提出无需调参的最优向量压缩感知算法，高效处理高维数据
Optimal Vector Compressed Sensing Using James Stein Shrinkage
- 基于James-Stein收缩思想设计轻量迭代算法，无需训练与先验知识
- 在高维度下理论证明最优，实测表现优于传统凸优化方法
- 适合大规模高维信号恢复，对数据分布鲁棒性强
现代科学与技术趋势是采用向量测量而非标量，维度持续攀升。过去二十年，标量压缩感知通常依赖基于凸优化的基追踪（Basis Pursuit）方法。在向量恢复场景中，自然做法是直接扩展基追踪，同样基于凸优化。然而，凸优化在 $B$ 较大时被证明为次优。本文提出 SteinSense，一种轻量级迭代算法，在 $B$ 较大时可证明最优。该算法无调参、无需训练数据、不依赖稀疏性知识，实现简单且易于扩展至高维。通过大量真实与合成实验验证其有效性，并基于近似消息传递理论提供理论支持。令人惊讶的是，SteinSense 对真实数据及理论假设偏离情况均表现出强鲁棒性，性能稳定。
原文摘要 · Abstract (English)
The trend in modern science and technology is to take vector measurements rather than scalars, ruthlessly scaling to ever higher dimensional vectors. For about two decades now, traditional scalar Compressed Sensing has been synonymous with a Convex Optimization based procedure called Basis Pursuit. In the vector recovery case, the natural tendency is to return to a straightforward vector extension of Basis Pursuit, also based on Convex Optimization. However, Convex Optimization is provably suboptimal, particularly when $B$ is large. In this paper, we propose SteinSense, a lightweight iterative algorithm, which is provably optimal when $B$ is large. It does not have any tuning parameter, does not need any training data, requires zero knowledge of sparsity, is embarrassingly simple to implement, and all of this makes it easily scalable to high vector dimensions. We conduct a massive volume of both real and synthetic experiments that confirm the efficacy of SteinSense, and also provide theoretical justification based on ideas from Approximate Message Passing. Fascinatingly, we discover that SteinSense is quite robust, delivering the same quality of performance on real data, and even under substantial departures from conditions under which existing theory holds.
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