An Adaptive Rayleigh-Laplacian Based MAP Estimation Technique for Despeckling SAR Images using Stationary Wavelet Transform

An Adaptive Rayleigh-Laplacian Based MAP Estimation Technique for Despeckling SAR Images using Stationary Wavelet Transform

Amlan Jyoti Das (Department of Electronics and Communication Engineering, Gauhati University, Guwahati, Assam, India), Anjan Kumar Talukdar (Department of Electronics and Communication Engineering, Gauhati University, Guwahati, Assam, India) and Kandarpa Kumar Sarma (Department of Electronics and Communication Technology, Gauhati University, Guwahati, Assam, India)
Copyright: © 2013 |Pages: 15
DOI: 10.4018/ijaec.2013100106
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Abstract

Removal of speckle noise from Synthetic Aperture Radar (SAR) images is an important step before performing any image processing operations on these images. This paper presents a novel Stationary Wavelet Transform (SWT) based technique for the purpose of removing the speckle noise from the SAR returns. Maximum a posteriori probability (MAP) condition which uses a prior knowledge is used to estimate the noise free wavelet coefficients. The proposed MAP estimator is designed for this purpose which uses Rayleigh distribution for modeling the speckle noise and Laplacian distribution for modeling the statistics of the noise free wavelet coefficients. The parameters required for MAP estimator is determined by technique used for parameter estimation after SWT. Moreover an Laplacian – Gaussian based MAP estimator is also applied and the parameter estimation is done using the same method used for the proposed algorithm. For the purpose of enhancing the visual quality and to restore more edge information, a wavelet based resolution enhancement technique is also used after applying the Inverse stationary Wavelet Transform (ISWT), using interpolation technique. The experimental results show that the proposed despeckling algorithm efficiently removes speckle noise from the SAR images and restores the edge information as well.
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1. Introduction

Synthetic aperture radar (SAR) is a system operating under all weather conditions, night and day, and it provides us useful information in many applications allowing the acquisition of high resolution images of different places on the earth. These SAR images are corrupted by special kind of noise known as speckle noise. SAR imaging systems use long range propagation characteristics of radar signals and provide us high resolution high contrast images of the topographic features by using the backscattered signals generated by reflection, scattering, refraction or absorption. Brighter areas are produced by strong radar backscattered signals and darker areas are produced by weak signals. The strength of the backscattering signals is greatly dependent on wavelength, polarization, incidence angle of the radar signal and orientation. The phases of these backscattered signals are randomly distributed and cause interference. Due to this interference, the SAR images are heavily affected by the signal dependent speckle noise. Its granular appearance in an SAR image makes it very difficult to visualize the SAR data. Therefore, in many SAR image processing operations like segmentation, speckle filtering is a crucial preprocessing step (Xie, Pierce & Ulaby, 2002). Many denoising algorithms have been developed for despeckling SAR images by using the Lee filter (Lee, 1981), the Frost filter (Frost, Stiles, Shanmugan & Holtzman, 1980), LG-MAP filter (Argenti, Bianchi, Lapini & Alparone, 2012), the Gamma MAP filter (Lopes, Nezry, Touzi & Laur, 1990), and their variations (Lopes, Touzi & Nezry, 1990; Oliver & Quegan, 1988). These filters usually exhibit well in despeckling the SAR images. However, they lack in restoring sharp edge features and details of the original SAR image (Gagnon & Jouan, 1997).

Due to the multiplicative nature of the SAR images, many wavelet-based despeckling algorithms apply the log-transform to SAR images to statistically convert the multiplicative noise to additive noise prior to applying further denoising technique (Gagnon & Jouan, 1997; Guo, Odegard, Lang, Gopinath, Selesnick & Burrus, 1994). An exponential operation is applied to convert the log-transformed images back to the nonlogarithmic format after wavelet denoising (Guo, Odegard, Lang, Gopinath, Selesnick & Burrus, 1994).

Several solutions have been proposed in the recent years, based on maximum a posteriori probability (MAP) criteria and different distributions: the gamma distribution (Solbo & Eltoft, 2004), the α-stable distribution (Achim, Tsakalides & Bezerianos, 2003), the Pearson system of distributions (Foucher, Benie & Boucher, 2001), and the generalized Gaussian (GG) (Argenti, Bianchi & Alparone, 2006), Laplacian and Gaussian distribution (Argenti, Bianchi, Lapini & Alparone, 2012) etc. MAP estimator generates a posterior probability by using a prior, likelihood and evidence probability density functions (pdf). The MAP estimate finds a solution for a noise-free image. The speckle noise pdf is approximated by a likelihood pdf of a prior which determines the knowledge of the scene and the best model can be evaluated by maximizing the evidence pdf.

A MAP criterion is derived by Argenti, Bianchi, Lapini and Alparone (2012) by considering Gaussian distribution for modelling speckle noise and Laplacian distribution for modelling noise free wavelet coefficients. The noise-free image was approximated by a Gauss-Markov random field prior and the speckle noise was modelled using Gamma pdf by Walessa and Datcu (2000).

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