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arXiv · 2105.02995

Approximate inversion of discrete Fourier integral operators

Jordi Feliu-Fabà·Lexing Ying
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Abstract

This paper introduces a factorization for the inverse of discrete Fourier integral operators that can be applied in quasi-linear time. The factorization starts by approximating the operator with the butterfly factorization. Next, a hierarchical matrix representation is constructed for the hermitian matrix arising from composing the Fourier integral operator with its adjoint. This representation is inverted efficiently with a new algorithm based on the hierarchical interpolative factorization. By combining these two factorizations, an approximate inverse factorization for the Fourier integral operator is obtained as a product of $O(\log N)$ sparse matrices of size $N\times N$. The resulting approximate inverse factorization can be used as a direct solver or as a preconditioner. Numerical examples on 1D and 2D Fourier integral operators, including a generalized Radon transform, demonstrate the performance of this new approach.

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Jordi Feliu-Fabà, Lexing Ying. 2021-05-06. Approximate inversion of discrete Fourier integral operators. https://doi.org/10.1016/j.jcp.2021.110654

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