Structured low-rank matrix recovery via optimization methods
From single-molecule microscopy in biology, to collaborative filtering in recommendation systems, to quantum state tomography in physics, many scientific discoveries involve solving ill-posed inverse problems, where the number of parameters to be estimated far exceeds the number of available measurements. To make these daunting problems solvable, low-dimensional geometric structures are often exploited, and regularizations that promote underlying structures are used for various inference tasks. To date, one of the most effective and plausible low-dimensional models for matrix data is the low-rank ...
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