Synthetic Aperture Radar (SAR) images are used in a large number of applications over different fields, such as remote sensing for mapping, surface surveillance, search and rescue, mine detection, automatic target recognition, etc. However, they are affected by a multiplicative speckle process, considered as noise-like, which reduces the radiomet- ric quality and makes difficult the extraction of important information within the image.
4.3. BAYESIANSARIMAGE ANALYSIS 55
The speckle presence in SAR images reduce the detectability of objects in the image and also the capability to separate and classify distributed targets (Oliver and Quegan, 1998). Therefore, the analysis of SAR images involves both despeckling and information ex- traction methods. In the following, the most known speckle filters and how they were improved are explained in section 4.3.1. Later, the feature extraction methods for SAR images, with a special emphasis on methods which are based on stochastic models and their parameters, are presented in section 4.3.2.
4.3.1 SAR despeckling filters
Along the years many methods have been proposed to remove the speckle of SAR im- agery. The main goal of despeckling filters is to remove the speckle with preservation of small details within the image such as: texture, edges, geometry (Fjortoft et al., 2000), (Xiao et al., 2003).
Speckle can be removed by filtering using the multi-looking techniques. Multi-look processing is applied during image formation, and this procedure averages several statis- tically independent looks of the same scene to reduce speckle (Porcello et al., 1976). It is considered as a pre-image formation filter. A major disadvantage of this technique is that the resulting images suffer from a reduction of the ground resolution that is proportional to the number of looks L (Martin and Turner, 1993). Improvement of the radiometric resolution is obtained at the cost of the geometric resolution (De Vries, 1998).
Later many despeckling techniques have been emerged, which perform the despeck- ling after the image formation. This section presents a review of post-image formation despeckling techniques, which are grouped into non-Bayesian (or non-Parametric) and Bayesian (or Parametric) filters.
4.3.1.1 Non-Bayesian despeckling filters
The non-Bayesian or non-parametric filters do not use parameters about the scene to be modeled, they only consider the speckle model and are generally based on local statis- tics, which are computed in sliding windows. This kind of filters uses the Minimum Mean Squared Error (MMSE) as estimator. The adaptive filters, which are based on lo- cal statistics belongs to this category. The most used adaptive filters are described in the following:
1. Adaptive filters
Lee (1980) suggested a method to enhance a digital image and noise filtering by using the local statistics considering additive and multiplicative noise, which follows the Gaussian distribution. This filter uses the sample mean and variance of pixels in a sliding window. In here, the a priori mean and variance of each pixel is derived from its local mean and variance, then it uses the MMSE estimator to obtain the noise filtered image.
An improvement of Lee filter was proposed by (Kuan et al., 1985). Here, the authors presented a generalization of the local statistics of Lee filter using a different algorithm to compute the local variance. The author considered only a multiplicative speckle model and designed a linear filter based on the MMSE criterion that has an optimal performance when both the scene and the detected intensity follow a Gaussian distribution. However, a common characteristics of local statistic filters is that the noise in the edge areas is not
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smoothed. A solution for this problem was proposed by (Lee, 1981). The author intro- duced the Refined MMSE filter known as Refined Lee filter, which gives better results than the original filter presented in (Lee, 1980), at the presences of edges. In order to deal with the common problem of noisy edge boundaries, Lee revised the algorithm using edge directed windows. Eight non-square windows for eight edge orientations are cre- ated within 7 x 7 windows. The local mean and local variance are computed using only those pixels in the edge directed windows and then, the local statistics filter is applied. Later (Frost et al., 1982) introduced the Frost filter, which is based on the local statistics. It models the speckle as multiplicative noise. It differs from the Lee filter in the fact that the scene reflectivity is estimated by convolving the observed image with the impulse response of the SAR system and it averages less over the edged areas to preserve edges.
As conclusion all the adaptive filters operate in spatial domain and they use the MMSE as estimator. Most of them assume that the speckle follows a Gaussian distri- bution, which is not the case of SAR images (Oliver and Quegan, 1998) and most of them model only the speckle noise without considering a model for the reflectivity of the scene (data). In the following, we introduce the Bayesian filters, which take the SAR proper- ties into consideration. These filters enable to use statistical schemes to model the data, thereby, they are considered as advanced speckle filtering techniques (Lopes et al., 1993).
4.3.1.2 Bayesian despeckling filters
The Bayesian or parametric approach is based on models and estimation of model’s pa- rameters, which determine how well the estimated data corresponds to the image data. It enhances local adaptation by using a prior model, which learns the image structure, enabling thus despeckling without resolution loss, whilst estimating local descriptions of the structures. Therefore, this approach is considered as Bayesian approach since it relies on models and parameters to fit the data. An example of this approach is the Gamma-Gamma MAP filter (Lopes et al., 1993), which is based on the Maximum a pos-
teriori (MAP) estimation. The MAP approach has several advantages compared to the
previous filters. In fact, it can simultaneously take into account realistic first and second order statistical models for both speckle and underlying scene reflectivity, and combine them through Bayes’ rule. The Bayesian filters can operate in an original spatial (image) domain or in a frequency domain, using wavelets. They are presented in the following.
