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The contributions in this thesis are: (1) a fast, approximate minimum mean-squared error (MMSE) estimation algorithm for sparse signal reconstruction, called Randomized Iterative Hard Thresholding (RIHT).This algorithm has applications in compressed sensing, image denoising, and other sparse inverse problems.
In particular, three new image denoising methods are proposed: context-based wavelet thresholding, predictive fractal image denoising and fractal-wavelet image denoising.
The proposed context-based thresholding strategy adopts localized hard and soft thresholding operators which take in consideration the content of an immediate neighborhood of a wavelet coefficient before thresholding it.
The need for image enhancement and restoration is encountered in many practical applications.
For instance, distortion due to additive white Gaussian noise (AWGN) can be caused by poor quality image acquisition, images observed in a noisy environment or noise inherent in communication channels. After reviewing standard image denoising methods as applied in the spatial, frequency and wavelet domains of the noisy image, the thesis embarks on the endeavor of developing and experimenting with new image denoising methods based on fractal and wavelet transforms.
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Image Denoising Thesis