Bir boyutlu ve iki boyutlu sinyallerin polinom uyumu ve toplam değişime dayalı gürültü bastırma teknikleri

New techniques are developed for signal denoising and texture recovery. Geometricaltheory of total variation (TV) is explored, and an algorithm that usesquadratic programming is introduced for total variation reduction. To minimizethe staircase effect associated with commonly used total variation basedtechniques, robust algorithms are proposed for accurate localization of transitionboundaries. For this boundary detection problem, three techniques are proposed.In the first method, the 1?D total variation is applied in first derivative domain.This technique is based on the fact that total variation forms piecewise constantparts and the constant parts in the derivative domain corresponds to lines intime domain. The boundaries of these constant parts are used as the transitionboundaries for the line fitting. In the second technique proposed for boundarydetection, a wavelet based technique is proposed. Since the mother wavelet canbe used to detect local abrupt changes, the Haar wavelet function is used for thepurpose of boundary detection. Convolution of a signal or its derivative familywith this Haar mother wavelet gives responses at the edge locations, attaining local maxima. A basic local maximization technique is used to find the boundarylocations. The last technique proposed for boundary detection is the wellknown Particle Swarm Optimization (PSO). The locations of the boundaries arerandomly perturbed yielding an error for each set of boundaries. Pursuing thepersonal and global best positions, the boundary locations converge to a set ofboundaries. In all of the techniques, polynomial fitting is applied to the part ofthe signal between the edges.A more complicated scenario for 1?D signal denoising is texture recovery. Inthe technique proposed in this thesis, the periodicity of the texture is exploited.Periodic and non-periodic parts are distinguished by examining total variationof the autocorrelation of the signal. In the periodic parts, the period size wasfound by PSO evolution. All the periods were averaged to remove the noise, andthe final signal was synthesized.For the purpose of image denoising, optimum one dimensional total variationminimization is carried to two dimensions by Radon transform and slicingmethod. In the proposed techniques, the stopping criterion for the procedures ischosen as the error norm. The processes are stopped when the residual norm iscomparable to noise standard deviation. 1?D and 2?D noise statistics estimationmethods based on Maximum Likelihood Estimation (MLE) are presented.The proposed denoising techniques are compared with principal curve projectiontechnique, total variation by Rudin et al, total variation by Willsky et al, andcurvelets. The simulations show that our techniques outperform these widelyused techniques in the literature.