Approximate inversion of discrete Fourier integral operators

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