An efficient method for the reconstruction of band-limited images and the approximation of arbitrary images from nonuniform sampling values is developed. The novel method is based on the observation that the reconstruction problem can be formulated as linear system of equations using 2-D trigonometric polynomials, where the matrix is of block-Toeplitz type with Toeplitz blocks. This system is solved iteratively by the conjugate gradient method. We show that the usage of so-called adaptive weights in the establishment of the block Toeplitz matrix can be seen as efficient preconditioning. The superiority of the new method over conventional approaches is demonstrated by numerical experiments.

Keywords: algorithms, irregular sampling, numerical work, image reconstruction, Toeplitz matrix, conjugate gradients, preconditioning
Published: IEEE Trans. Image Proc.,6/4:540-548, 1997.

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