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Two Proposals for Robust PCA using Semidefinite Programming
Michael McCoy, Joel Tropp
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 progr…
Improved analysis of the subsampled randomized Hadamard transform
Joel A. Tropp
This paper presents an improved analysis of a structured dimension-reduction map called the subsampled randomized Hadamard transform. This argument demonstrates that the map preser…
Restricted Isometries for Partial Random Circulant Matrices
Holger Rauhut, Justin Romberg, Joel A. Tropp
In the theory of compressed sensing, restricted isometry analysis has become a standard tool for studying how efficiently a measurement matrix acquires information about sparse and…
User-friendly tail bounds for sums of random matrices
Joel A. Tropp
This paper presents new probability inequalities for sums of independent, random, self-adjoint matrices. These results place simple and easily verifiable hypotheses on the summands…
The Sparsity Gap: Uncertainty Principles Proportional to Dimension
Joel A. Tropp
In an incoherent dictionary, most signals that admit a sparse representation admit a unique sparse representation. In other words, there is no way to express the signal without usi…