Phase Retrieval by Linear Algebra

TL;DR

This paper introduces a null vector linear algebra method for phase retrieval, providing theoretical error bounds and demonstrating its effectiveness comparable to spectral methods in complex Gaussian measurement scenarios.

Contribution

It proposes a novel null vector approach for phase retrieval and derives non-asymptotic error bounds for complex Gaussian measurements.

Findings

Error bounds are established for the null vector method.

The method achieves accuracy comparable to spectral vector methods.

The approach is effective in the asymptotic regime for complex Gaussian matrices.

Abstract

The null vector method, based on a simple linear algebraic concept, is proposed as a solution to the phase retrieval problem. In the case with complex Gaussian random measurement matrices, a non-asymptotic error bound is derived, yielding an asymptotic regime of accurate approximation comparable to that for the spectral vector method.