Fast superresolution based on a network structure trained using sparse coding

In this thesis I present a novel approach to superresolution using a network structure. Sparse representation of image signals forms the cornerstone of our approach and the goal is to obtain resolution enhancement of the low resolution images. I will discuss various dictionary learning methods and also a joint dictionary training approach. Superresolution is used to enhance the resolution of low quality and low resolution images from electronic devices such as surveillance cameras, which have limitations on the number of sensors they can accommodate. Many medical diagnostic devices and military applications demand increased image resolution for a better and a more detailed analysis and a deeper understanding of the minute and subtle details. These details are rendered incomprehensible in their original low resolution form. Sparse coding is a technique of finding an optimal sparse code vector corresponding to an input vector. This sparse representation minimizes the error energy function that includes the square of the L2 norm and a regularization term containing the L1 norm of the sparse vector. This sets up a regularized least squares solution. The L1 norm is preferred because it promotes the sparseness of the solution. The L0 norm term in the regularization parameter may result in the solution being obtained in a combinatorial manner, and that may result in finding the solution of the problem to be NP-hard. The regularization term can have an L2 norm, which is called the Tikhonov regularization. The Learning of the Iterative Shrinkage and Thresholding Algorithm (ISTA) is achieved by learning a regression function which accepts a test signal vector as the input and provides a corresponding sparse vector as an output for that signal. The testing part is based on the forward-propagation which is similar to the ISTA network structure. The learning part of the network encoder is however based on a back-propagation model and uses the stochastic-gradient descent method. The error function is the difference between the sparse representations obtained from either ISTA, the Basis Pursuit, or any other L1 regularization solver such as LASSO or LARS, and the regression function obtained by training on the sparse vector obtained from the sparse recovery algorithm. The error function is minimized with respect to the three network parameters. We learn regression function parameters such that the error difference between the regression function and the sparse coding solution vector obtained from the optimization solver is minimized. The sparse representation can also be originally obtained from any convenient L1 regularization solver. Once the regression function is learned, the high resolution patches are simply the product of the high resolution dictionary and the sparse solution obtained from the trained regression function. The low resolution and high resolution dictionaries are usually trained jointly so the sparse coded solution is the same for both the low resolution and high resolution image patches. Our approach increases the computational speed and tries to decrease its cost as, having learned the regression function, we try to bypass the optimization problem