SIGNAL ENHANCEMENT IN NOISE AND CLUTTER CORRUPTED

SIGNAL ENHANCEMENT IN NOISE AND CLUTTER CORRUPTED IMAGES USING ADAPTIVE PREDICTIVE FILTERING TECHNIQUES ' Tarun Soni*, J. R. Zeidler *,+Bhaskar D. Rao, and Walter H. Ku* * Department of Electrical and Computer Engineering University of California, San Diego, La Jolla, CA 92093-0407 + U.S. Naval Ocean Systems Center San Diego, CA 92152-5000

Abstract The recovery of an original image from its corrupted version is of importance in a number of applications. The detection of small and dim targets is one such problem, requiring the enhancement of target signals and suppression of noise and clutter in the image. Conventional methods like matched filtering require a priori knowledge of the target intensity spread function, the clutter correlation characteristics etc. These techniques are difficult to implement if the image is nonstationary. This paper describes an adaptive clutter whitening technique which increases signal detectability in colored noise and clutter. Signal enhancement is based on the intrinsic differences in the spatial extent of the target relative to the clutter. An adaptive spatial filter is used to whiten the clutter present in the image. The output of such an adaptive spatial filter, termed the Adaptive Clutter Whitener(ACW), is then passed on to a matched filter based detector. The receiver operating characteristics are found using Monte-Carlo simulation techniques, both for the ACW augmented matched filter detector and a conventional matched filter detector. It is seen that for highly correlated clutter, the ACW augmented detector has a better ROC than one without a a pre-whitening filter.

1 Introduction Target detection and location at long range is a difficult and challenging task. Images obtained using passive infra red (IR) sensors have often been used for this purpose [1J[2J[3][4]. However these images usually have a very low signal to noise (and clutter) ratio as the targets are in the form of a dim point source embedded in clutter. Also the clutter is usually correlated, and often nonstationary, further complicating the problem. Conventional methods like matched

filtering require a priori knowledge of the target point spread function as well as the clutter and noise correlation characteristics. Furthermore these techniques are difficult to implement ifthe image characteristics are non stationary. In this paper, we describe a detection scheme which employs an adaptive spatial filter prior to matched filtering. The configuration (fig. 1) consists of a adaptive spatial filter, termed the Adaptive Clutter Whitener (ACW), followed

by a matched filter. The main motivation for this arrangement is the fact that the ACW can be designed to learn the statistics of the clutter obviating the need for prior knowledge about the clutter characteristics, and can deal with mild non stationarities. This arrangement thereby circumvents a crucial requirement and difficulty encountered when using conventional matched filtering techniques.

2 Conventional Matched Filtering An often used technique of detection in JR images is matched filtering. In a conventional matched filter the target signal template is assumed to be known and is matched to every pixel of the image. The output of the matched filter is then compared to some pre-determined threshold to make a decision about the presence or absence of the target. Thus the output of such a detector is a set of " detection statistics" , one for each pixel of the image and a comparison of these with the threshold gives the existence and location of the targets. If the target is taken to be of size M x M and the image is taken to be of size N x N, then the detection statistics, in the presence of white noise, are given by

t(i, j) =

s(l, k)I(i — M/2 + 1, j — M/2 + k)

i, j =

1, .., N

1=1 k=1 1 This work was supported by the NSF 1/UC Research Center on Ultra High Speed Integrated Circuits and Systems (ICAS) at the University of California, San Diego, The Office of Naval Research and the National Science Foundation under grant #ECD89-16669 and the U.S. Naval Ocean Systems Center Independent Research Program.

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Detection Statistic

Input Image

Detector without augmentation

Detection Statistic

Input Image Detector with ACW augmentation

Figure 1: The two detector structures: with and without ACW augmentation where s(., .) is the signal template and I(.,.) are the input image pixel intensity values. To determine if there is a target at the (i, j)th pixel, t(i, j) is compared to a preset threshold. The threshold would typically be decided based on a desired false alarm rate and the probability distribution functions of the input. However, quite often these are not available and this threshold is then decided on the basis of Monte-Carlo simulations or other such criteria. If the image has correlated clutter, this can be incorporated into the matched filter, by using any known statistics of the correlation. However in general, the filter is quite sensitive to any deviations of the input from the assumed model, and cannot handle non stationarities very well.

