An Alternating lp Approach to Compressed Sensing

Recent theoretical developments in Compressed Sensing (CS) show that if a signal has sparse representation in some basis, then it is possible to reconstruct this signal exactly from remarkably few measurements. Significant attention in CS has been focused on a nonconvex extension, where the l₁ norm is replaced by the l_p norm for p isin(0,1). In this paper, we propose a new Maximum Entropy Function (MEF) method as a computational method to solve the I_p optimization problem via smoothing the objective function with maximum entropy function. MEF intimately relates to the homotopy method and the theoretical results concerning its global convergence property are guarantee of perfect signal reconstruction. The extensive experiments show that our new method is an effective algorithm for signal reconstruction with much fewer measurements than l₁ norm and it has better performance than Affine Scaling Transformation (AST) algorithm for solving I_p norm optimization. In the CS framework, MEF method is a usefully alternating approach as to signal reconstruction.