Hyperspectral Target Detection in Noisy Environment ...

Hyperspectral Target Detection in Noisy Environment Using Wavelet filter and Correlation based detector Erol Sarigula and M.S. Alamb* a

Department of Advanced Technology, Alcorn State University, 1000 ASU Drive #360 Alcorn State, Mississippi 39096 b

Department of Electrical and Computer Engineering, University of South Alabama Mobile, AL 36688-0002, ABSTRACT

In this paper, we propose an algorithm for detecting man made targets in hyperspectral imagery using correlation based detection after wavelet domain filtering. In the proposed method, each spectral pixel in noisy hyperspectral data cube is filtered by wavelet domain filtering. Wavelet domain filtering looks at every spectral pixel as noisy signal and filter out noise through wavelet shrinkage based method. Then correlation between the provided target spectral signature and spectral signal from data cube is calculated. The algorithm scans each pixel in data cube then calculates correlation with target signature. The process yields correlation image. Applying threshold operation for correlation image provides detection image. The detection performance of the algorithm is tested with several hyperspectral datasets. Using ROC analysis and comparing with ground truth image, it is observed that wavelet based filtering provides better detection performance for noisy data. The simulation results indicate that the proposed algorithm efficiently detects object of interest in all datasets. Keywords: Target detection, hyperspectral imaging, wavelet filtering, normalized cross correlation.

1

INTRODUCTION

Detection of man-made object through airborne or space borne vehicles is challenging problem both for civilian and for military applications. The main principle of object detection in hyperspectral imagery is to detect and identify the material of interest based on how much they absorb or reflect the light at different spectral bands [1]. From this perspective, detection of man-made objects using hyperspectral imagery is similar to material detection by using spectroscopy method in laboratory setting. When hyperspectral image is acquired from airborne vehicles, the reliability of the detector application highly depends on the quality of the captured data. Although significant advances have been made in improving hyperspectral image sensors, the captured data contains enough noise to affect the information extraction and detection of man-made objects. One of the important parameter in the design of a hyperspectral sensor is its signal-to-noise ratio (SNR), which determines the sensitivity and the cost of the imager. A sufficiently high SNR can be obtained first-hand by adopting some excessive measures in the instrument design, e.g. increasing the size of optical system, increasing integration time, increasing sensor size, etc. Normally, these solutions prohibitively increase the cost of detection system which can provide better detection performance. Alternatively, noise reduction methods can provide economic solutions that are becoming more and more affordable in terms of speed and expense due to availability of cost effective advanced signal processing processors. *

Further author information: (Send correspondence to A.) A.: E-mail: [email protected], Phone: 601-877-2484, Fax: 601- 877-3941 B..: E-mail: [email protected], Phone: 251-460-6117, Fax: 251-460-6028

Automatic Target Recognition XIX, edited by Firooz A. Sadjadi, Abhijit Mahalanobis, Proc. of SPIE Vol. 7335, 73350F · © 2009 SPIE · CCC code: 0277-786X/09/$18 · doi: 10.1117/12.820312

Proc. of SPIE Vol. 7335 73350F-1

Our detection algorithm has two-stage processing: (1) Filtering of hyperspectral dataset to improve signal to noise ration and reduce noise in the dataset that uses wavelet based noise reduction method, and (2) correlation based detection method is used to detect targets of interest in the dataset. In the first stage, wavelet based filtering is applied to reduce the effect of noise and improve signal quality of the dataset. To do that, we have utilized the algorithm that is outlined in [5]. In that method, wavelet transform used to analyze the hyperspectral dataset spatial and spectral characteristics and then wavelet shrinkage method applied to reduce noise in spatial and spectral domains. In the second stage, we use the noise reduced dataset which is the output of the first stage as an input to correlation based detector to detect object of interests. To do that, the processed dataset is analyzed by normalized cross correlation based method with a given reference spectral signature to find correlation between the spectral signal in the dataset and the reference signal. The normalized cross correlation method provides illumination invariant correlation which is immune to spectral intensity of signal. The paper is organized as follows. Section 2 describes the wavelet based noise reduction stage which improves signal-to-noise ratio and improve signal quality of dataset. Section 3 provides the details on correlation based detection method, experimental results and discussion are presented in section 4 and concluding remarks are included in section 5.

