An Inexact Augmented Lagrangian Method For 1-bit Compressed Sensing Problems

Compressed sensing(CS)is a rapidly growing field that has attracted considerable attention in signal processing,statistics and computer science,as well as the broader scientific community.Compressed sensing is a new signal acquisition technology that can reduce the number of measurements required for compressible signals.Instead of uniformly sampling the signal,compressed sensing uses the random dictionary of the test function to calculate the inner product,and then recovers the signal through convex optimization to ensure that the recovered signal is consistent with the measured result and sparse.1-bit compressed sensing is a 1-bit limit quantization of the measured value,which only needs to measure the value above or below 0.The 1-bit quantizer is robust to the amount of nonlinear distortion measured,and the 1-bit quantizer is not affected by the dynamic range problem.Based on these advantages,more and more scholars pay attention to 1-bit compressed sensing.Based on the unilateral l0 norm model,this paper presents a nonlinear programming problem with sparse constraints.The convergence and convergence rate of the imprecise augmented Lagrangian method for this problem are discussed.Finally,under the assumption of second-order sufficient conditions,it is proved that the sequences generated by the imprecise augmenting Lagrangian method converge q-linearly.As the penalty parameter approaches infinity,the sequence converges superlinearly.