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In this note, we analyze an iterative soft/hard thresholding algorithm with homotopy continuation for recovering a sparse signal x<sup>&#x2020;</sup> from noisy data of a noise level &#x03B5;. Under suitable regularity and sparsity conditions, we design a path, along which the algorithm can find a solution x*, which admits a sharp reconstruction error ||x* - x<sup>&#x2020;</sup>|| &#x2113;&#x221E; = O(&#x03B5;) with an iteration complexity O((ln &#x03B5;)/(ln &#x03B3;)np), where n and p are problem dimensionality and &#x03B3; &#x03B5; (0,1) controls the length of the path. Numerical examples are given to illustrate its performance.

Iterative Soft/Hard Thresholding With Homotopy Continuation for Sparse Recovery