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The authors propose a variance-component probabilistic model for sparse signal reconstruction and model selection. The measurements follow an underdetermined linear model, where the unknown regression vector (signal) is sparse or approximately sparse and noise covariance matrix is known up to a constant. The signal is composed of two disjoint parts: a part with significant signal elements and the complementary part with insignificant signal elements that have zero or small values. They assign distinct variance components to the candidates for the significant signal elements and a single variance component to the rest of the signal; consequently, the dimension of their model's parameter space is proportional to the assumed sparsity level of the signal.
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