Blind Gain and Phase Calibration via Sparse Spectral Methods
Blind Gain and Phase Calibration via Sparse Spectral Methods
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DOI：
10.1109/tit.2018.2883623
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发表时间：
2019-05-01
影响因子：
2.5
通讯作者：
Bresler, Yoram
中科院分区：
文献类型：
--
作者：
Li, Yanjun;Lee, Kiryung;Bresler, Yoram
盲增益相位校正（BGPC）是一个双线性逆问题，涉及到传感系统的未知增益和相位以及未知信号的确定。BGPC出现在许多应用中，例如，逆绘制中的盲估计、合成孔径雷达自动聚焦和传感器阵列自动校准。在某些情况下，未知信号中的稀疏结构说明了BGPC的不适定性。最近，人们重新对BGPC的解产生了兴趣，并仔细分析了误差界。在本文中，我们制定BGPC作为一个特征值/特征向量的问题，并建议解决它通过电源迭代，或在稀疏或联合稀疏的情况下，通过截断电源迭代。在一定的假设条件下，可以同时恢复未知增益、相位和未知信号。数值实验表明，幂迭代算法不仅工作在我们的主要结果所预测的制度，但也在制度的理论分析是有限的。我们还表明，我们的权力迭代算法BGPC比较有利的竞争算法在对抗性条件下，例如，具有噪声测量或具有坏的初始估计。
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 illposedness 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.