This thesis has two related goals: the first involves the concept of self-similarity of images. Image self-similarity is important because it forms the basis for many imaging techniques such as non-local means denoising and fractal image coding. Research so far has been focused largely on self-similarity in the pixel domain. That is, examining how well different regions in an image mimic each other. Also, most works so far concerning self-similarity have utilized only the mean squared error (MSE). In this thesis, self-similarity is examined in terms of the pixel and wavelet representations of images. In each of these domains, two ways of measuring similarity are considered: the MSE and a relatively new measurement of image fidelity called the Structural Similarity (SSIM) Index. We show that the MSE and SSIM Index give very different answers to the question of how self-similar images really are. The second goal of this thesis involves non-local image processing. First, a generalization of the well known non-local means denoising algorithm is proposed and examined. The groundwork for this generalization is set by the aforementioned results on image self-similarity with respect to the MSE. This new method is then extended to the wavelet representation of images. Experimental results are given to illustrate the applications of these new ideas.

This thesis has two related goals: the first involves the concept of self-similarity of images. Image self-similarity is important because it forms the basis for many imaging techniques such as non-local means denoising and fractal image coding. Research so far has been focused largely on self-similarity in the pixel domain. That is, examining how well different regions in an image mimic each other. Also, most works so far concerning self-similarity have utilized only the mean squared error (MSE). In this thesis, self-similarity is examined in terms of the pixel and wavelet representations of images. In each of these domains, two ways of measuring similarity are considered: the MSE and a relatively new measurement of image fidelity called the Structural Similarity (SSIM) Index. We show that the MSE and SSIM Index give very different answers to the question of how self-similar images really are. The second goal of this thesis involves non-local image processing. First, a generalization of the well known non-local means denoising algorithm is proposed and examined. The groundwork for this generalization is set by the aforementioned results on image self-similarity with respect to the MSE. This new method is then extended to the wavelet representation of images. Experimental results are given to illustrate the applications of these new ideas.

Darbe nagrinėjamas vienas iš vaizdų kokybės vertinimo metodų (metrikų) – SSIM (struktūrinio panašumo) indekso metodas bei šio metodo naudojimas tiriant didelius vaizdus. Darbo eigoje: • nustatyta kai kurių įgyvendintų SSIM indekso algoritmų problematika, vertinant aukštos raiškos vaizdus; • nustatytos gaunamų skaitinių reikšmių priklausomybės nuo tiriamų vaizdų dydžio; • pagrindžiamas vaizdo duomenų mažinimas SSIM indekso algoritmuose; • pasiūlyti tam tikri sprendimai SSIM indekso algoritmo sudarymui, skirto didelės raiškos vaizdų vertinimui; • palyginti SSIM indekso algoritmų veikimo laikai tarp skirtingų algoritmų; • sukurta programinė įranga, kuri yra pritaikyta Windows operacinei sistemai bei gali būti patogiai įdiegta kompiuteryje. Programoje: – patobulintas SSIM indekso įgyvendinimo algoritmas; – atvaizduojamas SSIM skirtumų žemėlapis; – sukurta patogi vartotojui vizualinė aplinka. Realizuota programinė įranga gali būti naudojama edukaciniais tikslais bei užsakomiesiems apdorotų vaizdų kokybės vertinimo tyrimams. / The paper analyzes one of image quality assessment methods (metrics) – SSIM (structural similarity) index method, and this method in order to analyze the large images. In work process: • problems of some SSIM index algorithms for high-resolution images have been identified; • dependence of image size and SSIM index values has been found; • some solutions for SSIM index algorithm for high-resolution images have been proposed; • the image data down sampling in SSIM index algorithms has justified; • SSIM index algorithm run times between different algorithms has been compared; • Software which is designed for MS Windows operating system and can be easily installed on the computer has been developed. In this software: – SSIM index algorithm is updated; – program Displays the SSIM index map; – User-friendly visual environment is developed. Implemented software can be used for educational purposes and commercial use for analyzing processed image quality assessment.