Image Denoising using Sparse and over complete representations

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An image is corrupted by noise during its acquisition, transmission or storage. Noise degrades the image quality and interpretability. The aim of image denoising is to remove the distortion resulted by the noise while keeping the detail features in the image intact. The sparse denoising methods represent a class of denoising algorithms based on the principle that a natural signal like the image is sparse over some basis set but the noise is not. This has led to the widespread application of these methods in image denoising. Recent works in the literature focus on the use of sparse and overcomplete representations to develop state-of-the-art image denoising techniques. The thesis addresses the problem of image denoising by the sparse and overcomplete representations. One of the recent additions to the greedy solution to the sparse representation problem is the Bayesian Pursuit Algorithm (BPA). The thesis critically examines the algorithm and proposes a modiDcation by integrating a new initialization scheme and a stopping criterion to enhance its per- formance. The modiDed BPA converges to the true solution much faster than the standard BPA. It is also applied for the removal of additive white Gaussian noise from gray-scale images. Experimental results demonstrate that the modiDed BPA successfully removes the noise at low noise levels. The thesis proposes two sparse denoising techniques based on the overcomplete dictionary for the removal of the impulse noise and the speckle noise. The novel sparse reconstruction Dlter is proposed for the removal of the impulse noise based on the principle of signal recovery by compressed sensing. The impulse-free pixels in the image are identiDed by an impulse detection algorithm and are used to reconstruct the noisy pixels using the orthogonal matching pursuit (OMP) algorithm with an overcomplete dictionary. The Dlter performs better than selected state-of-the-art impulse denoising Dlters. The thesis explores removal of the speckle noise from medical ultrasound images using the sparse representation on an overcomplete dictionary. Many of the denoising algorithms including the ones based on the sparse representation of the signal require the noise to be additive, white and Gaussian. However, this assumption fails for speckle in the medical ultrasound images in the log-transform domain. The thesis adopts an existing technique for the decorrelation and the Gaussianization of the speckle in the log-transform domain and the resulting image is denoised by using sparse and overcomplete representations. Two denoising methods are applied on the preprocessed ultrasound images in the log-transform domain. They are: (1) the undecimated wavelet transform (UDWT) based soft thresholding and (2) the OMP-based sparse representation. Both the methods show improvements over the existing techniques for despeckling of medical ultrasound images...
Supervisor: P. K. Bora