多参考对齐的矩约束与相位恢复
Moment Constraints and Phase Recovery for Multireference Alignment
AI总结：
针对多参考对齐问题，提出结合矩量法与统计建模思路的新方法，将功率谱作为约束信号的流形，通过梯度优化最大化似然并迭代模板对齐与流形投影，兼顾速度与精度。
摘要：
多参考对齐（MRA）是指从受随机循环移位影响的含噪样本中恢复信号的问题。期望最大化（EM）和变分方法使用统计建模来实现高精度，但代价是需要求解计算成本高昂的优化问题。而矩量法通过利用功率谱和双谱来确定信号（仅存在移位不确定性），从而实现快速重建。我们的方法结合了这两种思路，将功率谱视为约束信号的流形。随后我们采用基于梯度的方法在该流形上最大化数据似然函数，以估计真实信号。在算法层面，我们的方法包含在模板对齐与流形投影之间迭代的步骤。该方法相比EM速度更快，且相比基于双谱的方法精度更高。
英文摘要：
Multireference alignment (MRA) refers to the problem of recovering a signal from noisy samples subject to random circular shifts. Expectation--maximization (EM) and variational approaches use statistical modeling to achieve high accuracy at the cost of solving computationally expensive optimization problems. The method of moments, instead, achieves fast reconstructions by utilizing the power spectrum and bispectrum to determine the signal up to shift. Our approach combines the two philosophies by viewing the power spectrum as a manifold on which to constrain the signal. We then maximize the data likelihood function on this manifold with a gradient-based approach to estimate the true signal. Algorithmically, our method involves iterating between template alignment and projections onto the manifold. The method offers increased speed compared to EM and demonstrates improved accuracy over bispectrum-based methods.
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