtaining the actual gain correction factors that would produce an even image. In some occasions, especially after rocket launch, the system is affected in such a way that the characterization does not remove completely the noise. Also, this type of sensors degrade with time needing a recalibration (if possible). In those cases, a noise reduction algorithm must be applied after image reception in the pre-processing phase. In particular, this work analyses the Compact High Resolution Imaging Spectrometer (CHRIS)2 , which is mounted on board the European Space Agency (ESA) small satellite platform called PROBA (Project for On Board Autonomy)3 . As a push-broom sensor, the radiometric response of CHRIS instrument is determined by two overlapping components: the optical system response (a telescope forming an image onto the entrance slit of a spectrometer) and the CCD response (a thinned, back-illuminated, frame-transfer CCD)3 . With regard to the CCD response, the different pixel-to-pixel response comes from non-uniformities on dark current generation, non-uniformities on pixel response, threshold variations, and gain and off-set differences4 . But, in practice, these CCD imperfections are relatively stable with temperature and time5 resulting in a spatial fixed-pattern noise in the image that would be removed (e.g. the dark signal offsets are removed by subtracting a generic dark image). However, regarding the optical system response, spectral shift (shifted spectrum along the CCD columns) and spatial shift (slit irregularities across the CCD) appear due to the seasonal variation of the in-orbit CHRIS instrument temperature5 . Therefore, the effect of the slit adds up to the vertical pattern in a complex way, as it is heavily dependant on the sensors temperature (see Fig.1), and must be corrected and modeled. The paper is outlined as follows. Section 2 describes the standard techniques employed to remove the vertical stripping and the proposed improvements. In Section 3, a short description of the employed CHRIS images is given. Results of the methods and the characterization of CHRIS vertical stripping are shown in Section 4. Finally, discussion and concluding remarks are given in Section 5.
2. VERTICAL STRIPPING CORRECTION A hyperspectral image consists of two spatial dimensions (along-track and across-track) and one spectral dimension (wavelength). This hyperspectral image is registered by the instrument in a data-cube where the along-track dimension, y, corresponds to the image line l (distributed in the vertical direction of the image); the across-track dimension, x, corresponds to the line pixel p (distributed in the horizontal direction of the image and CCD); and the spectral dimension, λ, corresponds to the image band b (distributed in the vertical direction of the CCD). The size of the hyperspectral data-cube can be written in the form L × P × B, where L is the number of image lines, P is the number of pixels per line, and B is the number of spectral bands. The relation between the incoming at sensor radiance from the Earth surface, R(x, y, λ), and the registered value by the CCD, I(l, p, b), can be defined as: I(l, p, b) = [R(y, x, λ) ∗ H(x, λ)] · S(p, b) + S0 (l, p, b) , (1) where H(x, λ) is the optical system response, S(p, b) is the CCD sensitivity, and S0 (l, p, b) consist of all the analog offset errors and random noise. In this equation is worth noting that the vertical dimension of the image, y, represents the time when the associated image line, l, was acquired. In addition, the image values, I(l, p, b), and CCD sensitivity, S(p, b), are expressed as a function of the CCD columns and rows, (p, b), but usually a certain number of CCD columns or rows are binned in the final image (e.g. reducing the spatial or spectral resolution to increase the radiometric accuracy). If the instrument works correctly, the two orthogonal dimensions of the CCD (spatial and the spectral), are independent and they can be processed separately. Therefore, the optical system response can be separated in: H(x, λ) = H(x) · H(λ), which represent the slit response and the instrument chromatic response (that defines the wavelength and bandwidth of each band), respectively. As the slit response is constant for all the lines and bands of a given image, and independent from pixel-to-pixel, the convolution of the incoming light by the optical system response, [R(y, x, λ) ∗ H(x, λ)], can be expressed as: [R(y, x, λ) ∗ H(λ)] · H(x) = R(l, p, b) · H(p), which represents the radiance at the focal plane array of the CCD. Thus, considering the VS, eq. (1) is reduced to: I(l, p, b) = R(l, p, b) · H(p) · S(p, b) + S0 (l, p, b) = R(l, p, b) · ν(p, b) + η(l, p, b) ,
(2)
where ν(p, b) is a multiplicative noise coming from the slit and CCD, and η(l, p, b) represents an additive noise. In the particular case of CHRIS, the provided level 1A images are corrected of dark current offsets, thus making S0 (l, p, b) negligible (remaining only random noise of zero mean and low amplitude). A spectral band will be acquired by the same row, b = j, of CCD elements. Therefore, an image column p = i will be affected by a different CCD pixel response S(i, j), and a different optical slit response H(i) (equal for all spectral bands). The combination of these non-uniform spatial responses, which are constant in columns, superimposes a systematic pattern of noise organized by vertical lines (the stripe noise). The objective of VS correction methods is to estimate the correction factor, ν(p, b) = H(p) · S(p, b), of each spectral band to correct all the lines of this band. The main assumption consists in considering that both slit and CCD contributions change from one pixel to another (high spatial frequency) in the across-track but are constant in the along-track; while surface contribution, R(l, p, b), mainly presents smoother profiles (lower spatial frequencies).
