Iterative Blind Image Deconvolution in Space and Frequency Domains

In image acquisition, the captured image is often the result of the object being convolved with a blur function. Deconvolution is necessary in order to undo the effects of the blur. However, in real life we may have very little knowledge of the blur, and therefore we have to perform blind deconvolution. One major challenge of existing iterative algorithms for blind deconvolution is the enforcement of the convolution constraint. In this paper we describe a method whereby this constraint can be much more easily implemented in the frequency domain. This is possible because of Parseval's theorem, which allows us to relate projection in the space and frequency domains. Our algorithm also incorporates regularization of the estimated image through the use of Wiener filters. The restored images are compared to the original and noisy blurred images, and we find that the restoration process indeed provides an enhancement in visual quality.