A fast and accurate algorithm for l(1) minimization problems in compressive sampling

作者：Chen Feishe; Shen Lixin^*; Suter Bruce W; Xu Yuesheng

来源：EURASIP Journal on Advances in Signal Processing, 2015, 2015(1): 65.

DOI：10.1186/s13634-015-0247-5

• Compressive sensing
• l(1) minimization
• Proximity operator

An accurate and efficient algorithm for solving the constrained l(1)-norm minimization problem is highly needed and is crucial for the success of sparse signal recovery in compressive sampling. We tackle the constrained l(1)-norm minimization problem by reformulating it via an indicator function which describes the constraints. The resulting model is solved efficiently and accurately by using an elegant proximity operator-based algorithm. Numerical experiments show that the proposed algorithm performs well for sparse signals with magnitudes over a high dynamic range. Furthermore, it performs significantly better than the well-known algorithm NESTA (a shorthand for Nesterov's algorithm) and DADM (dual alternating direction method) in terms of the quality of restored signals and the computational complexity measured in the CPU-time consumed.

• 出版日期2015-8-1