Few algorithms for inverse problems in image processing

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Inverse problems are the problems that involve estimation of the parameters or data given certain observations. The available observations are often noisy and incomplete. Hence, the inverse problems are mostly ill-posed as there can be infinitely many solutions to a given inverse problem. Some priors based on the understanding of the physical phenomenon in the forward problem are used to estimate the solution of such problems. In this work, we provide algorithms for solving two inverse problems, (1) learning based single image super resolution and (2) reducing the solution space of non-negative matrix factorization. Single image super resolution (SISR) refers to the problem of estimating a high resolution (HR) from a single low resolution (LR) image. SISR is an ill-posed inverse problem as for SISR zoom by a factor of s in each dimension, there are s2 unknown HR pixels for each known LR pixel. Natural image statistics and an understanding of human visual perception, such as importance of accurate edge reconstruction, have been used to formulate image priors that can constrain the solution space of the desired HR image pixels. In this work, we present two SISR approaches that exploit scale invariant statistics of natural images.
Supervisor: Amit Sethi