压缩感知中信号重构的极大熵方法(英文)

本文针对压缩感知理论中BP算法的l1最优化问题,构造了一种新的信号重构的极大熵方法.极大熵方法克服了l1最优化问题的非光滑性,同时根据同伦方法构造极大熵函数的最优解序列来逼近全局最优稀疏解.数值实验表明极大熵方法是十分有效的信号重构方法.

Maximum Entropy Function Method for Signal Reconstruction in Compressed Sensing

The emerging theory of Compressed Sensing (CS) has led to the remarkable results that compressible signal can be reconstructed using only a small number of measurements. Significant attention in CS has been focused on Basis Pursuit (BP).exchanging the sparseness constraint with the l1 norm. In order to overcome the nonsmooth problem in l1 norm, this paper proposes a new Maximum Entropy Function Method (MEFM) to solve the l1 optimization problem via smoothing the objective function with maximum entropy function. Intimately relating to homotopy method. MEFM provides a systematic approach for deriving the global optimal sparse solution. Finally. the numerical results show that it is an effective technique for signal reconstruction. In a CS framework. MEFM is a usefully alternating method to solve the l1 optimization problem.