Noisy Low Rank Column-wise Sensing
This work provides incremental improvements in sample complexity for a specific mathematical problem in signal processing or machine learning, relevant for researchers in optimization and sensing.
The paper tackles the noisy low rank column-wise sensing problem by analyzing the AltGDmin algorithm, achieving a sample complexity improvement by a factor of max(r, log(1/ε))/r over existing guarantees, where r is the rank and ε is the accuracy.
This letter studies the AltGDmin algorithm for solving the noisy low rank column-wise sensing (LRCS) problem. Our sample complexity guarantee improves upon the best existing one by a factor $\max(r, \log(1/ε))/r$ where $r$ is the rank of the unknown matrix and $ε$ is the final desired accuracy. A second contribution of this work is a detailed comparison of guarantees from all work that studies the exact same mathematical problem as LRCS, but refers to it by different names.