A Model for Radar Images and Its Application to Adaptive Digital Filtering of Multiplicative Noise
01 Feb 1982-IEEE Transactions on Pattern Analysis and Machine Intelligence (IEEE)-Vol. 4, Iss: 2, pp 157-166
TL;DR: A model for the radar imaging process is derived and a method for smoothing noisy radar images is presented and it is shown that the filter can be easily implemented in the spatial domain and is computationally efficient.
Abstract: Standard image processing techniques which are used to enhance noncoherent optically produced images are not applicable to radar images due to the coherent nature of the radar imaging process. A model for the radar imaging process is derived in this paper and a method for smoothing noisy radar images is also presented. The imaging model shows that the radar image is corrupted by multiplicative noise. The model leads to the functional form of an optimum (minimum MSE) filter for smoothing radar images. By using locally estimated parameter values the filter is made adaptive so that it provides minimum MSE estimates inside homogeneous areas of an image while preserving the edge structure. It is shown that the filter can be easily implemented in the spatial domain and is computationally efficient. The performance of the adaptive filter is compared (qualitatively and quantitatively) with several standard filters using real and simulated radar images.
Citations
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TL;DR: This paper provides the derivation of speckle reducing anisotropic diffusion (SRAD), a diffusion method tailored to ultrasonic and radar imaging applications, and validates the new algorithm using both synthetic and real linear scan ultrasonic imagery of the carotid artery.
Abstract: This paper provides the derivation of speckle reducing anisotropic diffusion (SRAD), a diffusion method tailored to ultrasonic and radar imaging applications. SRAD is the edge-sensitive diffusion for speckled images, in the same way that conventional anisotropic diffusion is the edge-sensitive diffusion for images corrupted with additive noise. We first show that the Lee and Frost filters can be cast as partial differential equations, and then we derive SRAD by allowing edge-sensitive anisotropic diffusion within this context. Just as the Lee (1980, 1981, 1986) and Frost (1982) filters utilize the coefficient of variation in adaptive filtering, SRAD exploits the instantaneous coefficient of variation, which is shown to be a function of the local gradient magnitude and Laplacian operators. We validate the new algorithm using both synthetic and real linear scan ultrasonic imagery of the carotid artery. We also demonstrate the algorithm performance with real SAR data. The performance measures obtained by means of computer simulation of carotid artery images are compared with three existing speckle reduction schemes. In the presence of speckle noise, speckle reducing anisotropic diffusion excels over the traditional speckle removal filters and over the conventional anisotropic diffusion method in terms of mean preservation, variance reduction, and edge localization.
1,816 citations
TL;DR: The most well known adaptive filters for speckle reduction are analyzed and it is shown that they are based on a test related to the local coefficient of variation of the observed image, which describes the scene heterogeneity.
Abstract: The presence of speckle in radar images makes the radiometric and textural aspects less efficient for class discrimination. Many adaptive filters have been developed for speckle reduction, the most well known of which are analyzed. It is shown that they are based on a test related to the local coefficient of variation of the observed image, which describes the scene heterogeneity. Some practical criteria are introduced to modify the filters in order to make them more efficient. The filters are tested on a simulated synthetic aperture radar (SAR) image and an SAR-580 image. As was expected, the new filters perform better, i.e. they average the homogeneous areas better and preserve texture information, edges, linear features, and point target responses better at the same time. Moreover, they can be adapted to features other than the coefficient of variation to reduce the speckle while preserving the corresponding information. >
954 citations
TL;DR: This work model the speckle according to the exact physical process of coherent image formation and accurately represents the higher order statistical properties of speckel that are important to the restoration procedure.
Abstract: Speckle is a granular noise that inherently exists in all types of coherent imaging systems. The presence of speckle in an image reduces the resolution of the image and the detectability of the target. Many speckle reduction algorithms assume speckle noise is multiplicative. We instead model the speckle according to the exact physical process of coherent image formation. Thus, the model includes signal-dependent effects and accurately represents the higher order statistical properties of speckle that are important to the restoration procedure. Various adaptive restoration filters for intensity speckle images are derived based on different model assumptions and a nonstationary image model. These filters respond adaptively to the signal-dependent speckle noise and the nonstationary statistics of the original image.
