Fast restoration and superresolution with edge-preserving regularization

In applications of PMMW imaging such as real-time video, fast restorations are needed to keep up with the frame rate. Restoration based on 2-D FFT's provides a fast implemention but at the expense of assuming that the regularization term is constant over the image. Unfortunately, this assumption can create significant ringing artifacts in the presence of edges as well as edyes that are blurrier than necessary. Furthermore. shift-invariant regularization does not allow for the possibility of superresolution. Shift-variant regularization provides a way to vary the roughness penalty as a function of spatial coordinates to reduce edge artifacts and provide a degree of superresolution. Virtually all edge-preserving regularization approaches exploit this concept. However, this approach destroys the structure that makes the use of the 2-D FFT possible, since the deblurring operation is no longer shift-invariant. Thus, the restoration methods available for this problem no longer have the computational efficiency of the FFT. We propose a new restoration method for the shift-variant regularization approach that can be implemented in a fast and flexible manner. We decompose the restoration into a sum of two independent restorations. One restoration yields an image that comes directly from an FFT-based approach. This image is a shift-invariant restoration containing the usual artifacts. The other restoration involves a set of unknowns whose number equals the number of pixels with a local smoothing penalty significantly different from the typical value in the image. This restoration represents the artifact correction image. By summing the two, the artifacts are canceled. Because the second restoration has a significantly reduced set of unknowns, it can be calculated very efficiently even though no circular convolution structure exists.