Block-sparse Signal Recovery Based On L₁-l₂ Minimization

Compressive sensing?CS?is a newly developed theoretical framework for information acquisition and processing.By solving the non-linear optimization problems,we can recover the signals that are sparse and compressible from a small number of linear and non-adaptive measurements.Compressive sensing breaks through the limitations of the traditional Nyqiust sampling theory and has a broad application prospect in modern signal processing.Block-sparse signal is a typical sparse signal,which exhibits additional structure in the form of the non-zero coefficient occurring in blocks?or clusters?.In this paper,we study that block sparse signal which based on l₁-l₂ minimization.We have done the following work in this paper:?1?We introduce the theoretical framework of block sparse signal recovery which based on l₁-l₂ minimization,and extend the l₁-l₂ minimization recovery algorithm to the block model.Properties of the block l₁-l₂ minimization are proved.A sufficient condition for block-sparse signal recovery is also established.?2?DCA?difference of convex functions algorithm?is a non-linear search descent algorithm,which can be used to solve the minimum value of the objective function.ADMM?Alternating direction method of multipliers?is an optimization calculation framework,decomposing the global problem into sub multiple problems that is smaller and easier to solve,getting global solution of the problem through integrating the solutions of sub problems.We present an iterative method for block l₁-l₂ minimization which based on the DCA and ADMM.The simulation results demonstrate that the recovery probability of our algorithm is higher than popular existing algorithms.?3?In this paper,we introduce the application of high correlation measurement matrix in block sparse signal reconstruction.Numerical experiments show that the 1 2/pl-l l method has good performance in the case of using high correlation measurement matrix.