COMPUTATIONALLY ATTRACTIVE RECONSTRUCTION OF BAND-LIMITED IMAGES FROMIRREGULAR SAMPLES

An efficient method for the reconstruction of bandlimited images and t he approximation of arbitrary images from nonuniform sampling values i s developed. The novel method is based on the observation that the rec onstruction problem can be formulated as linear system of equations us ing two-dimensional (2-D) trigonometric polynomials, where the matrix is of block-Toeplitz type with Toeplitz blocks. This system is solved iteratively by the conjugate gradient (CG) method, We show that the us e of so-called adaptive weights in the establishment of the block Toep litz matrix can be seen as efficient preconditioning. The superiority of the new method over conventional approaches is demonstrated by nume rical experiments.