2.1. Vertical stripping correction methods In the literature, all the vertical stripping reduction approaches take advantage of the constant noise factors in the image columns. Basically, the image is averaged in lines (along-track) and then the noise profile is estimated in the across-track direction for each band. By averaging image lines (integrated line profile) the surface contribution is smoothed, the additive random noise is cancelled, and the VS profile remains constant. In consequence, the surface contribution presents lower spatial frequencies in the across-track direction and can be easily separated from the VS (high frequencies) applying a filter with a suited cutoff frequency. Figure 2a shows the three steps of the method proposed in Ref. 6: 1. Each band is averaged in lines (along-track direction) obtaining one integrated line profile per band: RL RL α(p, b) = 1 I(l, p, b)dl = ν(p, b) · 1 R(l, p, b)dl = ν(p, b) · β(p, b).
(a)
(b) 6
x 10
6
x 10
6.5 6 5.5 5
6.5 6 5.5 5
15.6 15.4
6
x 10 6.5 6
15.6
5.5
15.4
5 0 −0.05 −0.1 1 1
0.95
0.95 0.9
0.9 100
200
300 400 Column index
500
600
700
100
200
300 400 Column index
500
600
700
Figure 2. Example of the processing steps of two different vertical stripping correction methods proposed in the literature by Barducci6 (a) and Settle7 (b): profiles of the last band of CHRIS EI 060130 63A1 41 image taken over Heron Island.
2. A low pass filter (LPF) is applied using a moving-window algorithm that flattens the profile α(p, b) by R ˆ b) = w(p − k) · α(p, b)dk. In this kind of filter convolving it with a Gaussian weighting function w: β(p, the cutoff frequency defines the standard deviation of the Gaussian window (σ ∼ 1/fc ). ˆ b) mainly contains the surface contribution, the shape of the VS factors can be obtained by the 3. Since β(p, ˆ b). Thus, the corrected image is calculated as R(l, ˆ p, b) = I(l, p, b)/ˆ ratio νˆ(p, b) = α(p, b)/β(p, ν (p, b). Figure 2b shows the method that is used by SIRA Technology Ltd. to correct CHRIS images7 . The main difference with the previous method is the use of logarithms to transform the multiplicative noise into additive noise in order to improve the following filtering: 1. Each band is averaged in lines obtaining one integrated line profile per band, α(p, b). 2. Log-transform the averaged profile (use logarithms is because this striping is a multiplicative effect): lα(p, b) = log{α(p, b)} = log{ν(p, b)} + log{β(p, b)} 3. Applying a low pass filter in order to eliminate high frequency variations (coming from the noise ν) and ˆ estimate surface contribution: lβ(p, b) = LP F {lα(p, b)}. ˆ ˆ 4. Obtaining high frequency variations (considered as the noise): lν(p, b) = lα(p, b) − lβ(p, b) ˆ 5. The vertical stripping factors are obtained calculating the inverse of the logarithm νˆ(p, b) = exp{lν(p, b)}. Theoretically, the first approach should give poor results when filtering the line profile because it is affected by a multiplicative noise and this is equivalent to a convolution in the frequency domain. This is the main reason to propose the second approach but, in practice, both approaches give equivalent results. This can be explained because the features of the multiplicative noise, which presents a mean close to one (f = 0 and A = 1) and high frequency components of low amplitude (A ∼ 0.1). Therefore, when performing the convolution of the signal and noise in the frequency domain, the power spectral density of the signal at low frequencies is not affected. These methods can fail for several reasons, such as high anomalous values in the VS. These high values affect the performance of the low pass filter (wrong estimation of the surface contribution) producing an overestimation or underestimation in the correction factors of the neighboring columns. Ref. 8 presents an iterative method that corrects the effect of these high stripping values. However, as is proposed in the next section, these effects can be also avoided using more advanced filtering techniques that use a robust weight function, which makes the process robust to outliers.
