Papers Published
- Reeves, G; Gastpar, MC, Approximate sparsity pattern recovery: Information-theoretic lower bounds,
Ieee Transactions on Information Theory, vol. 59 no. 6
(May, 2013),
pp. 3451-3465, Institute of Electrical and Electronics Engineers (IEEE) [doi] .
(last updated on 2021/05/11)Abstract:
Recovery of the sparsity pattern (or support) of an unknown sparse vector from a small number of noisy linear measurements is an important problem in compressed sensing. In this paper, the high-dimensional setting is considered. It is shown that if the measurement rate and per-sample signal-to-noise ratio (SNR) are finite constants independent of the length of the vector, then the optimal sparsity pattern estimate will have a constant fraction of errors. Lower bounds on the measurement rate needed to attain a desired fraction of errors are given in terms of the SNR and various key parameters of the unknown vector. The tightness of the bounds in a scaling sense, as a function of the SNR and the fraction of errors, is established by comparison with existing achievable bounds. Near optimality is shown for a wide variety of practically motivated signal models. © 1963-2012 IEEE.