Linear shift-variant filtering for POCS of reconstruction irregularly sampled images

The reconstruction of a regularly-sampled image from irregularly-spaced samples is a stumbling block in various video processing tasks. In the past, we have developed a POCS-based (projection onto convex sets) reconstruction method that applies two operators sequentially: bandwidth limitation and sample substitution. Although the method works well, we have observed an interesting paradox: wide-band filtering results in better-looking images, but lower PSNR values, than narrow-band filtering (increased blur). This can be explained by a too-short impulse response of the wide-band filter unable to "fill-in" the missing samples in sparsely populated areas. In this paper, we propose an improved version of our algorithm where linear shift-invariant (LSI) filtering is replaced by linear shift-variant (LSV) filtering. The LSV filtering is implemented as a parallel bank of LSI filters, each with different bandwidth (impulse response). We demonstrate experimentally a significant reduction of the reconstruction error due to the new LSV filtering.