Electronic Journal of Statistics

Recovering block-structured activations using compressive measurements

Sivaraman Balakrishnan, Mladen Kolar, Alessandro Rinaldo, and Aarti Singh

Full-text: Open access

Abstract

We consider the problems of detection and support recovery of a contiguous block of weak activation in a large matrix, from noisy, possibly adaptively chosen, compressive (linear) measurements. We precisely characterize the tradeoffs between the various problem dimensions, the signal strength and the number of measurements required to reliably detect and recover the support of the signal, both for passive and adaptive measurement schemes. In each case, we complement algorithmic results with information-theoretic lower bounds. Analogous to the situation in the closely related problem of noisy compressed sensing, we show that for detection neither adaptivity, nor structure reduce the minimax signal strength requirement. On the other hand we show the rather surprising result that, contrary to the situation in noisy compressed sensing, the signal strength requirement to recover the support of a contiguous block-structured signal is strongly influenced by both the signal structure and the ability to choose measurements adaptively.

Article information

Source
Electron. J. Statist., Volume 11, Number 1 (2017), 2647-2678.

Dates
Received: August 2016
First available in Project Euclid: 27 June 2017

Permanent link to this document
https://projecteuclid.org/euclid.ejs/1498528883

Digital Object Identifier
doi:10.1214/17-EJS1267

Mathematical Reviews number (MathSciNet)
MR3679905

Zentralblatt MATH identifier
1366.62034

Subjects
Primary: 62F03: Hypothesis testing
Secondary: 62F10: Point estimation

Keywords
Adaptive sensing linear measurements structured normal means

Rights
Creative Commons Attribution 4.0 International License.

Citation

Balakrishnan, Sivaraman; Kolar, Mladen; Rinaldo, Alessandro; Singh, Aarti. Recovering block-structured activations using compressive measurements. Electron. J. Statist. 11 (2017), no. 1, 2647--2678. doi:10.1214/17-EJS1267. https://projecteuclid.org/euclid.ejs/1498528883


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