most recent 30 from http://mathoverflow.net 2013-05-21T09:47:33Z http://mathoverflow.net/feeds/question/81680 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/81680/recovering-a-matrix-instead-of-a-vector Richard 2011-11-23T02:52:02Z 2011-11-23T07:25:57Z

<p>It is known that given corrupt measurements $y = Af+e$ one can recover an input vector $f \in \textbf{R}^n$ exactly by solving a convex optimization problem. What if $f$ is instead a square matrix? Can we recover a matrix from corrupt measurements instead of just a vector?</p>

http://mathoverflow.net/questions/81680/recovering-a-matrix-instead-of-a-vector/81689#81689 Dirk 2011-11-23T07:25:57Z 2011-11-23T07:25:57Z

<p>First, I emphasize S. Carnahan's comment: Exact recovery from noisy measurements is not that simple. "Exact recovery" usually means "recovery of the exact support of $f$". Moreover, sparsity assumptions for $f$ and special assumptions for $A$ and the size of $e$ are needed. </p> <p>To address your question: This again depends on a lot of things. Of course you can view this as $n$ multiple instances of the original problem and basically use the previous theory. Other structural assumption lead to other results (e.g. having a "joint sparsity pattern in the columns of $f$"). Buzzwords here are "joint sparsity" or "multiple measurement vectors".</p>