1. Bayesian filters operating in the spatial domain
Kuan et al. (1987) were the first to propose the Maximum a posteriori (MAP) approach for filtering SAR images by the assumption that the speckle follows a multiplicative model. This filter is called Gamma-MAP. In here, a prior knowledge of the probability density function of the scene is required and it was assumed to be Gaussian distributed while the speckle was assumed to have a Gamma distributed intensity. Later, in the work of (Lopes et al., 1993, 1990), they modified the Gamma-MAP filter by assuming a Gamma distributed scene and setting up two thresholds, resulting in the Gamma-Gamma MAP filter, which nowadays is one of the most prominent and broadly used despeckling filter. Gamma-Gamma MAP is based on a Bayesian analysis of the statistics considering that both the signal and the speckle noise follow a Gamma distribution. This filter achieved at the same time a good preservation of the textural properties and a good enhancement of the structural features present in the image, as well as a very high degree of speckle
4.3. BAYESIANSARIMAGE ANALYSIS 57
smoothing. Even though the modeling of Gamma-Gamma MAP is more elaborated than the approaches previously presented, the visual impression and quantitative despeck- ling results are similar to Kuan and Lee filters (Medeiros et al., 2003). In fact, it uses a simple data model (Gamma distribution) described by only two parameters (mean and variance). This means that Gamma prior seems not to be sufficient to model a SAR scene. Geman and Geman (1984) introduced the use of Gibbs Random Fields (GRFs) models as prior model of the scene for despeckling SAR images. In here, these filters use stochastic models in order to describe the spatial structures in the images. They encapsulate more information than only mean and variance by using more complex parametric models. For example, the use of Gauss Markov Random Field (GMRF), which belongs to GRFs family was proposed in (Walessa and Datcu, 2000; Walessa, 2001). This filter is based on Bayesian inference, using the Gamma distribution as speckle noise model (likelihood) and the GMRF as prior to represent the knowledge of the scene. GMRF uses a neighbour- hood system around a central pixel in order to give the value of the central analyzed pixel considering its relations with its neighbors. This filter estimates the MAP of the noise-free image through multiplying the likelihood by the prior. Recently, in (Hebar et al., 2009), the authors proposed the use of an Auto-binomial model, which also belongs to GRFs family, as prior model and the Gamma distribution as speckle model. This technique is based on Bayesian inference and MAP estimation. The main advantage of both filters is the fact that they are able to extract information from the SAR image. Both despeckling techniques operate in spatial domain and they are fully described in chapter 5.1.
2. Bayesian filters operating in the frequency domain
It is worth noting that in the last 10 years an important improvement in the field of de- speckling images was given by multi-resolution processing, using wavelets. Wavelets have been recognized as a powerful tool for the analysis of non-stationary signals and images (Mallat, 1989). Wavelet despeckling approaches are based on modifying the (log- transformed) speckle noisy wavelet coefficients according to some rules (shrinkage) and reconstructing the filtered image from them (Achim et al., 2003).
Examples of wavelet based despeckling algorithms were proposed in (Foucher et al., 2001), (Xie et al., 2002), (Dai et al., 2004), (Argenti and Alparone, 2002),(Argenti et al., 2006), (Gleich and Datcu, 2007), (Gleich and Datcu, 2009), etc. The work of (Xie et al., 2002) proposed a despeckling algorithm that fuses Bayesian wavelet denoising with a regularizing prior.
The wavelet-based denoising using un-decimated wavelet transform and MAP estima- tion were performed in (Dai et al., 2004) (Argenti and Alparone, 2002); (Argenti et al., 2006) and (Foucher et al., 2001). Specifically, the work of (Dai et al., 2004) discussed a Bayesian shrinkage which relies on edge information. (Argenti et al., 2006) proposed de- speckling in the undecimated wavelet decomposition and MAP using a space-varying generalized Gaussian distribution for the wavelet coefficients. The solution of the MAP equation yields to the MAP estimate of the wavelet coefficients of the noise-free image. A MAP estimator with an alpha-stable prior within the wavelet framework is proposed in (Achim et al., 2003). Later, an adaptive MAP estimator with a heavy-tailed Rayleigh signal model has been suggested in (Achim et al., 2006). Here, it uses log-transform to convert multiplicative noise to additive noise. The work of (Gleich and Datcu, 2007) proposed a despeckling filter based on the combination of wavelet transform and GMRF. Here, noise in the wavelet domain is modeled as an additive signal-dependent noise
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with Gaussian distribution and the distribution of the noise-free scene is Generalized GMRF (GGMRF). In (Gleich and Datcu, 2009) the denoising of SAR images within the dyadic wavelet domain using a particle filter was introduced. The objective was to model the SAR image statistics and perform denoising and information extraction within the decimated wavelet domain. The dyadic transform is a shift variant; therefore, many authors use stationary or non-decimated wavelet transform, which is a shift invariant. The second-generation wavelets Chirplet (Cui and Wong, 2006), Contourlet (da Cunha et al., 2006), Bandelet (Pennec and Mallat, 2005) have appeared over the past few years. Despeckling using Contourlet transform (da Cunha et al., 2006) and Bandelet (Pennec and Mallat, 2005) transforms show superior despeckling results for SAR images com- pared with the wavelet-based methods (Gleich et al., 2010).
