POCS-based image reconstruction from irregularly-spaced samples

This paper presents a method for the reconstruction of a regularly-sampled image from its irregularly-spaced samples. Such reconstruction is often needed in image processing and coding, for example when using motion compensation. The proposed approach is based on the theory of projections onto convex sets. Two projection operators are used: bandwidth limitation and sample substitution. The approach is similar to some methods presented in the literature in the past, but differs in the implementation. The bandwidth limitation is implemented in the frequency domain on an oversampled grid thus allowing substantial flexibility in spectrum shaping of the reconstructed image. Additionally, a fast Fourier transform algorithm specifically designed for irregularly-sampled images is used to reduce the computational complexity. A number of experimental results on natural images are presented.