The inherent speckle noise in synthetic aperture radar (SAR) images severely degrades the image interpretation and affects the follow-up image-processing tasks. Thus, speckle suppression is a critical step in SAR image preprocessing. We propose a novel locally adaptive speckle reduction algorithm based on Bayesian maximum a posteriori (MAP) estimation in wavelet domain. First, the presented method performs logarithmical transform to original speckled SAR image and an undecimated wavelet transform (UWT). The Rayleigh distribution is used to model the statistics of the speckle wavelet coefficients, and the Laplacian distribution models the statistics of wavelet coefficients due to signal. A Bayesian estimator with a closed-form solution is derived from MAP criterion estimation, and the resulting formula is proved to be equivalent to soft thresholding in nature, which makes our algorithm very simple. Furthermore, the parameters of the Laplacian model are estimated from the coefficients in a neighboring window, thus making the presented method spatially adaptive in the wavelet domain. Theoretical analysis and simulation experiment results show that the proposed method is simple and effective. It significantly improves the visual quality of the SAR images and yields better performance than spatial filterings and traditional wavelet despeckling algorithms.
In this paper, a novel spatially adaptive wavelet thresholding method based on Bayesian maximum a posteriori (MAP)
criterion is proposed for speckle removal in medical ultrasound (US) images. The method firstly performs logarithmical
transform to original speckled ultrasound image, followed by redundant wavelet transform. The proposed method uses
the Rayleigh distribution for speckle wavelet coefficients and Laplacian distribution for modeling the statistics of
wavelet coefficients due to signal. A Bayesian estimator with analytical formula is derived from MAP estimation, and
the resulting formula is proven to be equivalent to soft thresholding in nature which makes the algorithm very simple. In
order to exploit the correlation among wavelet coefficients, the parameters of Laplacian model are assumed to be
spatially correlated and can be computed from the coefficients in a neighboring window, thus making our method
spatially adaptive in wavelet domain. Theoretical analysis and simulation experiment results show that this proposed
method can effectively suppress speckle noise in medical US images while preserving as much as possible important
signal features and details.
Among the variety of approaches proposed in literature, we can clearly distinguish the Wiener filter and the wavelet transform based ones for their effectiveness and, in many cases, simplicity. By exploiting the characteristics of both wavelet thresholding denoising and spatial Wiener filtering, the paper presents a combined scheme for the noise removal in images. We first perform thresholding denoising in wavelet domain to obtain a pre-denoised image, then spatial adaptive Wiener filter, i.e. Lee filtering, is used to increase the quality of the image restored. The crux of our method lies in the simple yet effective estimation of the optimal noise variance for Lee filter. By numerical computation, this optimal noise variance of Lee filter is presented which can nearly minimize the mean square error (MSE) of the pre-denoised image. Experiment results show that mean square error and signal-to-noise ratio (SNR) of our combined denoising approach have been improved, compared with the denoising solely in wavelet or spatial domain.
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