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In recent years, nonnegative matrix factorization (NMF) methods of a reduced image data representation attracted the attention of computer vision community. These methods are considered as a convenient part-based representation of image data for recognition tasks with occluded objects. A novel modification in NMF recognition tasks is proposed which utilizes the matrix sparseness control introduced by Hoyer. We have analyzed the influence of sparseness on recognition rates (RRs) for various dimensions of subspaces generated for two image databases, ORL face database, and USPS handwritten digit database. We have studied the behavior of four types of distances between a projected unknown image object and feature vectors in NMF subspaces generated for training data. One of these metrics also is a novelty we proposed. In the recognition phase, partial occlusions in the test images have been modeled by putting two randomly large, randomly positioned black rectangles into each test image.

Some issues of the direct Fourier method (DFM) implementation are discussed. A hybrid spline-linear interpolation for the DFM is proposed. The results of comprehensive simulation research are presented. The following reconstruction problems and parameters are emphasized: interpolation, increasing the radial density of the polar raster, filtering, the 2-D inverse Fourier transformation dimension, and considering the cases of noiseless and noisy input data. For the a priori prescribed resolution of the reconstructed image, values of reconstruction parameters have been determined which are optimal with regard to reconstruction quality and computation cost. The computational requirements of the DFM algorithm which correspond to distinct interpolation schemes are compared to one another for CT and MR tomography, respectively. The estimations obtained are compared to computational characteristics of the convolution backprojection method.