Blind Gain and Phase Calibration via Sparse Spectral Methods
This work addresses calibration issues in sensing systems for applications like inverse rendering and radar, but it is incremental as it builds on existing methods with improved algorithms.
The paper tackles the blind gain and phase calibration (BGPC) problem by formulating it as an eigenvalue/eigenvector problem and solving it via power iteration methods, achieving simultaneous recovery of unknown gains, phases, and signals under certain assumptions, with numerical experiments showing favorable performance in noisy or adversarial conditions.
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.