Stable principal component pursuit
In this paper, we study the problem of recovering a low-rank matrix (the principal
components) from a high-dimensional data matrix despite both small entry-wise noise and
gross sparse errors. Recently, it has been shown that a convex program, named Principal
Component Pursuit (PCP), can recover the low-rank matrix when the data matrix is corrupted
by gross sparse errors. We further prove that the solution to a related convex program (a
relaxed PCP) gives an estimate of the low-rank matrix that is simultaneously stable to small …
components) from a high-dimensional data matrix despite both small entry-wise noise and
gross sparse errors. Recently, it has been shown that a convex program, named Principal
Component Pursuit (PCP), can recover the low-rank matrix when the data matrix is corrupted
by gross sparse errors. We further prove that the solution to a related convex program (a
relaxed PCP) gives an estimate of the low-rank matrix that is simultaneously stable to small …
Compressive principal component pursuit
We consider the problem of recovering a target matrix that is a superposition of low-rank and
sparse components, from a small set of linear measurements. This problem arises in
compressed sensing of structured high-dimensional signals such as videos and
hyperspectral images, as well as in the analysis of transformation invariant low-rank
structure recovery. We analyse the performance of the natural convex heuristic for solving
this problem, under the assumption that measurements are chosen uniformly at random. We …
sparse components, from a small set of linear measurements. This problem arises in
compressed sensing of structured high-dimensional signals such as videos and
hyperspectral images, as well as in the analysis of transformation invariant low-rank
structure recovery. We analyse the performance of the natural convex heuristic for solving
this problem, under the assumption that measurements are chosen uniformly at random. We …
