L1 model-driven recursive multi-scale denoising network for image super-resolution

Abstract Most existing deep learning based single-image super-resolution (SISR) methods mainly improve the reconstruction performances from the perspective of data-driven, i.e., widening or deepening the networks according to the huge scale of the training data. However, it will bring a huge amount of weights and biases, and cost the expensive computations. Recently, some people have proposed a new frame for designing the deep networks according to the algorithms deduced from the l 2 -optimization problem. But they did not consider the case with outliers. Since l 1 -norm can describe the sparsity of the outliers better than l 2 -norm, we propose an effective deep network designed according to the new algorithm deduced from the l 1 -optimization problem. In our proposed method, an effective iterative algorithm for the l 1 reconstructed optimization problem is deduced based on the split Bregman algorithm, majorization–minimization algorithm, and soft thresholding operator. Then according to the deduced iterative algorithm, an effective deep network, named l 1 Model-Driven Recursive Multi-Scale Denoising Network ( l 1 -MRMDN), is designed. Due to the iteration form of the deduced algorithm, the proposed l 1 -MRMDN contains an inner recursion and an outer recursion. Therefore, our proposed method can not only relieve its sensitiveness to the outliers because of the l 1 data fidelity term, but also avoid designing the deep network blindly via the guidance of prior knowledge. Extensive experimental results illustrate that our proposed method is superior to some related popular SISR methods.