Example-Based Priors for Inverse Problems in Image Processing
August 31st, 2005
Int. Conference on Super-Resolution, Hong-Kong - Invited talk.

In our field, when composing a super-resolved image, two ingredients contribute to the ability to get a leap in resolution: (i) the existence of many and diverse measurements, and (ii) the availability of a model to reliably describe the image to be produced. This second part, also known as the regularization or the prior, is of generic importance, and could be deployed to any inverse problem, and used by many other applications (compression, image synthesis, and more). The well-known recent work by Baker and Kanade (’02) and the work that followed (Lin and Shum ’04, Robinson and Milanfar ’05) all suggest that while the measurements are limited in gaining a resolution increase, the prior could be used to break this barrier. Clearly, the better the prior used, the higher the quality we can expect from the overall reconstruction procedure. Indeed, recent work on super-resolution (and other inverse problems) departs from the regular Tikhonov method, and tends to the robust counterparts, such as TV or the bilateral prior (see Farsiu et. al. ’04).

A recent trend with a growing popularity is the use of examples in defining the prior. Indeed, Baker and Kanade were the first to introduce this notion to the super-resolution task. There are several ways to use examples in shaping the prior to become better. The work by Mumford and Zhu (’99) and the follow-up contribution by Haber and Tenorio (02′) suggest a parametric approach. Baker and Kanade (’02), Freeman et. al. (several contributions ’01), Nakagaki and Katzaggelos (’03) all use the examples to directly learn the reconstruction function, by observing low-res. versus high-res. pairs.

In this talk we survey this line of work and show how it can be extended in several important ways. We show a general framework that builds an example-based prior that is independent of the inverse problem at hand, and we demonstrate it on several such problems, with promising results.

Joint work with Dima Dastenko.