Super Resolution of the Image by Sparse Bayesion Method

Abstract

We propose a Classical method for image expansion such as bilinear interpolation or splines can be understood as linear filtering operations on a given image. This interpolator that is trained in advance with training data, based on sparse Bayesian estimation for determining the optimal and compact support for efficient image expansion. In our framework, the interpolator expands the image by replacing each pixel in the given low-resolution image by an (r x r) high-resolution image patch. Since estimating pixel values is impossible from only one pixel value, we use the low-resolution pixel patch surrounding the pixel to be replaced. This local interpolation is repeated for every pixel in the given image, and the expanded image is constructed by fitting the high-resolution patches. The compactness of the support is beneficial when we want a fast and high-quality image interpolator, especially when we apply it in small embedded systems such as digital cameras and mobile phones. In this paper, we aim to resolve the tradeoff between high quality and low cost. thorough investigation of the application of support vector regression (SVR) to the superresolution problem is conducted through various frameworks. Prior to the study, the SVR problem is enhanced by finding the optimal kernel. This is done by formulating the kernel learning problem in SVR form as a convex optimization problem, specifically a semi-definite programming (SDP) problem.