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Recent empirical research indicates that many convex optimization problems with random constraints exhibit a phase transition as the number of constraints increases. For example, this phenomenon emerges in the 1 minimization method for identifying a sparse vector from random linear samples. Indeed, this approach succeeds with high probability when the… (More)

The performance of principal component analysis (PCA) suffers badly in the presence of outliers. This paper proposes two novel approaches for robust PCA based on semidefinite programming. The first method, maximum mean absolute deviation rounding (MDR), seeks directions of large spread in the data while damping the effect of outliers. The second method… (More)

- Dennis Amelunxen, Martin Lotz, Michael B. McCoy, Joel A. Tropp
- ArXiv
- 2013

Recent empirical research indicates that many convex optimization problems with random constraints exhibit a phase transition as the number of constraints increases. For example, this phenomenon emerges in the l1 minimization method for identifying a sparse vector from random linear samples. Indeed, this approach succeeds with high probability when the… (More)

- Michael B. McCoy, Joel A. Tropp
- ArXiv
- 2013

Demixing is the problem of identifying multiple structured signals from a superimposed, undersampled, and noisy observation. This work analyzes a general framework, based on convex optimization, for solving demixing problems. When the constituent signals follow a generic incoherence model, this analysis leads to precise recovery guarantees. These results… (More)

- Gilad Lerman, Michael B. McCoy, Joel A. Tropp, Teng Zhang
- Foundations of Computational Mathematics
- 2015

Consider a dataset of vector-valued observations that consists of noisy inliers, which are explained well by a low-dimensional subspace, along with some number of outliers. This work describes a convex optimization problem, called REAPER, that can reliably fit a low-dimensional model to this type of data. This approach parameterizes linear subspaces using… (More)

- Michael B. McCoy, Joel A. Tropp
- Foundations of Computational Mathematics
- 2014

Demixing refers to the challenge of identifying two structured signals given only the sum of the two signals and prior information about their structures. Examples include the problem of separating a signal that is sparse with respect to one basis from a signal that is sparse with respect to a second basis, and the problem of decomposing an observed matrix… (More)

- Michael B. McCoy, Volkan Cevher, Quoc Tran-Dinh, Afsaneh Asaei, Luca Baldassarre
- IEEE Signal Processing Magazine
- 2014

Source separation, or demixing, is the process of extracting multiple components entangled within a signal. Contemporary signal processing presents a host of difficult source separation problems, from interference cancellation to background subtraction, blind deconvolution, and even dictionary learning. Despite the recent progress in each of these… (More)

- Michael B. McCoy, Joel A. Tropp
- ArXiv
- 2012

- Michael B. McCoy, Joel A. Tropp
- Discrete & Computational Geometry
- 2014

The intrinsic volumes of a convex cone are geometric functionals that return basic structural information about the cone. Recent research has demonstrated that conic intrinsic volumes are valuable for understanding the behavior of random convex optimization problems. This paper develops a systematic technique for studying conic intrinsic volumes using… (More)

- Gilad Lerman, Michael B. McCoy, Joel A. Tropp, Teng Zhang
- ArXiv
- 2012

Consider a dataset of vector-valued observations that consists of a modest number of noisy inliers, which are explained well by a low-dimensional subspace, along with a large number of outliers, which have no linear structure. This work describes a convex optimization problem, called reaper, that can reliably fit a low-dimensional model to this type of… (More)