In applications of PMMW imaging such as real-time video, 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 blurring and deblurring are based on circular convolution. Unfortunately, when the opposite sides of the image do not match up well in intensity, this assumption can create significant artifacts across the image. The mathematically correct way to avoid boundary artifacts is to model the pixels outside the measured image window as unknown values in the restored image. However, this approach destroys the structure that makes the use of the FFT possible, since the unknown image is no longer the same size as the measured image. 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 unknown boundary 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 a modified FFT-based approach. This image can be thought of as a type of FFT restoration containing the usual boundary artifacts. The other restoration involves a set of unknowns whose number equals that of the unknown boundary values. 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.