Sparse Grouping and Invariant Representations for Estimation and Recognition

This thesis develops several contributions for signal and image processing as well as for computer vision. The first part includes a new audio denoising algorithm and a superresolution algorithm for image zooming. These algorithms are based on some new sparse representations by blocks. A time-frequency block thresholding procedure is introduced for the audio denoising, which enables noise reduction without introducing artifacts, with the results superior to the state-of-the-art. This first part also develops a general approach to solve inverse problems with some piecewise linear sparser representations over the blocks. The application to the image super-resolution allows obtaining a fast algorithm, which clearly improves the PSNR relatively to the existing algorithms. The second part of the thesis introduces an algorithm (ASIFT) of establishing correspondences between images, which is invariant to affine transforms. It is demonstrated that this algorithm satisfies the invariance constraints and it is able to make correspondences between objects observed under arbitrary angles. Its numeric complexity is of the same order as the most efficient algorithms, with a significantly higher robustness thanks to its affine invariance. The third part of the thesis introduces a biologically plausible implementation of visual grouping. Inspired by the mechanism of neural synchronization in perceptual grouping, a general algorithm based on neural oscillators is proposed to make visual grouping. The same algorithm is shown to achieve promising results on several classical visual grouping problems, including point clustering, contour integration, and image segmentation.