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In this paper, we focus on compressed sensing and recovery schemes for low-rank matrices, asking under what conditions a low-rank matrix can be sensed and recovered from incomplete, inaccurate, and noisy observations. We consider three schemes, one based on a certain Restricted Isometry Property and two based on directly sensing the row and column space of… (More)

- E . Candes, Ben Recht
- 2008 46th Annual Allerton Conference on…
- 2008

Suppose that one observes an incomplete subset of entries selected uniformly at random from a low-rank matrix. When is it possible to complete the matrix and recover the entries that have not been seen? We show that in very general settings, one can perfectly recover all of the missing entries from a sufficiently large random subset by solving a convex… (More)

- E . Candes, J. Romberg
- Data Compression Conference (DCC'06)
- 2006

We address the problem of encoding signals which are sparse, i.e. signals that are concentrated on a set of small support. Mathematically, such signals are modeled as elements in the /spl lscr//sub p/ ball for some p < 1. We describe a strategy for encoding elements of the /spl lscr//sub p/ ball which is universal in that 1) the encoding procedure is… (More)

The critical problem shared by these methods is that finding the minimum of the empirical risk requires an exhaustive search over all possible models. This search is completely intractable for even moderate values of p. We will get back to this later when we discuss the LASSO. First, we will present a lower bound, arguing that one cannot expect to do much… (More)

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