Initial Proposal

In general, we will focus on the issue of image restoration, by which we mean the removal or reduction of degradations that were incurred while obtaining an image, or as side effects of a manipulation of the image. Our aim is to make the image look as close to the original image as possible, with a minimum of blurring or other degradation. This will be useful because it will improve the fidelity, and therefore the usefulness, of digital images.

This project will involve doing research on deconvolution (inverse filtering). We will start off with some classical restoration filters, specifically at least the Wiener filter, and try to implement these in Matlab. Once we have a good understanding of these basic restoration techniques, we will look at the more general but also more complicated problem of blind deconvolution. Blind deconvolution refers to the class of problems of the form

g(x) = integral(f(x-y)h(y)dy) + n(x)

where g(x) is the observed data, f(x) is an unknown source, h(x) is the impulse response of the system, and n(x) is noise ("A projection-based approach to the blind deconvolution problem", Yang, Stark, and Galatsanos, 1993). This method, unlike the Wiener filter, does not assume knowledge about the cause of degradation, and therefore can be used in a broader range of cases.

We plan to have implemented the classical restoration filters within the next two weeks and then to begin examining the more general methods.