A novel Bayesian image despeckling method using 2D CGARCH-M model in 2D dost framework

Abstract

Image denoising is a crucial task in the field of image processing, and Bayesian estimation has emerged as a prominent approach. To effectively employ Bayesian estimation, it is essential to assume a priori distribution corresponding to the transform coefficients of the noise-free image. In this paper, we propose a novel Bayesian image despeckling method that leverages the 2D Complex Generalized Autoregressive Conditional Heteroscedasticity Mixture (CGARCH-M) model within the framework of the 2D Discrete Orthonormal Stockwell Transform (DOST). Prior to introducing this method, we present a novel statistical analysis of the 2D DOST coefficients of log-transformed images. Speckle noise, commonly found in synthetic aperture radar (SAR) images, is modeled as multiplicative noise. To effectively suppress speckle noise, our proposed method utilizes a novel adaptive Bayes risk estimator known as compound maximum a posteriori (CMAP). By employing CMAP, we estimate the noise-free 2D DOST coefficients from the noisy ones, which are modeled using the 2D CGARCH-M. Notably, this paper introduces the 2D CGARCH-M model for 2D complex stochastic processes for the first time, extending the capabilities of the GARCH model and its subsequent extensions that were limited to real-valued processes. The proposed model incorporates location-dependent conditional variances to capture the non-Gaussian statistics of 2D DOST coefficients of log-transformed images and the dependencies between them. Through our statistical analysis, we establish the compatibility between the 2D CGARCH-M model and these coefficients. Our proposed method takes into account both magnitude and phase by utilizing the real and imaginary components of the DOST coefficients concurrently. It provides an optimal and closed-form solution, significantly reducing memory and computational requirements. Moreover, unlike state-of-the-art approaches in this domain, our method exhibits robustness to initial parameter settings. To evaluate the effectiveness of our approach, we conduct comparisons with other denoising methods on artificially speckled aerial images and actual SAR images. The results demonstrate the superior performance of our method.