Technical Report MSC-2006-32

Title: Example-Based Regularization in Inverse Problems
Authors: Dmitry Datsenko
Supervisors: Michael Elad
Abstract: Regularization plays a vital role in inverse problems in image processing, and especially in ill-posed ones. Along-side to classical regularization techniques based on smoothness, entropy, and sparsity, an emerging powerful regularization is one that leans on image examples. Today's literature offers a variety of example-based techniques for regularization. Generally speaking, these techniques can be divided into two main categories: (i) methods using parametrized priors, with a learning method for setting these parameters; and (ii) methods that use examples directly. This work starts by reviewing existing contributions, and carefully pointing to their shortcomings. More specifically, the first family of methods are often too limited in grasping the richness conveyed by the examples database, which naturally lead to inferior performance. The use of examples directly, as the second family of methods advocates, is often coupled with lack of a clear global quality criteria, leading unavoidably to heuristic schemes.

In this work we propose an efficient scheme for using image examples as driving a powerful regularization, applied to several classic inverse problems in image processing - denoising, deblurring, and super-resolution. The proposed framework fuses existing elements from example-based reconstruction algorithms, as described above, and overcome many of their shortcomings. The proposed algorithm starts by assigning per each location in the degraded image several candidate high-quality patches. Those are found as the nearest-neighbors in an image-database that contains pairs of corresponding low- and high-quality image patches. The found examples are used for the definition of an image prior expression, merged into a global MAP penalty function. We use this penalty function both for rejecting some of the irrelevant outlier examples, and then for reconstructing the desired image.

The proposed algorithm strives to enjoy from benefits of both example-based approaches mentioned above, in order to achieve a solution that would be both analytically and visually pleasing. Along with promising results on the denoising and the deblurring problems, this work also addresses the single-image super-resolution problem - a far more challenging task. We demonstrate our algorithm on scanned text, graphics, and drawings and face images, showing high quality outcome.

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