Open AccessReconstruction analysis of block‐sparse signal via truncated ℓ 2 / ℓ 1 ‐minimisation with redundant dictionaries
Author(s) -
Liu Jiayi,
Wang Jianjun,
Zhang Feng
Publication year - 2018
Publication title -
iet signal processing
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.384
H-Index - 42
ISSN - 1751-9683
DOI - 10.1049/iet-spr.2018.0004
Subject(s) - minimisation (clinical trials) , signal recovery , computer science , algorithm , signal reconstruction , signal processing , mathematical optimization , block (permutation group theory) , mathematics , pattern recognition (psychology) , compressed sensing , artificial intelligence , statistics , telecommunications , combinatorics , radar
Here, the authors discuss the recovery of signals from under‐sampled data in which signals are nearly block sparse via a truncated ℓ 2 / ℓ 1 method with redundant dictionaries. The authors show that the obtained results are better than the previous recovery result in the existence of noise. Furthermore, the authors conduct an alternating direction method of multipliers algorithm to solve the signals recovery problem. Moreover, the numerical experiments prove the strong robustness and stability of truncated ℓ 2 / ℓ 1 method with redundant dictionaries ( t ‐ D ‐ block ‐ ℓ 1 ) in the presence of noise.