摘要
This paper explores the recovery of block sparse signals in frame-based settings using the l_(2)/l_(q)-synthesis technique(0<q≤1).We propose a new null space property,referred to as block D-NSP_(q),which is based on the dictionary D.We establish that matrices adhering to the block D-NSP_(q)condition are both necessary and sufficient for the exact recovery of block sparse signals via l_(2)/l_(q)-synthesis.Additionally,this condition is essential for the stable recovery of signals that are block-compressible with respect to D.This D-NSP_(q)property is identified as the first complete condition for successful signal recovery using l_(2)/l_(q)-synthesis.Furthermore,we assess the theoretical efficacy of the l2/lq-synthesis method under conditions of measurement noise.
研究了基于l_(2)/l_(q)(0<q≤1)-综合法重构框架下具有组稀疏结构信号的重构条件及理论性能.我们定义了一个框架意义下的新的零空间性质,称为D-NSP_(q),并证明了测量矩阵满足D-NSP_(q)性质是l_(2)/l_(q)-综合法精确重构框架下组稀疏信号的充要条件.更进一步地,我们还证明了该零空间性质还是保障l_(2)/l_(q)-综合法稳定重构框架下组稀疏信号的充要条件,并刻画了稳定重构的理论表现.从现有研究文献来看,这是第一个保障l2/lq-综合法稳定重构框架下组稀疏信号的充要条件.
出处
《中山大学学报(自然科学版)(中英文)》
北大核心
2025年第3期173-182,共10页
Acta Scientiarum Naturalium Universitatis Sunyatseni
基金
Supported by The Featured Innovation Projects of the General University of Guangdong Province(2023KTSCX096)
The Special Projects in Key Areas of Guangdong Province(ZDZX1088)
Research Team Project of Guangdong University of Education(2024KYCXTD018)。
