Dictionary Learning Algorithms and Applications

Abstract

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Aiding Dictionary Learning Through Multi-Parametric Sparse Representation

“…Our model is a good fit for online representation scenarios which is why we plan on investigating in the future its adaptation to online dictionary learning [25], where the dictionary is also updated with each new signal that is sparsely represented. Existing methods have shown that the dictionary update problem can be reduced to a simple rank-1 update D ← D + Γ ( [15], Chapter 5) and we are currently working on changing Γ in order to exploit the existing multi-parametric model of the existing dictionary.…”

On learning with shift-invariant structures

“…Dictionary learning [33] provides heuristics that approximate solutions to the following problem: given a dataset Y ∈ R n×N , a sparsity level s and the size of the dictionary S we want to create a dictionary D ∈ R n×S and the sparse representations X ∈ R S×N then solve…”

Adaptive-Size Dictionary Learning Using Information Theoretic Criteria

“…If n ITC is much smaller than the current n, we decrease the size by δ − (this number is 5 in our experiments); if n ITC is only slightly smaller, than we decrease the size by one; finally, we interpret n ITC = n as a sign that the size needs to be increased and add δ + atoms to the dictionary (we take δ + = 5). There are several methods for generating new atoms [3] (Section 3.9); we choose the simplest: random atoms.…”

“…Dictionary learning (DL) is now a mature field [1][2][3], with several efficient algorithms for solving the basic problem or its variants and with numerous applications in image processing (denoising and inpainting), classification, compressed sensing and others. The basic DL problem is: given N training signals gathered as the columns of the matrix Y ∈ R m×N and the sparsity level s, find the dictionary D ∈ R m×n by solving min…”