Fast and direct image restoration with edge-preserving regularization

In many applications, fast restorations are needed to keep up with the frame rate. FFT-based restoration provides a fast implementation, but it does so at the expense of assuming that the degree of regularization is constant over the image. Unfortunately, this assumption can create significant ringing artifacts in the presence of edges as well as edges that are blurrier than necessary. Shift-variant regularization provides a way to vary the roughness penalty as a function of spatial coordinates. Virtually all edge-preserving regularization approaches exploit this concept. However, this approach destroys the structure that makes the use of the 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 mariner. 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.