In this thesis we are interested in the topic of sparse digital image representation through adaptive multiscale basis. We develop for this two numerical methods: the Region Based Easy Path Wavelet Transform and the Haardict. The first method finds paths in regions of a segmented image and applies to these a wavelet transform. The second method uses a clustering procedure and the associated binary tree to define atoms for the dictionary learning problem which have the same structure as the wavelet coefficients of the classical Haar transform for one-dimensional signals. Both methods are analyzed in detail and numerical experiments proving their viability are discussed.
Keywords: multiscale adaptive basis; clustering; wavelet transform; image segmentation; region of interest; dictionary learning