2.2. Robust vertical stripping correction method The proposed correction method is also based on the hypothesis that the vertical disturbance presents higher spatial frequencies than the surface radiance. However, it models the noise pattern by suppressing the surface contribution in the across-track in two different ways: first, avoiding the high frequency changes due to surface, and then subtracting the low frequency profile. One of the main drawbacks of the three referenced methods is the fact that they do not take into account the possible high frequency components of the surface explicitly. In images presenting structures or patterns in the vertical direction, the averaged profile α(p, b) can present high frequencies due to the surface that will be interpreted as vertical stripping when estimating ν(p, b) (see the selected example in Fig.2), and some columns will be corrected with wrong values, worsening the final image. The surface can present high spatial frequencies due to the surface texture (with low amplitude changes) or changes in the land-cover type (that can produce great changes in amplitude being a problem in the destripping process). In principle, in one spectral band, both the surface and noise contributions are mixed and is not possible to distinguish which of them causes the changes in the radiance amplitude between contiguous columns. However, the spectral signature of pixels from present hyperspectral sensors can provide helpful information about the land cover changes. Considering the spectra of two contiguous pixels, p1 and p2 , just in the boundary between to land-cover types, there are three factors affecting the spectral change: (i) differences between the true spectra of both surfaces (in shape and magnitude); (ii) the different CCD sensitivity S(p, b) (that modulates the spectral signature as a multiplicative noise of low variance); and (iii) the different multiplicative factor due to the slit H(p) (that scales the magnitude of the whole spectral signature). Among these three factors, the first one will produce the major change, the second one will be a second-order factor when comparing the spectral similitude, and the third one will not affect if the selected spectral distance is invariant to scaling by a positive factor. Therefore, we can filter in the across-track direction of the hyperspectral image in order to find the surface borders that introduce high frequencies in the across-track profile. The next sections explain how pixels corresponding to borders are not employed when computing the integrated line profiles. 2.2.1. Spatio-Spectral Edge Detection In this work, we propose a spatial-spectral filter that is based on the two-dimensional convolution filters (commonly used in grayscale image processing), like the Derivation filter or the Roberts operator (edge finding gradient-based methods)9 . To find edges in the horizontal direction (across-track) the kernel matrix of these methods can be KDerivative = −10 01 , KDerivative = 10 −10 , KRoberts = −10 10 , KRoberts = 01 −10 , or a linear combination of them. To apply these techniques to hyperspectral images, taking into account the spectral dimension, it is not possible to directly compute the convolution of the kernel matrix and the three-dimensional hypercube. In our proposal, first a spectral distance is computed between the spectrum of the pixel linked to the position with value K(i, j) = −1 in the kernel matrix (reference pixel), and the rest of neighboring pixels (forming a matrix D of distances with value D(i, j) = 0 for the reference P P pixel). Then, the sum of the product of the elements of the kernel and the distance matrix is computed, i j K(i, j) · D(i, j), and the resulting value is assigned to the reference pixel. The main difference of this method, compared to the case of grayscale image processing, is that only one position of K can present the value −1, which indicates at each moment the pixel that is used as a reference to compute the spectral distances. When this process is completed for all the pixels of the hyperspectral image, a sensitivity threshold must be specified, being ignored all edge values that are weaker than this threshold, i.e. where neighbouring pixels have a similar spectral signature. The approach followed in this work to find edges in the processed hyperspectral images only uses the derivative filter in the horizontal direction K = 10 −10 . Concerning the spectral distance, the Spectral Angle Distance10 (SAD) is used since it is invariant to multiplicative scaling, being not affected by the vertical stripping of the slit: SAD(x1 (λ), x2 (λ)) = arccos{hx1 , x2 i/(kx1 k · kx2 k)}, where h·, ·i is the dot product operator, and k · k is the quadratic norm. Finally, to make the threshold adaptable to each image, but assuring a significant number of lines to compute the smoothed integrated line profiles, an iterative procedure is followed. This procedure starts from threshold zero and iteratively increase it until find the threshold that assures an 80% of non-edge pixels in the column that presents more edge pixels.
11 9
log( I )
p
0.5 ï0.5 0.005 ï0.005
L
1
·dl
0.1 0
·dp
0.12 0.04
LPF(·)
0 ï0.02
D-E
1 0.98
exp{·} 100
200
300 400 Column index
500
600
A logarithm
B derivative domain
C no-edges average
D radiance domain
E low frequencies
F high frequencies
Vertical stripping
700
Figure 3. Example of the processing steps of proposed vertical stripping correction method (profiles of the last band of CHRIS EI 060130 63A1 41 image taken over Heron Island).
