Statistical Model for Sparse Dictionary Learning
Dictionary learning aims at finding a transform domain on which the training data admits a sparse representation. Most approaches are based on deterministic regularization techniques (e.g., the minimization of L1 norm). We have recently developed a new statistical formulation to learn the dictionary, where the data are modeled as a random vector. The key novelty is to use probabilistic models in line with the sparsity paradigm called symmetric-alpha-stable. The goal of the project is to further extend the mathematics beyond this novel dictionary learning framework. In particular, we aim at formulating the dictionary learning as an optimization problem where the regularization corresponds to a mutual information estimator in the transform domain, under the symmetric-alpha-stable hypotheses. Several extensions shall be investigated in order to increase the applicability of the model on real data.
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