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Principal Component Pursuit with Reduced Linear Measurements
Principal Component Pursuit Reduced Linear Measurements low-rank matrix sparse matrix
2012/3/1
In this paper, we study the problem of decomposing a superposition of a low-rank matrix and a sparse matrix when a relatively few linear measurements are available. This problem arises in many data pr...
Sparse approximation property and stable recovery of sparse signals from noisy measurements
Sparse approximation property noisy measurements Information Theory
2011/9/21
Abstract: In this paper, we introduce a sparse approximation property of order $s$ for a measurement matrix ${\bf A}$: $$\|{\bf x}_s\|_2\le D \|{\bf A}{\bf x}\|_2+ \beta \frac{\sigma_s({\bf x})}{\sqrt...
Non-adaptive probabilistic group testing with noisy measurements: Near-optimal bounds with efficient algorithms
Non-adaptive probabilistic group noisy measurements Near-optimal bounds efficient algorithms
2011/9/19
Abstract: We consider the problem of detecting a small subset of defective items from a large set via non-adaptive "random pooling" group tests. We consider both the case when the measurements are noi...
On the information-theoretic structure of distributed measurements
information-theoretic structure Information Theory Category Theory
2011/8/26
Abstract: The internal structure of a measuring device, which depends on what its components are and how they are organized, determines how it categorizes its inputs. This paper presents a geometric a...