A Simple and Exact Algorithm to Solve Linear Problems with \ell ^1 -Based Regularizers

This paper considers \(\ell ^1\)-based regularized signal estimation that are often used in applications. The estimated signal is obtained as the solution of an optimization problem and the quality of the recovered signal directly depends on the quality of the solver. This paper describes a simple algorithm that computes an exact minimizer of \( \Vert D \cdot \Vert _1\) under the constraints \(A\mathbf {x}=\mathbf {y}\). A comparative evaluation of the algorithm is presented. An illustrative application to real signals of bacterial flagellar motor is also presented.

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