2

WAVELET BASED NOISE REDUCTION

In order to improve signal quality and reduce the effect of noise to improve detection rate, wavelet based noise reduction method [5] is used. This method provides efficient method to tackle filtering problem where the noise variance is varying with the signal amplitude along the spectral band dimension at relatively high signal-to-noise ratio. It proposes two-dimensional method that exploits the spatial and spectral features of hyperspectral imagery and operates in the derivative domain. Several noise reduction algorithms have been proposed recently based on wavelet transform. Some of wavelet based noise reduction algorithms are linear minimal mean squared error method [2], using both wavelet transform with using probability of the presence features of interest [3], [4]. Most of the hyperspectral/multispectral imagery filtering methods perform well fixed variance and additive noise conditions but the noise characteristics of hyperspectral imagery system does not fit in that category. In fact, the hyperspectral signal may change dramatically from band to band with variable smoothness in the visible and near-infrared (VNIR) region compared to the smoothness in the shortwave infrared (SWIR) region. Since this method takes this consideration into account, we implemented this method as noise reduction method in our algorithm.

Noisy Dataset

d dλ

Spatial-Spectral Filtering

∫ dλ

-

+

Moving Average Filtering

Spatial-Spectral filtering in the Spectral Derivative Domain

Correction of the accumulated error

Figure 1. Block diagram of spatial-spectral derivative domain wavelet shrinkage noise filtering algorithm.


Filtered Dataset

The major advantage of this filtering is to tackle with variable noise level. The noise level is varying with intensity of the signal based on spectral sensor characteristics. In addition to that, noise characteristics in spectral dimension is different than spatial dimension. The procedure of the noise reduction filtering is shown in Figure 1. The process exploits the dependency between spatial-spectral noise variation characteristics. The 3-D wavelet shrinkage filtering algorithm in [6] benefits from this dependency, but implicitly assumes noise variance is the same in the three dimensions. In this noise reduction method, the noise level is amplified temporarily and perform denoising process in this condition, then reversibly weaken the noise level. This method is compatible with wavelet shrinkage noise reduction due to its nonlinear nature. Amplification of the noise level is performed by transforming hyperspectral dataset into the spectral derivative domain, which is essentially analogous to high-pass filtering. This process makes increasing noise-to-signal ratio since the signal power is concentrated in the low frequency region. The process of transforming spectral band image into derivative domain can be mathematically described as:

θ (λ , p , l ) = where

λ

∂y (λ , p, l ) y (λ + δ λ , p, l ) − y (λ , p, l ) = δλ ∂λ

is a spectral band center, p is a cross-track pixel number,

l

is an along-track line number, and

(1)

δ λ is a small

displacement in the spectral dimension. The transformed signal, which has amplified noise signal, is processed by hybrid spatial-spectral noise reduction in the spatial and spectral domains independently, removing more noise with less signal distortion. Then the signal is transformed back from the derivative domain, i.e.,

~

θ = IDWT 2(η spatial ( DWT 2(θ )))

(2)

~

where

~

θ ,θ

θˆ = IDWT (η spectral ( DWT (θ )))

, and θˆ are the spectral derivative of the noisy hyperspectral dataset , the spatially denoised derivative of

the noisy dataset, and the spatially spectrally denoised derivative of the noisy dataset, respectively. DWT 2 is the 2-D discrete wavelet transform applied to the along-track dimension, IDWT 2 is the associated 2-D inverse discrete wavelet transform, DWT is the one-dimensional (1-D) discrete wavelet transform , η spatial is a threshold function that is applied on band-by-band basis and

η spectral

is a threshold function that is applied to the spectral dimension pixel-by-

pixel basis. Filtered signal xˆ (λ , p, l ) is then obtained by spectral integration as shown in the following equation:

where

λi

and

λj

⎧ x1 ( p, l ), ⎪ j −1 xˆ (λ , p, l ) = ⎨ x1 ( p, l ) + ∑ θˆ(λi , p, l ) ⋅ δ λ , ⎪⎩ i =1

j =1 j >1

(3)

are the center wavelength of the ith and the jth spectral bands, respectively and

x1 ( p, l ) = y (λ1 , p, l ) . Apparently, there will be an integration error introduced due to integration process with growing lambda and the total number of spectral bands. Normally, hyperspectral data contains a large number of spectral bands, e.g. 205 which may result in accumulating an error that is significantly larger than the initial noise. This means that the error accumulated in the integration process may not result in degradation of the signal quality if no corrective action is taken. The corrective action is shown in Figure 1. Given the large amount of data to be filtered simple low pass filter can be chosen. In this method, moving average (MA) is chosen since it requires no multipliers other than the gain factor.

