论文标题
无限尺寸中低维模型的非凸逆问题全局最小化的吸引力的盆地
The basins of attraction of the global minimizers of non-convex inverse problems with low-dimensional models in infinite dimension
论文作者
论文摘要
对于凸技术的替代方案，已经出现了针对低维模型的线性反问题的非凸方法。我们提出了一个理论框架，可以研究有限维度和无限尺寸线性反问题。我们展示了此类问题最小化器吸引人吸引的盆地的大小与可用测量的数量有关。该框架恢复了有关低率矩阵估计和离网稀疏尖峰估计的已知结果，并为线性测量结果提供了高斯混合物估计的新结果。关键字：低维模型，非凸方法，低级别矩阵恢复，网格稀疏恢复，线性测量的高斯混合模型估计。
Non-convex methods for linear inverse problems with low-dimensional models have emerged as an alternative to convex techniques. We propose a theoretical framework where both finite dimensional and infinite dimensional linear inverse problems can be studied. We show how the size of the the basins of attraction of the minimizers of such problems is linked with the number of available measurements. This framework recovers known results about low-rank matrix estimation and off-the-grid sparse spike estimation, and it provides new results for Gaussian mixture estimation from linear measurements. keywords: low-dimensional models, non-convex methods, low-rank matrix recovery, off-the-grid sparse recovery, Gaussian mixture model estimation from linear measurements.
