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The reduction of multiplicative speckle noise which always complicates the human and automatic interpretation of objects is very significant for the practical applications of synthetic aperture radar (SAR) image. In this paper, a new maximum a posteriori (MAP) despeckling method based on directionlet transform is proposed. To convert the multiplicative noise into an additive one, the logarithmic transform is first applied to the SAR images. Then, the directionlet coefficients of the noise-free (or underlying backscatter) image and of the speckle noise are modeled as Laplace mixture distribution with zero-mean and Gaussian distribution, respectively. Within Bayesian framework, a MAP estimator is constructed using these assumed prior distributions. After obtaining the parameter estimates using expectation–maximization algorithm, the noise-free coefficients are estimated by a non-linear shrinkage function based on the average version of Bayesian estimator. To improve the denoising performance, we combine the intra-scale dependency in terms of mutual information with the MAP estimator to refine the estimated results. Finally, we compare the proposed algorithm with several other speckle filters applied on synthetic and actual SAR images. Experimental results show that the proposed method outperforms other filters in terms of signal-to-noise ratio, edge preservation and equivalent number of looks measures in most cases. [ABSTRACT FROM AUTHOR]

A novel method based on directionlet transform is proposed for image denoising under Bayesian framework. In order to achieve noise removal, the directionlet coefficients of the uncorrupted image are modeled independently and identically by a two-state Laplacian mixture model with zero mean. The expectation-maximization algorithm is used to estimate the parameters that characterize the assumed prior model. Within the framework of Bayesian theory, the directionlet coefficients of noise-free image are estimated by a nonlinear shrinkage function based on weighted average of the minimum mean square error estimator. We demonstrate through simulations with images contaminated by additive white Gaussian noise that the proposed method is very competitive when compared with other methods in terms of both peak signal-to-noise ratio and visual quality. [ABSTRACT FROM AUTHOR]

Abstract: A novel image denoising algorithm using linear Bayesian maximum a posteriori (MAP) estimation based on sparse representation model is proposed. Starting from constructing prior probability distribution in representation vector, a linear Bayesian MAP estimator is constructed in order to acquire the most probable one behind the observations, which is adaptive to solve the generalized image inverse problems. Furthermore, a practical closed-form solution by affording some plausible approximations is obtained, and thus image denoising as a specialization can be easily solved. With our new method, we first extract all possible patches from noisy images and classify them to several sub-groups by their structural patterns, then train a different dictionary per each using the K-SVD algorithm, following by estimating corresponding parameters in MAP estimator. The final denoised image is obtained by applying denoising on each sub-group based on the estimator and averaging these outputs together. Simulated results show that the proposed method achieves a very competitive performance both in subjective visual quality and objective PSNR value, compared with other state-of-the-art denoising algorithms. [Copyright &y& Elsevier]