3

CORRELATION BASED DETECTOR

The correlation between two signals (cross correlation) is a standard method to find similarity between these two signals. The use of cross correlation for finding similarity between spectral signature from hyperspectral dataset and


reference spectral signal can be seen as template matching which is motivated by the distance measure (squared Euclidean distance) can be written as:

c f ,t (u ) = ∑ f ( x) ⋅ t ( x − u )

(4)

x, y

where f is the spectral signal from hyperspectral dataset and t is the reference signal which is provided. This finds similarity between the spectral signal from the dataset and the reference spectral signature. But there are some drawbacks and disadvantages of this correlation measure. If the signal energy and illumination changes over the dataset due to environmental effects, matching and correlation process is severely affected by that. To address those drawbacks, normalized cross correlation is developed [7][8] which can be shown mathematically as:

γ (u ) =

∑λ [ f (λ ) − f

u

][t (λ − u ) − t ]

∑λ [ f (λ ) − f ] ∑λ [t (λ − u ) − t ] 2

(5)

2

u

where f , and t is d.c component of hyperspectral dataset and reference signal, respectively.

4

EXPERIMENTAL RESULTS

The performance of the proposed algorithm has been tested various hyperspectral datasets. The dataset has been simulated using real HYDICE terrain data shown in Fig. 2(a), and 2(b).) and CASI battleship park dataset show in Fig. 3(a), and 3(b). which contains object of interest. Heavy noise is present in all of the hyperspectral datasets which makes the detection of man-made object challenging. The HYDICE hyperspectral dataset contains 203 spectral bands and each spectral image is in size of 256x256. The CASI dataset contains 36 spectral bands and each spectral image is in the size of 512x512. The both datasets contain 10 man-made objects and its reference spectral signatures were provided. For the HYDICE dataset, we tested the performance of the algorithm. As we described above, wavelet based noise reduction algorithm was applied to reduce amount of noise in the dataset and then correlation based detection algorithm was run to detect man-made objects in the dataset. ROC performance of the algorithm with HYDICE dataset is given in Fig. 2(c), 2(d). To obtain ROC performance of the algorithm for all datasets by using special purpose program, we also obtained some of the standard algorithms (SAM, ECGLRT, PARRX, RX, and WSMF) detection performance as well as the proposed algorithm (WL-XCORR) which is shown in Fig. 2(e). For the CASI dataset, we have two cases (see Fig. 3 and 4). The algorithms performance tested similarly as described above to detect object of interests. ROC performance for the CASI dataset was obtained against some of the standard algorithms as well. The results are presented in Fig 3(e), and Fig. 4(e).

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Figure 2. HYDICE Terrain dataset. (a) One of the spectral band image of HYDICE dataset. (b) Ground Truth image for the dataset. (c) The result of detection. (d) The output of thresholding operation. (e) ROC performance of the algorithm against some standard detection algorithms.


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Figure 3. CASI dataset. (a) One of the spectral band image of CASI dataset. (b) Ground Truth image for the dataset. (c) The result of detection. (d) The output of threshold operation. (e) ROC performance of the algorithm against some standard detection algorithms


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Figure 4. CASI dataset. (a) One of the spectral band image of CASI dataset. (b) Ground Truth image for the dataset. (c) The result of detection. (d) The output of threshold operation. (e) ROC performance of the algorithm against some standard detection algorithms


5

CONCLUSION

A new method for detection of object of interest in the presence of noise or interference has been proposed and demonstrated in this paper. This algorithm mainly focuses on wavelet based denoising of hyperspectral imagery to improve detection rate. The correlation based detector is used to detect objects of interests. To evaluate the performance of the proposed algorithm, we used ROC analysis and compared its detection performance with some standard detection algorithms. Our results indicate promising detection performance in the presence of noise.

ACKNOWLEDGMENTS The part of this work was supported by a grant from the US Army Space and Missile Defense Command.

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