用豪斯霍尔德反射加速正交字典学习，计算更快且精度有保障。
Fast Structured Orthogonal Dictionary Learning using Householder Reflections
- 基于豪斯霍尔德反射构造正交字典，保证理论收敛性。
- 在样本有限情况下，恢复误差满足l∞界，计算复杂度最优。
- 适用于需要高效正交表示的信号处理场景，如压缩感知。
本文提出并研究了结构化正交字典学习算法。首先针对字典为豪斯霍尔德矩阵的情形，给出了样本复杂度结果，并理论上证明在l∞意义下可实现近似恢复，且计算复杂度最优。随后将该方法推广至字典为若干豪斯霍尔德矩阵乘积的情形。在样本受限条件下通过数值实验验证，性能与现有方法相当或更优，同时计算效率显著提升。
原文摘要 · Abstract (English)
In this paper, we propose and investigate algorithms for the structured orthogonal dictionary learning problem. First, we investigate the case when the dictionary is a Householder matrix. We give sample complexity results and show theoretically guaranteed approximate recovery (in the $l_{\infty}$ sense) with optimal computational complexity. We then attempt to generalize these techniques when the dictionary is a product of a few Householder matrices. We numerically validate these techniques in the sample-limited setting to show performance similar to or better than existing techniques while having much improved computational complexity.
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