Blind Gain and Phase Calibration via Sparse Spectral Methods

TL;DR

This paper introduces a spectral method based on power iteration for solving blind gain and phase calibration problems, especially leveraging sparsity, with strong empirical performance and theoretical guarantees.

Contribution

It formulates BGPC as an eigenvalue problem and proposes power iteration algorithms that recover unknown gains, phases, and signals, even under noisy or adverse conditions.

Findings

Power iteration effectively solves BGPC under certain assumptions.

Algorithms perform well beyond theoretical regimes, including noisy scenarios.

Compared to competitors, the proposed methods are more robust in adversarial conditions.

Abstract

Blind gain and phase calibration (BGPC) is a bilinear inverse problem involving the determination of unknown gains and phases of the sensing system, and the unknown signal, jointly. BGPC arises in numerous applications, e.g., blind albedo estimation in inverse rendering, synthetic aperture radar autofocus, and sensor array auto-calibration. In some cases, sparse structure in the unknown signal alleviates the ill-posedness of BGPC. Recently there has been renewed interest in solutions to BGPC with careful analysis of error bounds. In this paper, we formulate BGPC as an eigenvalue/eigenvector problem, and propose to solve it via power iteration, or in the sparsity or joint sparsity case, via truncated power iteration. Under certain assumptions, the unknown gains, phases, and the unknown signal can be recovered simultaneously. Numerical experiments show that power iteration algorithms work not only in the regime predicted by our main results, but also in regimes where theoretical analysis is limited. We also show that our power iteration algorithms for BGPC compare favorably with competing algorithms in adversarial conditions, e.g., with noisy measurement or with a bad initial estimate.