POCS Reconstruction of Irregularly-Sampled Images Based on Oversampling and Linear Space-Variant Filtering

Image reconstruction from irregularly-spaced samples is becoming a pivotal element of advanced video processing and compression tasks. Typically, irregular sample positions are due to the process of motion or disparity compensation, and can result in areas void of data (divergent motion, occlusion areas). Since sample positions do not obey constraints required by irregular-sampling theorems, alternative, for example approximate, reconstruction methods are needed. In this paper, we describe an image reconstruction method from irregularly-spaced samples based on the theory of projection onto convex sets (POCS). Similar to other POCS-based image reconstruction methods, our approach applies two projection operators: bandwidth limitation and sample substitution. Unlike other methods, however, our algorithm is implemented on an oversampled lattice. Although the method performs well, it can deal efficiently only with either densely- or sparsely-sampled image areas, but not with both area types simultaneously. In order to address this issue, we propose a replacement of the usual linear space-invariant filtering with linear space-variant filtering. We develop a filter adaptation strategy that selects suitable filter depending on the local density of irregularly-spaced input samples. We further improve the method by adapting filter bandwidth to the progress of image reconstruction. We experimentally demonstrate efficacy of the method on disparity compensation in the context of stereoscopic 3-D imaging.