Image Super-Resolution Using Analytical Edge Model

Assuming having only one low-resolution image, the study aims to obtain an equivalent image with a higher resolution. This problem is usually referred to as “Super-resolution”. Since the number of unknown target values is far more than that of known values given in the input image, the super-resolution is a severely ill-posed problem. In this paper, a model is developed in order to narrow down the solution space. The underlying assumption in the modeling is that the image blocks, in small-enough dimensions, usually contain only one linear edge. To model this behavior, an analytical model with five parameters is presented which greatly reduces the efficient dimensionality of the unknowns. Simple and analytical formulation of this model makes it possible to convert the image super-resolution to a convex optimization problem and effectively solve the problem using the well-known gradient descent optimization method. Experiments on standard test images indicate that the proposed algorithm increases PSNRabout 0.5 to 4 dB, in comparison with other interpolation-based methods.