A Measurement Rate-MSE Tradeoff for Compressive Sensing Through Partial Support Recovery
| Autor: | Ragnar Thobaben, Ricardo Blasco-Serrano, Mikael Skoglund, Dennis Sundman, Dave Zachariah |
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| Jazyk: | angličtina |
| Rok vydání: | 2014 |
| Předmět: |
Mathematical optimization
Mean squared error 02 engineering and technology 01 natural sciences Set (abstract data type) 010104 statistics & probability Matrix (mathematics) MSE Dimension (vector space) 0202 electrical engineering electronic engineering information engineering Fraction (mathematics) 0101 mathematics Electrical and Electronic Engineering support recovery Mathematics performance tradeoff Estimator 020206 networking & telecommunications Compressive sensing Binary logarithm Telekommunikation Compressed sensing Signal Processing Telecommunications Algorithm sparse signal |
| Popis: | We consider the problem of estimating sparse vectors from noisy linear measurements in the high dimensionality regime. For a fixed number k of nonzero entries, we study the fundamental relationship between two relevant quantities: the measurement rate, which characterizes the asymptotic behavior of the dimensions of the measurement matrix in terms of the ratio m/log n (with m being the number of measurements and n the dimension of the sparse vector), and the estimation mean square error. First, we use an information-theoretic approach to derive sufficient conditions on the measurement rate to reliably recover a part of the support set that represents a certain fraction of the total vector power. Second, we characterize the mean square error of an estimator that uses partial support set information. Using these two parts, we derive a tradeoff between the measurement rate and the mean-square error. This tradeoff is achievable using a two-step approach: first support set recovery, and then estimation of the active components. Finally, for both deterministic and random vectors, we perform a numerical evaluation to verify the advantages of the methods based on partial support set recovery. |
| Databáze: | OpenAIRE |
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