An efficient formulation and parameter selection for multiple image super-resolution

Abstract

Enhancing the resolution of an image using the data available from multiple low-resolution images is termed as multiple image super-resolution. It is an ill-posed, inverse problem, the mathematical model of which takes the form of standard image reconstruction problem. The standard mathematical model of the imaging system involves matrix based operators for various effects that the scene undergoes in the process of imaging. The super-resolution problem formulation using this model has intensive storage and processing requirements. We propose an alternative approach to tackle the problem of super-resolution, wherein we view the image not as a vector to be estimated, but as a collection of pixel values on which the operators of the imaging system work. We show that this perspective eliminates the need for large storage requirements and processing times. We also propose a technique to automate the selection of the regularization parameter when the available low-resolution images are free of noise. We observe that this technique is intuitive and follows the variation of the true mean squared error with the regularization parameter.