<ul><li>This paper focuses on developing new and fast algorithms for recovering a sparse vector from a small number of measurements in compressive sensing (CS).</li><li>Conventional methods like L1 minimization do not work well for coherent systems, so the paper explores the L1-L2 norm as a superior alternative.</li><li>The paper derives an analytical solution for the proximal operator of the L1-L2 metric, making fast L1 solvers like forward-backward splitting (FBS) and alternating direction method of multipliers (ADMM) applicable for L1-L2.</li><li>The resulting algorithms are shown to be convergent under mild conditions and significantly more efficient than the original implementation of L1-L2 based on a difference-of-convex approach in numerical experiments.</li></ul>

Understanding L1/L2 minimization technique part4(Machine Learning 2024)

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