Adaptive Linearized Alternating Direction Method of Multipliers for Non-Convex Compositely Regularized Optimization Problems

We consider a wide range of non-convex regularized minimization problems, where the non-convex regularization term is composite with a linear function engaged in sparse learning. Recent theoretical investigations have demonstrated their superiority over their convex counterparts. The computational challenge lies in the fact that the proximal mapping associated with non-convex regularization is not easily obtained due to the imposed linear composition. Fortunately, the problem structure allows one to introduce an auxiliary variable and reformulate it as an optimization problem with linear constraints, which can be solved using the Linearized Alternating Direction Method of Multipliers （LADMM）. Despite the success of LADMM in practice, it remains unknown whether LADMM is convergent in solving such non-convex compositely regularized optimizations. In this research, we first present a detailed convergence analysis of the LADMM algorithm for solving a non-convex compositely regularized optimization problem with a large class of non-convex penalties. Furthermore, we propose an Adaptive LADMM （AdaLADMM） algorithm with a line-search criterion. Experimental results on different genres of datasets validate the efficacy of the proposed algorithm.

Application of the direct blast adaptive suppression method to the forward scattered broadband signals

The basic principles of target detection by forward acoustic scattering are presented.A direct blast suppression approach based on adaptive filtering(DBS-AF) is proposed to suppress the direct blast.The DBS-AF technique is extended to the linear frequency modulation(LFM) signal,where the envelope of the signal is regarded as a 'general waveform' and imported into the adaptive filter.Application of the DBS-AF method to the data collected from a lake trial yields an output detection curve,in which the direct blast is mapped to the background while the acoustic field aberration is represented by the peak value fluctuation.The inhibitory effect in single hydrophone is approximately- 5 dB,and is then enhanced by exploiting the mean value removal approach as a preprocessing technique.The direct blast is further suppressed to a level of-10 dB by making full use of multichannel receptions.The main factors affecting the algorithm performance are as follows:the fluctuation degree of the receptions during the weighting vector training period and the power ratio of the forward scattered wave to the direct blast when the target is present.