4.3.2 SAR information extraction
Information extraction is an important issue when designing automatic image interpre- tation systems, as it provides intrinsic features in few parameters. After that, a classifier can use these parameters as features for categorizing and indexing the image content. An image is characterized by its primitive features such as color, shape (Jain and Vailaya, 1996), texture (Tuceryan and Jain, 1998). Thus an image will be represented as a multidi- mensional feature vector acting as a signature.
Texture is considered as an important feature in an image since it provides a valu- able clue in identifying homogeneous regions and characteristics in the images. We recognize texture when we see it but it is very difficult to define. In (Tuceryan and Jain, 1998), the authors divided the principal approaches used to describe texture into statisti- cal, geometrical, and model-based. The statistical approaches define texture as a spatial distribution of the gray values and analyze their relations. An example of this approach is the gray level co-occurrence matrix (GLCM) proposed by (Haralick et al., 1973; Har- alick, 1979). Here, the authors used gray level co-occurrence features to analyze remote sense images. They computed GLCM for a distance of one with four directions, using seven classes in the classification problem, they obtained approximately 80 percent clas- sification accuracy using texture features. The work of (Rignot and Kwok, 1990) used texture features computed from GLCM for classifications of SAR images. In addition, despeckling algorithms were used to remove speckle in SAR images in order to improve classification results.
In geometrical approaches, texture is considered to be composed of texture elements or primitives. Then, the methods which follow these approaches are based on the ge- ometrical properties of these texture elements. Analysis according to this paradigm in- cludes extraction of texture elements, their shape analysis, and the estimation of their placement rule. An example of this approach was presented in (Tuceryan and Jain, 1990). Here, the authors proposed the extraction of texture tokens by using the properties of the Voronoi tessellation of a given image.
The model-based approaches assume that the image can be modeled using texture and that the parameters of the texture represent information about the scene. The mod- eled parameters capture the essential qualities of the texture being able to characterize the image content. An example of this approach was presented in (Datcu et al., 1998). Here, the authors aim at characterizing the image-content using stochastic models within a Bayesian framework. In particular, they draw the potential usage of Gibbs Random Fields (GRFs) models for the extraction of spatial information from remote sensing im-
4.4. CONCLUSION 59
ages. The authors demonstrated that it is possible to characterize texture through the estimation of the parameters of the model.
In fact, the most common models used for texture modeling are Markov Random Fields (MRFs) (Hassner and Sklansky, 1980) and GRFs models (Besag, 1974), (Geman and Geman, 1984). The justification for using GRFs for image modeling is given by the Hammersly - Clifford Theorem (Besag, 1974), (Hammersley and Clifford, 1971), which asserts that there is one-to-one correspondence between MRF and GRF. Since any random field can be modeled by a MRF with an enough large neighbourhood system, and any random field can be modeled by a GRF with an enough large clique system (Schr ¨oder, 2000). Since then, many model-based methods have emerged for information extraction based on the GRFs. For example, originally, the auto-binomial model was introduced for information extraction in (Cross and Jain, 1983). Later, in (Schr ¨oder et al., 1998) had highlighted the potential of Gibbs-Markov Random Fields models as a powerful and robust descriptor of spatial information of remote sensing image data. Here, the authors demonstrated the usefulness of GRF for spatial information extraction using both optical and SAR images. Specifically, the authors also introduce the Auto-binomial model (ABM) as major contribution in their work (Schr ¨oder, 2000). Recently, in (Hebar et al., 2009), the authors used the ABM model for information extraction and despeckling simultaneously using SAR images.
Gauss Markov Random Field (GMRF) also belongs to the Gibbs family and consti- tutes a quite simple image model. It is widely used for texture description and segmenta- tion. For example (Chellappa and Chatterjee, 1985) used GMRF for image synthesization proving the generation of texture using this model. In (Derin and Elliott, 1987) GMRF was also used for segmentation. In (Jeng and Woods, 1991), the GMRF model was used to extract information from remote sensing images. The authors consider the MAP and MMSE estimate for both image estimation and image restoration. The work of (Walessa and Datcu, 2000) proposed a method that combines despeckling and feature extraction from remote sensing SAR images using GMRF.
As a conclusion of this review we remark that the methods, which perform despeck- ling and information extraction from SAR images (e.g. (Walessa and Datcu, 2000) and (Hebar et al., 2009) cover a quite complete analysis of SAR images. These methods are involved in the data-driven evaluation approach of this thesis. Their workflows are fully discussed in section 5.1.