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- Emmanuel J. Candès, Terence Tao
- IEEE Transactions on Information Theory
- 2005

This paper considers a natural error correcting problem with real valued input/output. We wish to recover an input vector f/spl isin/R/sup n/ from corrupted measurements y=Af+e. Here, A is an m by n (coding) matrix and e is an arbitrary and unknown vector of errors. Is it possible to recover f exactly from the data y? We prove that under suitable conditions… (More)

- Emmanuel J. Candès, Xiaodong Li, Yi Ma, John Wright
- J. ACM
- 2011

This article is about a curious phenomenon. Suppose we have a data matrix, which is the superposition of a low-rank component and a sparse component. Can we recover each component individually? We prove that under some suitable assumptions, it is possible to recover both the low-rank and the sparse components <i>exactly</i> by solving a very… (More)

- Emmanuel J. Candès, Justin K. Romberg, Terence Tao
- IEEE Transactions on Information Theory
- 2006

This paper considers the model problem of reconstructing an object from incomplete frequency samples. Consider a discrete-time signal f/spl isin/C/sup N/ and a randomly chosen set of frequencies /spl Omega/. Is it possible to reconstruct f from the partial knowledge of its Fourier coefficients on the set /spl Omega/? A typical result of this paper is as… (More)

Suppose we wish to recover a vector x 0 ∈ R m (e.g. a digital signal or image) from incomplete and contaminated observations y = Ax 0 + e; A is a n by m matrix with far fewer rows than columns (n m) and e is an error term. Is it possible to recover x 0 accurately based on the data y? To recover x 0 , we consider the solution x to the 1-regularization… (More)

It is now well-known that one can reconstruct sparse or compressible signals accurately from a very limited number of measurements , possibly contaminated with noise. This technique known as " compressed sensing " or " compressive sampling " relies on properties of the sensing matrix such as the restricted isometry property. In this Note, we establish new… (More)

- Emmanuel J. Candès, Benjamin Recht
- Commun. ACM
- 2009

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

- Jian-Feng Cai, Emmanuel J. Candès, Zuowei Shen
- SIAM Journal on Optimization
- 2010

This paper introduces a novel algorithm to approximate the matrix with minimum nuclear norm among all matrices obeying a set of convex constraints. This problem may be understood as the convex relaxation of a rank minimization problem, and arises in many important applications as in the task of recovering a large matrix from a small subset of its entries… (More)

- Emmanuel J. Candès, Terence Tao
- IEEE Transactions on Information Theory
- 2006

Suppose we are given a vector f in a class FsubeRopf<sup>N </sup>, e.g., a class of digital signals or digital images. How many linear measurements do we need to make about f to be able to recover f to within precision epsi in the Euclidean (lscr<sub>2</sub>) metric? This paper shows that if the objects of interest are sparse in a fixed basis or… (More)

- Emmanuel J. Candès, Laurent Demanet, David L. Donoho, Lexing Ying
- Multiscale Modeling & Simulation
- 2006

This paper describes two digital implementations of a new mathematical transform, namely, the second generation curvelet transform [12, 10] in two and three dimensions. The first digital transformation is based on unequally-spaced fast Fourier transforms (USFFT) while the second is based on the wrapping of specially selected Fourier samples. The two… (More)

It is now well understood that (1) it is possible to reconstruct sparse signals exactly from what appear to be highly incomplete sets of linear measurements and (2) that this can be done by constrained ℓ 1 minimization. In this paper, we study a novel method for sparse signal recovery that in many situations outperforms ℓ 1 minimization in the sense that… (More)