A regularised deep matrix factorised model of matrix completion for image restoration

It has been an important approach of using matrix completion to perform image restoration. Most previous works on focus the low-rank property by imposing explicit constraints recovered matrix, such as constraint nuclear norm or limiting dimension factorization component. Recently, theoretical suggest that deep linear neural network implicit bias towards low rank completion. However, is not adequate reflect intrinsic characteristics a natural image. Thus, algorithms with only are insufficient restoration well. In this work, we propose Regularized Deep Matrix Factorized (RDMF) model for restoration, which utilizes networks and total variation. We demonstrate effectiveness our RDMF extensive experiments, in method surpasses state art models common examples, especially from very few observations. Our work sheds light more general framework solving other inverse problems combining learning regularization.