Adaptive Compressed Sensing for Support Recovery of Structured Sparse Sets

Abstract

This paper investigates the problem of recovering the support of structured signals via adaptive compressive sensing. We examine several classes of structured support sets, and characterize the fundamental limits of accurately recovering such sets through compressive measurements, while simultaneously providing adaptive support recovery protocols that perform near optimally for these classes. We show that by adaptively designing the sensing matrix we can attain significant performance gains over nonadaptive protocols. These gains arise from the fact that adaptive sensing can: (i) better mitigate the effects of noise, and (ii) better capitalize on the structure of the support sets. * The authors are with the

Compressive domain spatial–temporal difference saliency‐based realtime adaptive measurement method for video recovery

“…The adaptive objects of the classical ACS include sensing matrix, sparse basis, sparse dictionary, and so on [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20].…”

“…The adaptive target of references [1][2][3][4][5][6][7][8][9][10] is the sensing matrix. Castro and Tánczos [1] propose a method of recovering the support of structured signals by adaptively designing the sensing matrix. Kim et al [2] present an adaptive CS method for terahertz reflection tomography through two-stage sensing matrices.…”

An Adaptive Rate Blocked Compressive Sensing Method for Video

“…For the sampling device, the information that can be directly obtained is no longer the original signal, but the result of the CS measurement, which is called the "CS domain signal". In earlier studies, researchers mainly used the CS domain signal to reconstruct the original signal, then used the reconstructed signal to estimate the characteristics of the original signal, and adaptively adjusted the CS matrix [15][16][17], sparse basis [18,19], sparse dictionary [20,21] or sampling rate [22,23]. The advantage of these methods is that it can obtain the characteristics of the original signal with high accuracy, and then make full use of the characteristics of the signal to adjust one or more sampling elements.…”