Adaptive sensing performance lower bounds for sparse signal detection and support estimation

Lower Bounds for Adaptive Sparse Recovery

We give lower bounds for the problem of stable sparse recovery from adaptive linear measurements. In this problem, one would like to estimate a vector x ∈ R from m linear measurements A1x, . . . , Amx. One may choose each vector Ai based on A1x, . . . , Ai−1x, and must output x̂ satisfying ‖x̂− x‖p ≤ (1 + ) min k-sparse x′ ‖x− x‖p with probability at least 1−δ > 2/3, for some p ∈ {1, 2}. For p = ...

Complexity Theoretic Lower Bounds for Sparse Principal Component Detection

In the context of sparse principal component detection, we bring evidence towards the existence of a statistical price to pay for computational efficiency. We measure the performance of a test by the smallest signal strength that it can detect and we propose a computationally efficient method based on semidefinite programming. We also prove that the statistical performance of this test cannot b...

Lower Bounds for Estimation

Performance Bounds for Sparse Signal Reconstruction with Multiple Side Information

In the context of compressive sensing (CS), this paper considers the problem of reconstructing sparse signals with the aid of other given correlated sources as multiple side information (SI). To address this problem, we propose a reconstruction algorithm with multiple SI (RAMSI) that solves a general weighted n-`1 norm minimization. The proposed RAMSI algorithm takes advantage of both CS and th...

Ja n 20 10 DISTILLED SENSING : ADAPTIVE SAMPLING FOR SPARSE DETECTION AND ESTIMATION

Adaptive sampling results in dramatic improvements in the recovery of sparse signals in white Gaussian noise. A sequential adap-tive sampling-and-refinement procedure called distilled sensing (DS) is proposed and analyzed. DS is a form of multi-stage experimental design and testing. Because of the adaptive nature of the data collection, DS can detect and localize far weaker signals than possibl...