SONAR Images Denoising

International audienc

A New SURE Approach to Image Denoising: Interscale Orthonormal Wavelet Thresholding

This paper introduces a new approach to orthonormal wavelet image denoising. Instead of postulating a statistical model for the wavelet coefficients, we directly parametrize the denoising process as a sum of elementary nonlinear processes with unknown weights. We then minimize an estimate of the mean square error between the clean image and the denoised one. The key point is that we have at our disposal a very accurate, statistically unbiased, MSE estimate—Stein's unbiased risk estimate—that depends on the noisy image alone, not on the clean one. Like the MSE, this estimate is quadratic in the unknown weights, and its minimization amounts to solving a linear system of equations. The existence of this a priori estimate makes it unnecessary to devise a specific statistical model for the wavelet coefficients. Instead, and contrary to the custom in the literature, these coefficients are not considered random anymore. We describe an interscale orthonormal wavelet thresholding algorithm based on this new approach and show its near-optimal performance—both regarding quality and CPU requirement—by comparing with the results of three state-of-the-art nonredundant denoising algorithms on a large set of test images. An interesting fallout of this study is the development of a new, group-delay-based, parent-child prediction in a wavelet dyadic tree

A CURE for noisy magnetic resonance images: Chi-square unbiased risk estimation

In this article we derive an unbiased expression for the expected mean-squared error associated with continuously differentiable estimators of the noncentrality parameter of a chi-square random variable. We then consider the task of denoising squared-magnitude magnetic resonance image data, which are well modeled as independent noncentral chi-square random variables on two degrees of freedom. We consider two broad classes of linearly parameterized shrinkage estimators that can be optimized using our risk estimate, one in the general context of undecimated filterbank transforms, and another in the specific case of the unnormalized Haar wavelet transform. The resultant algorithms are computationally tractable and improve upon state-of-the-art methods for both simulated and actual magnetic resonance image data.Comment: 30 double-spaced pages, 11 figures; submitted for publicatio

HYPERSPECTRAL IMAGE DENOISING USING MULTIPLE LINEAR REGRESSION AND BIVARIATE SHRINKAGE WITH 2-D DUAL-TREE COMPLEX WAVELET IN THE SPECTRAL DERIVATIVE DOMAIN

In this paper, a new denoising method is proposed for hyperspectral remote sensing images, and tested on both the simulated and the real-life datacubes. Predicted datacube of the hyperspectral images is calculated by multiple linear regression in the spectral domain based on the strong spectral correlation of the useful signal and the inter-band uncorrelation of the random noise terms in hyperspectral images. A two dimensional dual-tree complex wavelet transform is performed in the spectral derivative domain, where the noise level is elevated temporarily to avoid signal deformation during the wavelet denoising, and then the bivariate shrinkage is used to shrink the wavelet coefficients. Simulated experimental results demonstrate that the proposed method obtains better results than the other denoising methods proposed in the reference, improves the signal to noise ratio up to 0.5dB to 10dB. The real-life data experiment shows that the proposed method is valid and effective