Multi-resolution techniques, and especially the wavelet transform provide unique benefits in image representation and processing not otherwise possible. While wavelet applications in image compression and denoising have become extremely prevalent, their use in image restoration and super-resolution has not been exploited to the same degree. One issue is the extension 1-D wavelet transforms into 2-D via separable transforms versus the non-separability of typical circular aperture imaging systems. This mismatch leads to performance degradations.; Image restoration, the inverse problem to image formation, is the first major focus of this research.{09}A new multi-resolution transform is presented to improve performance. The transform is called a Radially Symmetric Discrete Wavelet-like Transform (RS-DWT) and is designed based on the non-separable blurring of the typical incoherent circular aperture imaging system. The results using this transform show marked improvement compared to other restoration algorithms both in Mean Square Error and visual appearance. Extensions to the general algorithm that further improve results are discussed.; The ability to super-resolve imagery using wavelet-domain techniques is the second major focus of this research. Super-resolution, the ability to reconstruct object information lost in the imaging process, has been an active research area for many years. Multiple experiments are presented which demonstrate the possibilities and problems associated with super-resolution in the wavelet-domain.{09}Finally, super-resolution in the wavelet domain using Non-Linear Interpolative Vector Quantization is studied and the results of the algorithm are presented and discussed.
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