701 citations
TL;DR: Experiments carried out on two sets of multitemporal images acquired by the European Remote Sensing 2 satellite SAR sensor confirm the effectiveness of the proposed unsupervised approach, which results in change-detection accuracies very similar to those that can be achieved by a manual supervised thresholding.
Abstract: We present a novel automatic and unsupervised change-detection approach specifically oriented to the analysis of multitemporal single-channel single-polarization synthetic aperture radar (SAR) images. This approach is based on a closed-loop process made up of three main steps: (1) a novel preprocessing based on a controlled adaptive iterative filtering; (2) a comparison between multitemporal images carried out according to a standard log-ratio operator; and (3) a novel approach to the automatic analysis of the log-ratio image for generating the change-detection map. The first step aims at reducing the speckle noise in a controlled way in order to maximize the discrimination capability between changed and unchanged classes. In the second step, the two filtered multitemporal images are compared to generate a log-ratio image that contains explicit information on changed areas. The third step produces the change-detection map according to a thresholding procedure based on a reformulation of the Kittler-Illingworth (KI) threshold selection criterion. In particular, the modified KI criterion is derived under the generalized Gaussian assumption for modeling the distributions of changed and unchanged classes. This parametric model was chosen because it is capable of better fitting the conditional densities of classes in the log-ratio image. In order to control the filtering step and, accordingly, the effects of the filtering process on change-detection accuracy, we propose to identify automatically the optimal number of despeckling filter iterations [Step 1] by analyzing the behavior of the modified KI criterion. This results in a completely automatic and self-consistent change-detection approach that avoids the use of empirical methods for the selection of the best number of filtering iterations. Experiments carried out on two sets of multitemporal images (characterized by different levels of speckle noise) acquired by the European Remote Sensing 2 satellite SAR sensor confirm the effectiveness of the proposed unsupervised approach, which results in change-detection accuracies very similar to those that can be achieved by a manual supervised thresholding.
688 citations
Cites methods from "A Model for Radar Images and Its Ap..."
...To this purpose, various filters have been proposed in the SAR literature, among which we recall the Lee [21], the Kuan [22], the Frost [23], and the MAP filters [24]....
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...filters have been proposed in the SAR literature, among which we recall the Lee [21], the Kuan [22], the Frost [23], and the MAP filters [24]....
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TL;DR: Generally, a CAD system consists of four stages: preprocessing, segmentation, feature extraction and selection, and classification, and their advantages and disadvantages are discussed.
628 citations
Cites background from "A Model for Radar Images and Its Ap..."
...When CI(t) exists in between the two thresholds, standard Lee and Frost filters are applied....
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...The Lee [36], Kuan [35] and Frost [37] filters are well-known examples of adaptive mean filters....
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...The Frost filter can be represented as R̂(x, y) = ∑ i ∑ j m(x + i, y + j) × I(x + i, y + j) where i and j are the indices of the filter window and m is the weighting function [38]: m(x + i, y + j) = K0 exp[−KC2I (t) √ i2 + j2] where t = (x, y) where K0 is a normalizing constant, and K is a damping factor....
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...It compared wavelet coefficient shrinkage (WCS) filter and several standard speckle filters (Lee, Kuan, Frost, Geometric, Kalman, Gamma, etc.) It calculates the figure of merit (FOM) of the edge map to get a quantitative evaluation of edge preservation and the results show that wavelet domain filters preserve image details better (Table 1)....
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...[38] enhanced the Lee and Frost filters by dividing the image into three classes according to the local coefficient of variation CI(t)....
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References
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TL;DR: The second edition of this respected text considerably expands the original and reflects the tremendous advances made in the discipline since 1968 as discussed by the authors, with a special emphasis on applications to diffraction, imaging, optical data processing, and holography.
