Sparse Modeling with Universal Priors and Learned Incoherent Dictionaries(PREPRINT)

Abstract

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Learning Incoherent Dictionaries for Sparse Approximation Using Iterative Projections and Rotations

“…Our main contributions are that we employ this technique within the context of incoherent dictionary learning, as explained in Section III, and adapt it to the approximation objective through a novel rotation step. Section IV presents numerical experiments on musical audio data, and a comparison with the methods previously proposed in [19], [26]. Section V contains our conclusions and plans for further investigation.…”

“…Method of optimal coherence-constrained directions (MOCOD) Ramirez et al [26] proposed a dictionary learning algorithm inspired by the method of optimal directions (MOD) [13] in which the sparse approximation is performed using a novel penalty term derived from a probabilistic formulation of the sparse model (1), and the dictionary update step is modified in order to promote mutually incoherent atoms.…”

Universal Priors for Sparse Modeling(PREPRINT)

“…The third term was introduced in a related work [21] to encourage low mutual coherence and Gram matrix norm of D, properties which are known to have a direct impact on the speed of sparse coding algorithms such as Iterative Shrinkage [8], and on the success of sparse coding formulations in recovering the correct sparse solutions [10], [23]. The last term in (6) is just a normalization one.…”

“…The DU step is done using a Newton-like iteration similar to the one used in [12]. See [21] for details.…”

“…It can also be observed that using the RMC dictionary consistently improves the results in all cases. Again, we refer the reader to [21] for details on this line of research.…”