In recent years Convolutional Neural Networks (CNN) have been used extensively for Superresolution (SR). In this paper, we use inverse problem and sparse representation solutions to form a mathematical basis for CNN operations. We show how a single neuron is able to provide the optimum solution for inverse problem, given a low resolution image dictionary as an operator. Introducing a new concept called Representation Dictionary Duality, we show that CNN elements (filters) are trained to be representation vectors and then, during reconstruction, used as dictionaries. In the light of theoretical work, we propose a new algorithm which uses two networks with different structures that are separately trained with low and high coherency image patches and show that it performs faster compared to the state-of-the-art algorithms while not sacrificing from performance.
After proving that a neuron acts as an inverse problem solver for superresolution and a network of neurons is guarantied to provide a solution, we proposed a double network architecture that performs faster than state-of-the-art. Discusses using neural networks for super-resolution A new architecture for solving image super-resolution tasks, and an analysis aiming to establish a connection between CNNs for solving super resolution and solving sparse regularized inverse problems.