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Limited-angle tomography via multiresolution analysis and oversampling

In this paper we present a method for reconstructing a function f : R2 yields R from limited angle Fourier data. This problem is motivated by the limited angle tomography problem, which arises when physical limitations on the system prohibit the gathering of tomographic data at certain angles. The first portion of this paper we decompose the limited angle operator into a tensor product form which enables the computation of its inverse. The second portion of the paper uses a multiresolution analysis to mollify the problem and provide the inverse solution. It is shown that the proposed algorithm significantly outperforms the singular value decomposition of the operator.