Doctor of Philosophy (Ph.D.)
Stephen K Park
Digital image restoration is a fundamental image processing problem with underlying physical motivations. A digital imaging system is unable to generate a continuum of ideal pointwise measurements of the input scene. Instead, the acquired digital image is an array of measured values. Generally, algorithms can be developed to remove a significant part of the error associated with these measure image values provided a proper model of the image acquisition system is used as the basis for the algorithm development. The continuous/discrete/continuous (C/D/C) model has proven to be a better alternative compared to the relatively incomplete image acquisition models commonly used in image restoration. Because it is more comprehensive, the C/D/C model offers a basis for developing significantly better restoration filters. The C/D/C model uses Fourier domain techniques to account for system blur at the image formation level, for the potentially important effects of aliasing, for additive noise and for blur at the image reconstruction level.;This dissertation develops a wavelet-based representation for the C/D/C model, including a theoretical treatment of convolution and sampling. This wavelet-based C/D/C model representation is used to formulate the image restoration problem as a generalized least squares problem. The use of wavelets discretizes the image acquisition kernel, and in this way the image restoration problem is also discrete. The generalized least squares problem is solved using the singular value decomposition. Because image restoration is only meaningful in the presence of noise, restoration solutions must deal with the issue of noise amplification. In this dissertation the treatment of noise is addressed with a restoration parameter related to the singular values of the discrete image acquisition kernel. The restoration procedure is assessed using simulated scenes and real scenes with various degrees of smoothness, in the presence of noise. All these scenes are restoration-challenging because they have a considerable amount of spatial detail at small scale. An empirical procedure that provides a good initial guess of the restoration parameter is devised.
© The Author
Sandor, Viviana, "Wavelet-based digital image restoration" (1998). Dissertations, Theses, and Masters Projects. Paper 1539623937.