## Weak Stability of $\ell_1hBcminimization Methods in Sparse Data Reconstruction As one of the most plausible convex optimization methods for sparse data reconstruction,$\ell_1$-minimization plays a fundamental role in the development of sparse optimization theory. The stability of this method has been addressed in the literature under various assumptions such as restricted isometry property (RIP), null space property (NSP), and mutual coherence. In this paper, … Read more ## Alternating Direction Algorithms for$\ell_1hBcProblems in Compressive Sensing

In this paper, we propose and study the use of alternating direction algorithms for several $\ell_1$-norm minimization problems arising from sparse solution recovery in compressive sensing, including the basis pursuit problem, the basis-pursuit denoising problems of both unconstrained and constrained forms, as well as others. We present and investigate two classes of algorithms derived from … Read more