Blind image recovery approach combing sparse and low-rank regularizations

The only useful prior knowledge in blind compressive sensing is that a signal is sparse in an unknown dictionary. Usually, general dictionaries cannot sparsify all images well. It simultaneously optimizes the dictionary and sparse coefficient in the reconstruction process and has been demonstrated to obtain same results as those compressive sensing techniques based on the known dictionary. In this paper, we propose a novel blind compressive sensing method combing sparse and low-rank regularizations to obtain competitive recovery results. We employ truncated Schatten-p norm and l(q) norm to approximate rank and norm. At last, we give an optimization strategy based on alternating direction method of multipliers to solve the recovery model. Experimental results prove that our approach could obtain the higher Peak Signal to Noise Ratio values than other competitive methods.