Two fast extrapolation/superresolution algorithms

We propose two fast algorithms for the extrapolation of band-limited images (or, equivalently, for spectrum extrapolation of finite support objects). The algorithms are noniterative and based on the Cholesky decomposition of certain Hermitian positive-definite matrices. One of the algorithms is based on a image domain formulation of the problem, whereas the other is based on the dual frequency domain formulation. Both formulations lead to a wide range of possible algorithms, but the proposed techniques seem very adequate to the problem under consideration. It is shown that there are problems for which the algorithms that spring from one formulation will outperform those that arise from the other. Some of the issues that should be taken in consideration when designing algorithms for specific problems are discussed. The connection between these reconstruction algorithms and error control coding in the complex field is mentioned.