Ivaniuk N. Image restoration by conventional deconvolution method in Hadamard transformation basis

Restoration problem of one- and two-dimensional images in RTF and Hadamard transformation bases is solved in this dissertation. (RTF transformation is a "copy" of difference methods). The use of these bases lead to improvement of restored images quality compared to restored images in Fourier transformation basis and in natural coordinates. It can be achieved with the same cost of memory, number of arithmetic operations compared to restoration in Fourier transformation basis and the significant increase of operation compared to restoration speed in natural coordinates. The transition algorithms of information representation from Fourier to RTF transformation field is developed to use RTF transformation basis. Image restoration by conventional deconvolution method in Hadamard transformation base should also be seen as an extension of using the mathematical apparatus of multiple transformations. The comparing of restoration results is held. It gives better quality of restored signal in RTF transformation basis compared with quality of restored signal in Fourier transformation basis in most cases. In contrast to Fourier transformation base solving the conventional deconvolution problem in Hadamard transformation base is more responsive for signals with discontinuities of the first kind because of Hadamard functions nature. The method of forming the coefficients of the impulse response of the system counts is developed in this work. Impulse response of the system distorts the original image irrespective of its samples quantity. The inverse degradation matrix of image is found using symbolic algorithm of matrix operators forming with any order. Therefore, the main problem of algorithm realization is solved in Hadamard basis. The symbolic algorithm of matrix operators forming for estimation the restoration signal spectrum is developed to increase the operation speed and to improve the calculation accuracy by the transition from the natural coordinates to Hadamard transformation basis. It is achieved by exclusion of many additions and subtractions of identical values. This method becomes competitive (for speed) with conventional deconvolution method in the Fourier transformation basis because of using the proposed method of inverse degradation matrix forming. The developed modifications of conventional deconvolution method in Hadamard transformation base for one- and two-dimensional images restoration is realized in software environment. The results confirm the conclusions of quality and signal / noise ratio improvement of one- and two-dimensional images restoration in Hadamard transformation base compared with Fourier transformation base.