Abstract

This thesis is concerned with image restoration techniques using adaptively regularized constrained total least squares (ARCTLS) and wavelet transforms. The objective of the thesis is to improve the conventional ARCTLS algorithm by exploiting the subband properties of both the degraded image and the point spread function (PSF) of the degradation system. First of all, two most frequently used restoration algorithms, namely, the regularized constrained total least squares (RCTLS) and its adaptive version (ARCTLS) are investigated. The solutions of the two techniques in the DFT domain are emphasized in order to reduce the computational complexity. It is shown that both techniques are very suitable for the degradation situation where the (PSF) and the observed degraded image are subject to the same type of error. Secondly, a wavelet-domain image restoration technique using ARCTLS is presented. The 1-D and 2-D wavelet transform matrix representations are formulated for both the degraded image and the degradation convolution operator. A class of orthonormal wavelet based quadrature mirror filter bank is investigated and applied to the subband decomposition of the degraded image and the PSF as well such that the conventional ARCTLS algorithm can be employed for each subband image restoration.