2392 IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING, VOL. 40, NO. 11, NOVEMBER 2002 A Review of Speckle Filtering in the Context of Estimation Theory Ridha Touzi, Member, IEEE Abstract—Speckle filter performance depends strongly on the speckle and scene models used as the basis for filter develop- ment. These models implicitly incorporate certain assumptions about speckle, scene, and observed signals. In this study, the multiplicative and the product speckle models, which have been used for the development of most of the well-known filters, are analyzed, and their implicit assumptions with regard to the stationarity–nonstationarity nature of speckle are discussed. This leads to the definition of two categories of speckle filters: the stationary and the nonstationary multiplicative speckle model filters. The various approximate models used for the multiplica- tive speckle noise model are assessed as functions of speckle and scene characteristics to derive the requirements on scene signal variations for the validity of both the stationary and nonstationary multiplicative speckle models. Speckle filtering is then studied in the context of estimation theory, so as to develop a procedure for speckle filtering. It is shown that speckle filtering can be effective only in locally stationary scenes. Regions in which the signals are not stationary have to be filtered separately using a priori scene templates for the best matching of nonstationary scene features. The use of multiresolution techniques is crucial for accurate estimation of filter parameters. Under the guidance of the speckle filtering procedure, structural–multiresolution versions of the Lee and Frost et al. filters are developed for optimum application of these filters in the context of nonstationary scene signals. Index Terms—Edge detection, estimation theory, filtering, mul- tiresolution, nonstationary signal, point target detection, speckle, synthetic aperture radar (SAR), texture. LIST OF SYMBOLS scene complex reflectivity; scene signal intensity ( ); observed intensity; spatial position coordinates; speckle zero-mean complex Gaussian process; normalized speckle noise intensity; prefilter impulse function; filter impulse function; SAR system impulse function ( ); input signal to the SAR system ( ); additive system noise; Dirac function; incoherent image ( ); autocorrelation function; space-averaged autocorrelation function; slowly varying within the system impulse width . Manuscript received April 16, 2002; revised July 14, 2002. The author is with the Canada Centre for Remote Sensing, Natural Resources Canada, Ottawa, ON, Canada K1A OY7 (e-mail: ridha.touzi@ccrs.nrcan.gc.ca). Digital Object Identifier 10.1109/TGRS.2002.803727 I. INTRODUCTION S PECKLE FILTER performance depends strongly on the speckle and scene models used as the basis for filter development. The most well known models, which have been used as the basis for the development of almost all of the existing speckle filters, are the multiplicative and the product speckle models. The multiplicative speckle model served for the development of the minimum mean-square error (MMSE) Lee [16], Kuan et al. [14], and Frost et al. filters [5], whereas the product model was used as the basis for the development of the maximum a posteriori (MAP) Bayesian Gaussian [15], Gamma [24], [32], and model-based despeckling [54] filters. Various expressions have been used for the named “multiplicative speckle model” [5], [14], [16], [39], [52]. All these speckle-scene models implicitly incorporate certain assumptions about speckle, scene, and observed signals, and this strongly influences speckle filtering, as well as scene reconstruction, during the inversion process based on these models [3], [6], [53]. Unfortunately, even though speckle filtering has been active for about 20 years, no detailed analysis of the various speckle-scene models has been published. The distinction between the various multiplicative speckle models, as well as the distinction between the multiplicative speckle model and the product model, is very vague in the related literature (e.g., see [31]). For instance, both models are currently used to represent the multiplicative model [15], [31]. Speckle filtering is generally applied using a moving window of fixed size, and the same conventional size (11 11 for a one-look image and 7 7 for a four-look image [17], [25]) is used with the filters based on the multiplicative or the product model, even though these speckle-scene models incorporate different assumptions on the stationary–nonstationarity nature of speckle and scene signals. Lately, it has been noticed that the Gamma MAP filter [23], [32], which is based on the product model, might introduce a radiometric bias when it is applied on a one-look image with an 11 11 window [31], [40]. Such bias was not obtained with the Lee MMSE filter when it was applied in the same conditions. Recently, the most well known single-stage speckle filters, the refined Lee filter [17] and the Frost et al. [5] filter that have been used for about 20 years, were prematurely rejected in [31]: “Single-stage filters are inadequate for effective speckle- removal; MMSE reconstruction can be rejected because struc- ture is not retained upon iteration” [31, pp. 188, ch. 6]. On the other hand, the Hagg edge-preserving optimized speckle filter [8], which is basically a multiresolution box (average) filter, has been recognized as the best speckle filter [13], [51]. All this leads to a lot of confusion, and users are not able to iden- tify which filter to use in each application nor suitable window 0196-2892/02$17.00 © 2002 IEEE