Abstract :
Fast Fourier transform (FFT)-based restorations
are fast, but 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.
If the pixels outside the measured image window are modeled
as unknown values in the restored image, boundary artifacts
are avoided. However, this approach destroys the structure that
makes the use of the FFT directly applicable, 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. The other restoration involves a set of
unknowns whose number equals that of the unknown boundary
values. 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.