2.2.2. Vertical Stripping Removal A critical point of the proposed approach is how to remove edge pixels when computing the integrated line profiles. If all the image lines that present at least one edge pixel are removed, it is probable that only few or none lines can be used in the averaging. On the other hand, if only remove the edge pixels for averaging but using the remaining pixels of the line, the problem is not solved since the high frequencies are still there (think in a step profile where only one point is removed). The only way to remove the edges is to work in the across-track spatial derivative domain, where the homogeneous areas before and after the edge present values close to zero and the spikes of edge pixels can be substituted interpolating before doing the integration in the along-track direction. In this simple way, all surface contribution of high frequency to the integrated line profile is removed before the low pass filtering, and the estimated VS is independent of the surface patterns. Figure 3 shows the steps of the proposed method: 1. To apply logarithms in order to transform the multiplicative noise in additive noise (log{I(l, p, b)}). 2. To transform the hyperspectral data-cube into the across-track spatial derivative domain, which is equiva∂ log{I(l, p, b)} = log{I(l, p, b)} − log{I(l, p − 1, b)}, for p > 1 (note lent to high-pass filtering: θ(l, p, b) = ∂p that the first column is not defined and is fixed to zero, θ(l, 1, b) = 0). 3. The lines of each band are averaged in the along-track direction but ignoring the edge pixels found by the RL proposed spatio-spectral edge detection: ξ(p, b) = 1 θ(l, p, b)dl. To work in the derivative domain has allowed our method to avoid edge pixels, and it also leads to elevate the noise level temporarily because the surface power spectrum is concentrated in the low frequency region, whereas the vertical stripping is spread all-over the Fourier spectrum11 . Nevertheless, if the LPF is applied in the derivative domain, the committed errors by the LPF will accumulate throughout the integration in the across-track direction. Therefore, after applying the along-track LPF, data is integrated across-track to retrieve the signal in the radiance domain.
4. Integration Ppin the across-track direction (cumulative sum in p), which is equivalent to low-pass filtering: φ(p, b) = i=1 ξ(i, b) (the integration error is corrected at the end of the process). 5. To apply a LPF in the across-track direction in order to eliminate the high frequency variations (coming from the noise ν) and estimate the surface contribution: ϕ(p, b) = LP F {φ(p, b)}. 6. To obtain the high frequency variations (considered as the noise) by subtracting the low frequencies: ψ(p, b) = φ(p, b) − ϕ(p, b). The error committed during the integration process consists in a constant value for each band. But, as vertical stripping is corrected independently for each band, the vertical striping in the logarithmic domain should present zero mean (gain close to 1 in the radiance image). Therefore, the PP offset errors are corrected subtracting the mean value: ψ(p, b) = ψ(p, b) − 1/P · p=1 ψ(p, b). 7. Finally, the VS factors are obtained calculating the inverse of the logarithm νˆ(p, b) = exp{ψ(p, b)}.
3. DATA MATERIAL 3.1. CHRIS database CHRIS sensor2 provides multi-angular hyperspectral images in the spectral range from 400 nm to 1050 nm with a maximum spatial resolution of 17 or 34 m at nadir depending on the acquisition mode. CHRIS has five selectable acquisition modes, which mainly depend on the band wavelength configuration, and the four possible swath width and binning options available (more information on http://earth.esa.int/missions/thirdpartymission/proba.html). Regarding the vertical stripping, the acquisition modes can be differenced in binned (Mode 1; with 372 columns) and un-binned (Modes 2, 3, 4, 5; with 744 columns) modes in the across-track direction. In consequence, performance of the proposed algorithm has to be tested on a large number of sites of different nature, several acquisition modes and covering the full range of possible temperatures. For this study, a dataset consisting of 78 acquisitions (up to five multi-angular images per acquisition) over 21 of the core sites of the PROBA mission was considered. In particular, it contains 255 Mode 1 images from 54 acquisitions of 14 core sites, and 113 Mode 2 images from 24 acquisitions of 7 core sites. The instrument’s temperature of these acquisition ranges from 1o C to 9o C since platform temperature changes through the year, being the nominal temperature of the detector 5o C (CHRIS does not have thermal regulation). All the images used in this work have been reprocessed to the version 4.1 of the CHRIS HDF files12 in order to take advantage of (i) the improved radiometric calibration which was poor in previous versions (underestimation up to a factor two of the sensor measurements in the NIR)13 ; (ii) the additional acquisition information contained in the metadata attributes of the CHRIS HDF file (mode, sensor temperature, gain information, and the binning information that relates each spectral band with a set of CCD rows); and (iii) a quality mask added to the HDF data that includes pixel saturation information and occurrence of errors (Payload Processor Unit reset errors), which have to be removed in order to correct the stripping8, 14 .