Abstract: The second edition of this respected text considerably expands the original and reflects the tremendous advances made in the discipline since 1968. All material has been thoroughly updated and several new sections explore recent progress in important areas, such as wavelength modulation, analog information processing, and holography. Fourier analysis is a ubiquitous tool with applications in diverse areas of physics and engineering. This book explores these applications in the field of optics with a special emphasis on applications to diffraction, imaging, optical data processing, and holography. This book can be used as a textbook to satisfy the needs of several different types of courses, and it is directed toward both engineers ad physicists. By varying the emphasis on different topics and specific applications, the book can be used successfully in a wide range of basic Fourier Optics or Optical Signal Processing courses.
12,159 citations
Book•
01 Jan 1968
TL;DR: The second edition of this respected text considerably expands the original and reflects the tremendous advances made in the discipline since 1968 as discussed by the authors, with a special emphasis on applications to diffraction, imaging, optical data processing, and holography.
Abstract: The second edition of this respected text considerably expands the original and reflects the tremendous advances made in the discipline since 1968. All material has been thoroughly updated and several new sections explore recent progress in important areas, such as wavelength modulation, analog information processing, and holography. Fourier analysis is a ubiquitous tool with applications in diverse areas of physics and engineering. This book explores these applications in the field of optics with a special emphasis on applications to diffraction, imaging, optical data processing, and holography. This book can be used as a textbook to satisfy the needs of several different types of courses, and it is directed toward both engineers ad physicists. By varying the emphasis on different topics and specific applications, the book can be used successfully in a wide range of basic Fourier Optics or Optical Signal Processing courses.
9,800 citations
3,156 citations
TL;DR: Experimental results show that in most cases the techniques developed in this paper are readily adaptable to real-time image processing.
Abstract: Computational techniques involving contrast enhancement and noise filtering on two-dimensional image arrays are developed based on their local mean and variance. These algorithms are nonrecursive and do not require the use of any kind of transform. They share the same characteristics in that each pixel is processed independently. Consequently, this approach has an obvious advantage when used in real-time digital image processing applications and where a parallel processor can be used. For both the additive and multiplicative cases, the a priori mean and variance of each pixel is derived from its local mean and variance. Then, the minimum mean-square error estimator in its simplest form is applied to obtain the noise filtering algorithms. For multiplicative noise a statistical optimal linear approximation is made. Experimental results show that such an assumption yields a very effective filtering algorithm. Examples on images containing 256 × 256 pixels are given. Results show that in most cases the techniques developed in this paper are readily adaptable to real-time image processing.
2,701 citations
"A Model for Radar Images and Its Ap..." refers background in this paper
...Recently , Lee [27] suggested the use of local statistics to adapt image enhancement algorithms for both additive and multiplicative noise....
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...The idea of using local statistics as a basis for spatially varying image enhancement is not new [27] and its advantages, e.g., computational efficiency, are well known....
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TL;DR: In this paper, the distribution of scale sizes in a speckle pattern (i.e., the Wiener spectrum) is investigated from a physical point of view, and it is shown that adding M uncorrelated speckles on an intensity basis can reduce the contrast by 1/√M.
Abstract: A speckle pattern formed in polarized monochromatic light may be regarded as resulting from a classical random walk in the complex plane. The resulting irradiance fluctuations obey negative exponential statistics, with ratio of standard deviation to mean (i.e., contrast) of unity. Reduction of this contrast, or smoothing of the speckle, requires diversity in polarization, space, frequency, or time. Addition of M uncorrelated speckle patterns on an intensity basis can reduce the contrast by 1/√M. However, addition of speckle patterns on a complex amplitude basis provides no reduction of contrast. The distribution of scale sizes in a speckle pattern (i.e., the Wiener spectrum) is investigated from a physical point of view.
2,093 citations
"A Model for Radar Images and Its Ap..." refers background in this paper
...If noncoherent averaging is performed, then the pdf for the power follows a gamma distribution [2], i....
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...Obviously, it is applicable for coherent speckle reduction in general, as the noise processes are similar for all coherent sensors [2] ....
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