Image super resolution via non-local normalized graph Laplacian regularization
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Given we live in a digital age where images are regularly being viewed, posted, or utilized, spectators of such images on occasion could prefer a higher resolution perspective. The process of producing a high-resolution image given a single low-resolution noisy measurement is called single-frame image super resolution (SISR). Many interpolation schemes fail to preserve important edge information of images and cannot be used blindly for resolution enhancement. In general, apriori constraints can be imposed on the high resolution image approximation. This process is called regularization. We model our SISR problem as an energy minimization procedure which optimally balances data fidelity and the regularization term. The regularization term will incorporate natural image redundancy implicitly via the so called normalized graph Laplacian operator. This operator applies a non-local kernel similarity measure due to choice of a non-local operator for weight assignment. The data fidelity term is modeled as a likelihood estimator that is scaled using a sharpening term composed from the normalized graph Laplacian operator. Finally, a conjugate gradient scheme is used to minimize the objective functional. Promising results on resolution enhancement for a variety of digital images will be presented. Non-local methods can be further enhanced following a \boosting" procedure deemed to enhance a signal by reintroducing a \cleaned\ version of the signal back into the final approximation. This is beneficial for all non-local restoration approaches. We show analytically that successive applications of this boosting operation does not necessarily guarantee a superior final solution.