3.2. Synthetic Images In order to quantitatively validate the proposed method, not having available the pre-launch CCD/Slit characterizations, a set of realistic synthetic images have been generated from three CHRIS acquisitions taken over the site of Barrax (BR, Iberian Peninsula, Spain), Heron Island (EI, Great Barrier Reef, Australia), and Port of Valencia (PC, Mediterranean Coast, Spain). These images have been selected for the study in order to take into account different CHRIS acquisition modes, surface types, and spatial textures and patterns (soil, vegetation, sea, clouds, urban areas, etc). Figure 4 shows an RGB composite of the original and synthetic images over the test sites (BR-2005-07-17, EI-2006-01-30, and PC-2005-05-18). The synthetic images were generated free of noise in order to include a known multiplicative noise coming from the entrance slit and CCD array. • The effect of the uneven slit width on the light arriving to the CCD has been modeled using the superposition of four sinusoids of different characteristics (one high frequency component, two mid frequencies with small amplitude and one low frequency component). Two more sinusoids of very large amplitude with only one cycle length (about 5 pixels width) and half cycle respectively have been placed at two given positions to simulate the effect of dust particles stuck into the slit.
Figure 4. RGB composite of the CHRIS original (upper row) and synthetic (lower row) images over the test sites of BR-2005-07-17 (Mode1), EI-2006-01-30 and PC-2005-05-18 (Mode2).
• The simulated CCD consists of two distributions: first, a normal distribution of unit mean and very low variance, which would represent a fair response of a regular CCD; second, a Gamma distribution of order 3 for a few elements of the CCD, this distribution represents anomalous or defective pixels (leakers). This rather simple approach of synthetically generating noise for the simulated scenes allows an easy identification of which anomalies and frequencies have been properly detected by the noise-removal algorithms, and which have passed through undetected.
4. EXPERIMENTAL RESULTS 4.1. Method performance When comparing the vertical stripping reduction of methods presented in Section 2.1 and the proposed method, one of the main differences comes from the employed low pass filter. In the case of CHRIS images, in which some columns are affected by high noise factors due to the slit non-uniformities, it is critical to employ a filter robust to outliers. To perform a fair comparison between methods, the same LPF is used in both cases. The smoothing is based in a robust regression algorithm that assigns lower weight values to outliers. The filter bandwidth is adjusted for each band to pass low frequency components up to 99% of the cumulative power spectral density of the along-track integrated profile of each band. The assumption of having noise below about 1% of the total energy is a reasonable value from the data acquired prior to launch7 . Thanks to the synthetic images (with a known simulated noise pattern), it is possible to measure the noise reduction in the corrected images. Although it is possible to obtain and compare the SNR of the synthetic noisy images and the corrected ones, the VS is not a random noise. Therefore, Table 1 shows the error between the actual and the estimated VS factors (ˆ ν (p, b)) for both methods: mean error (ME), mean absolute error (MAE), and root mean-squared error (RMSE). Results show that the proposed method produce better estimations of the VS factors for all the images. The bias on the estimated VS, which yields negative ME for all the images and methods, is due to the low frequencies present in the simulated VS that can not be removed by none of them
Table 1. Mean error (ME), mean absolute error (MAE), and root mean-squared error (RMSE) between the actual and the estimated vertical stripping correction factors in the synthetic images. In addition, the relative improvement of RMSE obtained when using the proposed method is also computed. BR-2005-07-17 Standard Proposed -0.471 -0.429 0.131 0.127 0.104 0.101 2.48
Noise profile in the across−track direction 1.3
estimated noise factor
1.2
Noise factor
1.1
1
0.9
0.8
100
150 200 Column index
250
300
PC-2005-05-18 Standard Proposed -0.486 -0.413 0.149 0.145 0.198 0.192 3.09
y=0.74802x+0.24885; r=0.99989; actual estimated
50
EI-2006-01-30 Standard Proposed -0.452 -0.398 0.126 0.120 0.132 0.126 4.00
350
1.5
0.5
1.4
0.4
1.3
0.3
1.2
0.2
1.1
0.1
residuals
Image Method ME ·10−2 MAE ·10−1 RMSE·10−3 ∆RMSE [%]
1
0
0.9
−0.1
0.8
−0.2
0.7
−0.3
0.6
−0.4
0.5 0.5
1 actual noise factor
1.5
−0.5 0.5
1 actual noise factor
1.5
Figure 5. Performance of the proposed method in the estimation of the vertical stripping of image BR-2005-07-17 (Mode 1): (a) actual and estimated VS; (b) actual versus estimated correction factors; (c) actual versus residuals.
