Sparse image approximation

Abstract

This thesis addresses the problem associated with the approximation of signals as linear superposition of elementary components often called 'atoms'. `After highlighting the limitations of using only orthogonal elements, approximation technique is extended to consider the selection of atoms from a large redundant set, called a `dictionary'. In particular, a highly correlated `mixed dictionary' is considered, from which the atoms are selected through highly non-linear techniques known as Matching Pursuit Strategies. These techniques evolve by stepwise selection of dictionary atoms. In particular, a relatively new strategy named Block wise Orthogonal Matching Pursuit is considered. This technique operates on images divided into blocks and extends the stepwise selection of dictionary atoms to also select the blocks be approximated at each iteration step. The implementation of block selection introduces extra requirements, which has motivated the Macro Processing Scheme proposed in this thesis. The project also focuses on effectiveness of the approach with regards to processing time. In this respect, a C++ implementation of the Block wise Orthogonal Matching Pursuit technique has been developed to operate in MATLAB environment. Using the developed tools a number of comparative tests, with respect to sparse image representation, have been performed and analysed.