在稀疏恢复中，好的局部最小值是宽的吗？
Are good local minima wide in sparse recovery?
摘要：
压缩感测的想法是利用合适的（过完备）字典中的表示，其允许恢复远远超过奈奎斯特速率的信号，只要它们允许相应字典中的稀疏表示。后者引起的稀疏恢复问题，找到最好的稀疏线性近似给定的数据在一个给定的生成系统。在本文中，我们分析了迭代硬阈值（IHT）算法作为解决稀疏恢复问题的最流行的贪婪方法之一，并证明了系统地扰动IHT算法，通过添加噪声的中间迭代产生改进的结果。进一步的改进可以通过将问题完全重新表述为参数深度学习类型的优化问题来获得。通过引入扰动通过辍学，我们证明了显着优于经典的IHT算法，获得$3$到$6$倍的平均客观误差。
英文摘要：
The idea of compressed sensing is to exploit representations in suitable (overcomplete) dictionaries that allow to recover signals far beyond the Nyquist rate provided that they admit a sparse representation in the respective dictionary. The latter gives rise to the sparse recovery problem of finding the best sparse linear approximation of given data in a given generating system. In this paper we analyze the iterative hard thresholding (IHT) algorithm as one of the most popular greedy methods for solving the sparse recovery problem, and demonstrate that systematically perturbing the IHT algorithm by adding noise to intermediate iterates yields improved results. Further improvements can be obtained by entirely rephrasing the problem as a parametric deep-learning-type of optimization problem. By introducing perturbations via dropout, we demonstrate to significantly outperform the classical IHT algorithm, obtaining $3$ to $6$ times lower average objective errors.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