(see Fig.5a). When analyzing the regression and the residuals of Fig.5, one can also appreciate that both high and low values of VS are underestimated and overestimated respectively due to the low pass filtering. To better quantify the global performance of the proposed method, Table 1 also shows the relative improvement of RMSE when using our method (∼ 3%). That is, results from both methods seem to be very similar. In fact, doing a one-way analysis of variance (ANOVA) to compare the means of the residuals15 , no significant statistical differences are observed between both methods. That can be explained because our method intends to be more robust to surface changes, it will solve critical problems in some image columns, but in the rest of them both methods follow a very similar procedure. Figure 6a shows one example of these critical cases for the last band of the image EI-2006-01-30, which presents an abrupt change between the dark sea and the bright coast in some of its lines. From top to bottom, it shows the averaged profile in the along-track (which is still affected by the sea/land transition), the derivative of the profile, and finally we compute |ˆ νstandard − νˆproposed | − |νsimulated − νˆproposed |, where the first term indicates in which columns the standard and the proposed method differ, and the second term assures that the proposed method has estimated correctly the VS in these columns. The plots show the agreement between the residual high spatial frequencies of the surface and the mistakes committed only by the standard method. These differences can be critical for hyperspectral processing algorithms that use band ratios and require a very high radiometric accuracy (as the atmospheric water vapor retrieval or the fluorescence estimation from the oxygen absorption bands)14 . Without an accurate noise reduction, these small differences between columns are a significant source of error in both sea and land cover biophysical parameter retrieval. Thanks to the CHRIS sequential acquisition of five images, we can also prove the robustness of the proposed algorithm using the full database of real images. As has been mentioned before, the VS due to the instrument slit is temperature dependent. Although temperature changes higher than 8o C have been recorded, within a single acquisition (5 multi-angular images) the changes are less than 0.5o C. Therefore, the five angular images of one acquisition present the same vertical stripping pattern while they are recording Earth scenes with different spatial patterns (slightly rotated scenes). One can take advantage of this fact to compare the robustness of the methods to changes in the surface. Although observed surface spatial pattern is different, the vertical stripping
(a)
(b) Noise STD within one acquisition set
Average horizontal profile
0.016
8500 8000 7500 7000
0.012 200 300 400 500 600 Average horizontal profile derivative
700
1000 500
100
200
300 400 500 Difference bettwen methods
600
700
proposed method
100
0
Mode2 Mode1
0.014
0.01 0.008 0.006 0.004
0.05 0.002 0
100
200
300 400 Column index
500
600
700
0 0
0.005 0.01 standard method
0.015
Figure 6. (a) From top to bottom: averaged profile in the along-track; derivative of the averaged profile; and a difference index between methods |ˆ νstandard − νˆproposed | − |νsimulated − νˆproposed |. (b) Scatterplot of the standard deviation of the estimated VS factors (computed for each acquisition within the five angles) for both methods.
estimated for the five angles must be equal. Figure 6b shows the standard deviation of the estimated VS factors (computed for each acquisition within the five angles) for both the standard and the proposed methods. The scatterplot shows that in almost all cases the variation of the estimated noise pattern within one acquisition set is lower with the proposed approach, which demonstrates the robustness to surface changes.
4.2. Vertical stripping characterization Finally, a result of great value for the CHRIS community is the characterization of the vertical stripping and its dependence on temperature. With this purpose, we corrected all the images of the database obtaining an estimation of the vertical stripping pattern, νˆ(p, b) = H(p) · S(p, b), per image. The sensitivity of the CCD array, S(p, b), is assumed to be characterized by a Gaussian distribution with unit mean. However, by applying the logarithmic transformation to the estimated VS, the multiplicative nature of both terms is changed to additive one log νˆ(p, b) = log H(p) + log S(p, b), where log S(p, b) can be considered additive noise with zero mean distribution. In consequence, the VS profile due to the slit, which is constant in columns, can be obtained by an averaging RB in the spectral direction of the CCD and removing the logarithm: H(p) = exp( 1 log νˆ(p, b)db). Moreover, the slit-VS profiles of the five angular images can be averaged to obtain only one H(p) per acquisition, which will be associated to the platform