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## Palestras pelo Dr. Vladimir Katkovnik

21 Setembro 2007, 17:13 - Pedro Flores Correia

O Dr. Vladimir Katkovnik, Investigador Sénior no Instituto de Processamento de

Sinal da Universidade de Tecnologia, Finlândia, apresentará as seguintes palestras:

-- 24 Set, segunda-feira, 10:00, Complexo Interdisciplinar:

"Novel overcomplete (redundant) representation techniques for image denoising".

Abstract: Overcomplete representations arise naturally when data are processed by overlapping subsets, i.e. windows or blocks, and multiple estimates are obtained for each individual point. Estimation is composed from three successive steps: first data windowing (blocking); second, window-wise processing; and, third, calculation of the final estimate by fusing the multiple window-wise estimates. It is found, that this sort of redundant estimates essentially improves results versus the standard non-redundant transform-thresholding procedures. For example, it is well known that translation-invariant undecimated wavelets are dramatically more effective than the basic fully decimated orthogonal (or biorthogonal) wavelets for denoising by shrinkage. A number of advanced denoising algorithms demonstrating a very good performance have been recently developed (in Institute of Signal Processing, Tampere University of Technology) explicitly based on the over complete filtering in localized transform domain using a data-adaptive weighted average to combine the redundant local estimates. We focus our discussion on two algorithms: the discrete cosine transform (DCT) filtering with the starshaped adaptive neighborhoods found for each estimation point and the matching of the image blocks used for 3D grouping of 2D image data, then processed using the so-called collaborative filtering. In these algorithms we arrive to the multiple windowes estimates fused for calculation of the final estimate for each individual point. We discuss these algorithms in the context of evolution of the ideas and the algorithms from the fixed order point-wise local to adaptive order non-local approximations.

-- 27 Set, quinta feira, 10:00, Anfiteatro VA5, Pavilhão de Civil, Piso -1:

"Noisy phase unwrap for fringe techniques: adaptive local polynomial approximations"

Abstract: We apply the local polynomial approximation (LPA) in order to estimate the absolute phase as the argument of the sine and cosine functions. The LPA is a nonparametric regression technique with pointwise estimation in a sliding window. The adaptive window size is selected as pointwise varying using the intersection of confidence interval LPA algorithm giving the estimates close to the optimal ones in the mean squared sense. For estimate calculation we use a Gauss-Newton recursive procedure initiated by the estimates obtained for the neighboring pixels. This initialization enables tracking properties of the algorithm and its ability to go beyond the principal interval [0,2pi) and reconstruct the absolute phase from the wrapped phase observations. The numerical experiments demonstrate an ability of the algorithm to reconstruct the absolute phase even when the magnitude of the phase difference takes quite large values. The algorithm demonstrates a very good accuracy of the phase reconstruction which on many occasion overcomes the accuracy of the state-of-the-art algorithms developed for unwrap of noisy data.