Log In Sign Up

Multidimensional Phase Recovery and Interpolative Decomposition Butterfly Factorization

by   Ze Chen, et al.

This paper focuses on the fast evaluation of the matvec g=Kf for K∈C^N× N, which is the discretization of a multidimensional oscillatory integral transform g(x) = ∫ K(x,ξ) f(ξ)dξ with a kernel function K(x,ξ)=e^2πıΦ(x,ξ), where Φ(x,ξ) is a piecewise smooth phase function with x and ξ in R^d for d=2 or 3. A new framework is introduced to compute Kf with O(N N) time and memory complexity in the case that only indirect access to the phase function Φ is available. This framework consists of two main steps: 1) an O(N N) algorithm for recovering the multidimensional phase function Φ from indirect access is proposed; 2) a multidimensional interpolative decomposition butterfly factorization (MIDBF) is designed to evaluate the matvec Kf with an O(N N) complexity once Φ is available. Numerical results are provided to demonstrate the effectiveness of the proposed framework.


Rapid Application of the Spherical Harmonic Transform via Interpolative Decomposition Butterfly Factorization

We describe an algorithm for the application of the forward and inverse ...

Efficient Solutions for the Multidimensional Sparse Turnpike Problem

The turnpike problem of recovering a set of points in ℝ^D from the set o...

Multidimensional Variational Line Spectra Estimation

The fundamental multidimensional line spectral estimation problem is add...

Necessary Conditions for Discontinuities of Multidimensional Size Functions

Some new results about multidimensional Topological Persistence are pres...

Variational phase recovering without phase unwrapping in phase-shifting interferometry

We present a variational method for recovering the phase term from the i...

Efficient Algorithms for Multidimensional Segmented Regression

We study the fundamental problem of fixed design multidimensional segme...

ATC: an Advanced Tucker Compression library for multidimensional data

We present ATC, a C++ library for advanced Tucker-based lossy compressio...