temperature: H(p, T ). Changes in temperature produce a dilation of the slit changing its width and moving the image of the slit across the detector. These two effects produce a scaling of the slit-VS factors and a shift of its shape in the across-track producing a temperature dependent vertical stripping. Figure 7, on the left side, shows a peak of the obtained H(p) profiles for all the Mode 2 acquisitions of the database (Mode 2 is shown because it is not binned and presents higher resolution than Mode 1). The ‘∗’ symbols represent the actual H(p) values for each pixel column p, which are spline interpolated in the across-track (continuous line) in order to obtain a continuous (subpixel resolution) model of the stripping for each measured temperature T: H(x, T ). The curves clearly show the shift and scaling of the VS amplitude with temperature. Taking as reference the VS at T0 = 5.5o C, we compute the the shift in the across-track looking for the lag, ∆x (T ), of the maximum of the cross-correlation sequence between the analyzed vertical stripping, H(x, T ), and the reference one, H(x, T0 ). Once the shift is corrected, the scaling factor, GH (T ), is computed as the slope of the linear regression that better fits H(x, T ) with H(x, T0 ) in a least-squares sense. In the central and right plots of Fig.7 we represent the shift, ∆x (T ), and scale, GH (T ), of the slit-VS as a function of temperature, respectively. After correcting both the shift and scale of the slit-VS of each acquisition of the database, we model the “real ” slit-VS, denoted by H(x), as the average of all the curves to reject estimation errors. The modeled slit-VS for a given temperature can be recovered as H(x, T ) = GH (T )·H(x−∆x (T )), and the value for a given pixel column is R p+1/2 obtained integrating the width of the pixel photo-sensible area, H(p, T ) = p−1/2 H(x, T )dx. At this preliminary
0.5
1.1
1
−1.1
−1.2
63
64
65
66 67 68 CCD pixel index
69
70
71
Mode2 Mode1
0.3
2
0.2
Vertical stripping gain
Vertical stripping gain
1.2
2.5 Mode2 Mode1
0.4
Horizontal shift (CCD pixels)
2.68ºC 2.8ºC 3.08ºC 3.7ºC 3.85ºC 3.99ºC 4.14ºC 4.59ºC 4.67ºC 4.68ºC 5.3ºC 5.51ºC 5.67ºC 5.84ºC 5.99ºC 6.3ºC 6.82ºC 7.15ºC 7.9ºC 8.22ºC 8.63ºC 8.64ºC 8.66ºC 8.73ºC
1.3
0.1 0 −0.1 −0.2 −0.3
1.5
1
0.5
−0.4 −0.5 0
1
2
3
4 5 6 Temperature (deg)
7
8
9
0 0
1
2
3
4 5 6 Temperature (deg)
7
8
9
Figure 7. Dependence of CHRIS slit vertical stripping on temperature. From left to right: (a) detail of the slit-VS profiles for all the Mode 2 acquisitions of the database; (b) across-track shift of the slit-VS shape as a function of temperature; (c) scaling of the slit-VS factors as a function of temperature. Vertical stripping modeled from different CHRIS Modes
Model of the vertical stripping due CHRIS slit 1.1 Mode1 Mode2 Mode2 binning
1.2
y=0.85033x+0.14962; r=1; 1.08 1.06
1.15
1.04 Mode2 binning
Noise factor
1.1 1.05 1
1.02 1 0.98 0.96
0.95
0.94
0.9
0.92 0.85 58
60
62
64 66 68 CCD pixel index
70
72
74
0.9 0.9
0.95
1 Mode1
1.05
1.1
Figure 8. Detail of the “real” slit-VS modeled from Mode 1 and Mode 2 CHRIS images, and the binning of Mode 2 ‘∗’ closely matching Mode 1 curve (left). Scatterplot of the modeled Mode 1 and Mode 2 “real” slit-VS.
phase of the study, we can validate this methodology by comparing the slit-VS curves modeled independently from the Mode 1 and Mode 2 acquisitions (H1 (x) and H2 (x)). The main difference between both modes is that Mode 1 performs a binning of columns in pairs. Therefore, before comparing them, we compute their values for each pixel column p, and simulate the binning in the Mode 2: Hbinned (p/2) = 1/2 · (H2 (p − 1) + H2 (p)), where p = 2, 4, 6, . . . , 744 (to have the same number of columns than Mode 1). Figure 8 shows results of comparing slit-VS modeled from Mode 1 and Mode 2 CHRIS images. Agreement between both results is excellent, except in the highest and lowest anomalous values (VS peaks), where probably the interpolation used to obtain H(x) produces underestimated VS peaks, being this effect more noticeable in the binned Mode 1.
5. CONCLUSIONS In this paper, we have presented a new technique that faces the problem of removing the coherent noise known as VS (usually found in images acquired by push-broom sensors). Some algorithms already exist to reduce VS using simple approaches, but they assume that the imaged surface does not contain structures with spatial frequencies of the same order than noise, which is not always the case. The proposed method introduces a way to exclude the contribution of the spatial high frequencies of the surface from the process of noise removal that is based on the information contained in the spectral domain. In addition, a common element to all destripping techniques is the application of a low pass filter, which requires setting a cut-off frequency. Generally this frequency is set to a fixed value, which might not always be the optimal. In our approach, the most adequate cut-off frequency is estimated for each image.