3 ACW Augmented Matched Filtering The Adaptive clutter whitener(ACW) augmented detector consists of a two dimensional adaptive filter in the clufler whiiening configuration (ACW) and a matched filter as shown in fig. 1. The difference compared to a conventional

matched filter is that the first block which is designed to whiten the clutter is an adaptive filter. This alleviates the need for knowing the statistics of the clutter, and also provides the detector the ability to deal with mild nonstationarities. Such schemes have been quite successful for the problem of detecting sinusoids in noise [5]. If the adaptation parameter is chosen properly [6] [4], the ACW is able to track and predict the correlated clutter ignoring the target. Hence the error output of the ACW contains the target in white noise which is then fed into a matched filter designed assuming that the noise is white. The adaptive filter is discussed next followed by a discussion of its effectiveness in whitening the clutter only. The two dimensional adaptive filter used by the ACW is essentially an extension of its one dimensional counterpart [7]. Its input is a two dimensional array of pixel values, denoting the intensities at each pixel in the noisy image. The predicted pixel value at any given iteration is a weighted average of a small window of pixels around it and is given by N—i N-i

Y(rn, n) =

>.: : 1=0 k=O

(1, k)X(rn — 1, n — k)

rn, n = 0, . .. , M — 1

where j is the iteration number. The image is scanned from top to bottom and left to right (lexicographically) and hence j is found as j = mM + n. Here X is the input image, Y the predicted image and l4' the weight matrix at the th iteration. The images are assumed to be square of size M x M pixels and the weight matrix (hence the window

size ofthe pixels being used to predict) is taken to be square ofsize N x N. The predicted pixel value is now compared with the corresponding pixel of the reference IR image, to get a measure of the error. In the two dimensional ACW configuration (see fig. 2), the reference image is derived as a shifted. version

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Scene

Weight Matrix

Y(in,n)

The Recovered

Scene

Reference Scene

Figure 2: The Two Dimensional Adaptive Filter

of the primary. Thus the reference image D is now found as D(rn, n)

X(rn

- i, n - 2)

rn,n=O,...,M—1

with (4i, 42) being the shifts in both the dimensions. The error E is now found as E(m, n) = ci = D(rn, n) — Y(rn, n) Ideally the filter would minimize the expected value of the mean square error over the complete image. An ideal Weiner filter implementation of this would require a knowledge of the auto correlation and cross correlation's between the various regions of interest of the image, and would also assume that the image statistics are stationary. The ideal filter weights would then be given by the two dimensional Weiner-Hopf equation as N—i N—i

P(l,k)=

> W01(p,q)X(l_p,k_q)

l,k=O,...,N—1

(1)

p=O q=O

where P(l, k) is an element of the cross correlation matrix defined by

e(D(rn, n)X(rn, n))

.

.

. e(D(rn, n)X(m, n — N + 1))

S(D(m, n)X(rn — N + 1, n))

.

.

. e(D(m, n)X(m — N + 1, n — N + 1))

and R is the input auto correlation matrix with the elements R(l — p, k — q) defined as R(l — p, k — q)

=

— 1, n —

k)X(m — p, n — q))

Block techniques can be used to formulate and solve the 2-D Weiner Hopf equation given by eq. 1. However in the presence of colored noise, the optimum weights would predict both the target of interest and the colored noise.

340 I SPIE Vol. 1565 Adaptive Signal Processing(1991)

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x

IL

Figure 4: The Output Image where the energy of the sinusoid is a2/2 and W(x, y) is zero mean white Gaussian noise of varianceu2 The input image then becomes

Y(x,y) = I(x,y)+ C(x,y)

is shown in fig. 3. The error channel output from the adaptive clutter whitener, after the clutter was whitened is shown in fig. 4 The SNR of the system was then found as and

SNR = lOlogio( SEner) NEnergy

Where the average signal energy per pixel is given by SEnergy

= (I2ii) i=1 j=1

and similarly the noise energy per pixel is defined as NEnergy

= a2+ o2

The SNR used for our simulations was -27.55dB as defined above. The ACW-augmented detector was compared with an ordinary matched filter as follows. The probability of detection and the probability of false alarm were found for both the ACW-augmented detector and the conventional matched filter and the receiver operating characteristics plotted to compare the two.

Fig. 5 shows the ROC's of the detector with and without the pre-whitening ACW filter. The probability of

detection (Pd) was found by using the matched filter output (in both cases with and without the ACW) at the pixels at which the target was known and comparing it to some given threshold to make a decision about detection. The detector used was matched to the target intensity function in the first case(without ACW). In the second case, the detector was matched to the intensity function of the target at the output of the converged ACW. 500 independent runs were used to generate the probability of detection. The finite number of trials used for calculating Pd lead to a ROC which is not very smooth as seen in fig. 5 The probability of false alarm (Pja)was calculated by comparing the pixel output values of the same matched filter at pixel locations where the target was known to be absent. Calculating the threshold analytically becomes very

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Conventional Matched Filter

,.