Image De-Quantizing via Enforcing Sparseness in Overcomplete Representations

Artificial Intelligence

“…To compare greedy heuristics, we have implemented StOMP [23] and the method we presented in [24], called here DT+OP (from Direct Thresholding plus Least Squares-Optimisation). To choose the threshold used by StOMP, we previously set how many coefficients will be selected at each iteration.…”

“…In a previous work to this Thesis [24], we presented a method for removing spatial quantization artifacts through finding a sparse approximation to the observation. The resulting method selects the significant coefficients via direct thresholding the amplitudes of vector a LS , which can be also seen as a greedy strategy.…”

“…Next question is: Do these methods offer equally good solutions? In this section we review some surprising results proving that, under certain conditions, both greedy methods (OMP) 24 The Sparse Approximation Problem and convex relaxation methods reach the global optimum to the sparse representation problem, and provide a solution with an error proportional to the level of noise when dealing with the sparse approximation problem.…”

“…As our final target is to solve the sparse approximation problem of Equation (2.4), we should use some method in order to improve the quality of the approximation for a given set of selected functions. We use here a method based on alternating projections which has been previously used by a number of authors, as [11,13,24,32,96].…”

“…The main problem of these techniques is that, being very inefficient, they often get trapped in non-favourable local minima in terms of energy compaction. There are other greedy techniques based on different selection strategies, as [24], where, in a previous work to this Thesis, we selected the significant coefficients by directly thresholding the observed representation vector.…”