Synthetic realistic scenes have been created, adding modeled noise for validation of the method. The analysis shows that high frequency VS is successfully removed, although some low frequency components remain. The results are slightly better when compared to the standard methods, and this improvement becomes substantial when the retrieval of bio-physical parameters requires calculating ratios between bands. In addition, the proposed algorithm provides a more robust performance in different types of scenes, especially those with sharp transitions between contrasting surfaces; and greater stability of results in the sets of images within an acquisition. These characteristics have permitted to successfully model the shape of the slit with subpixel resolution, and find a relationship of the sensor temperature with the magnitude and distribution of the vertical stripping. The proposed approach has proven to be robust, stable in VS removal, and a tool for noise modeling. Finally, the general nature of the procedure allows it to be applied for destripping images from other spectral sensors.
ACKNOWLEDGMENTS This paper has been partially supported by the Spanish Ministry for Education and Science under project DATASAT ESP2005-07724-C05-03, and by the “Grups Emergents” programme of Generalitat Valenciana under project HYPERCLASS/GV05/011. The authors wish to thank ESA and SIRA Technology Ltd. for the availability of the image database and the assistance provided by Dr. Mike Cutter and Lisa Johns.
REFERENCES 1. A. Barducci, D. Guzzi, P. Marcoionni, and I. Pippi, “CHRIS-PROBA performance evaluation: Signal-tonoise ratio, instrument efficiency and data quality from acquisitions over San Rossore (Italy) test site,” in 3rd CHRIS/Proba Workshop, ESA-SP-593, ed., ESRIN, Frascati, Italy, June 2005. 2. M. Barnsley, J. Settle, M. Cutter, D. Lobb, and F. Teston, “The PROBA/CHRIS mission: a low-cost smallsat for hyperspectral, multi-angle, observations of the Earth surface and atmosphere,” IEEE Trans. Geosci. Remote Sensing 42(7), pp. 1512–1520, July 2004. 3. D. Bernaerts, F. Teston, and J. Bermyn, “PROBA (Project for Onboard Autonomy),” 5th International Symposium on Systems and Services for Small Satellites 1, 19-23 June 2000, La Baule, France (2000). 4. A. Theuwissen, Solid-State Imaging with Charge-Coupled Devices, Kluwer Acad. Publ., Boston, 1995. 5. M. Cutter, “Review of aspects associated with the CHRIS calibration,” in 2nd CHRIS/Proba Workshop, ESA-SP-578, ed., ESRIN, Frascati, Italy, April 2004. 6. A. Barducci and I. Pippi, “Analysis and rejection of systematic disturbances in hyperspectral remotely sensed images of the Earth,” Applied Optics 40(9), pp. 1464–1477, 2001. 7. J. Settle and M. Cutter, “personal comunication,” 2004. 8. J. Garcia and J. Moreno, “Removal of noises in CHRIS/Proba images: Application to the SPARC campaign data,” in 2nd CHRIS/Proba Workshop, ESA-SP-578, ed., ESRIN, Frascati, Italy, April 2004. 9. W. K. Pratt, Digital Image Processing: PIKS Inside, 3rd Edition, Wiley-Interscience, July 2001. 10. N. Keshava, “Distance metrics and band selection in hyperspectral processing with applications to material identification and spectral libraries,” Geoscience and Remote Sensing, IEEE Transactions on 42(7), pp. 1552–1565, 2004. 11. H. Othman and S.-E. Qian, “Noise reduction of hyperspectral imagery using hybrid spatial-spectral derivative-domain wavelet shrinkage,” Geoscience and Remote Sensing, IEEE Transactions on 44(2), pp. 397–408, 2006. 12. M. Cutter and L. Johns, “CHRIS data products – latest issue,” in 3rd CHRIS/Proba Workshop, ESA-SP593, ed., ESRIN, Frascati, Italy, June 2005. 13. L. Guanter, L. Alonso, and J. Moreno, “Methods for the surface reflectance retrieval from CHRIS/PROBA data over land and inland waters,” in 3rd CHRIS/Proba Workshop, ESA-SP-593, ed., ESRIN, Frascati, Italy, June 2005. 14. L. Gomez-Chova, J. Amoros, G. Camps-Valls, J. D. Martin, J. Calpe, L. Alonso, L. Guanter, J. C. Fortea, and J. Moreno, “Cloud detection for CHRIS/Proba hyperspectral images,” Remote Sensing of Clouds and the Atmosphere X 5979(1), p. 59791Q, SPIE, 2005. 15. L. L. Lapin, Probability and Statistics for Modern Engineering, Duxbury Press. PWS Publishers, 1983.
