Abstract
Sparsity regularization selects solutions with the minimum number of nonzero model parameters. In compressive sensing, sparsity regularization is applied in association with a change of basis, where the basis is chosen so that the desired model will be sparse, in the sense of having only a few nonzero coefficients in the model expansion. The Iterative Soft Threshholding (ISTA) and Fast Iterative Soft Threshholding (FISTA) algorithms are introduced. Total variation regularization uses a regularization term based on the 1-norm of the model gradient. Resulting models allow for discontinuous jumps so that solutions are biased towards piecewise-constant functions. An Iteratively Reweighted Least Squares (IRLS) algorithm and the Alternating Direction Method of Multipliers (ADMM) algorithm for solving the total variation problem are introduced.
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