中山大学学报（自然科学版）（中英文）2025，Vol.64Issue(3)：173-182,10.DOI:10.13471/j.cnki.acta.snus.ZR20240295
框架下组稀疏非凸压缩感知问题:零空间性质与l2/lq(0<q≤1)-综合法
Block sparse compressed sensing with frames:Null space property and l2/lq(0<q≤1)-synthesis
摘要
Abstract
This paper explores the recovery of block sparse signals in frame-based settings using the l2/lq-synthesis technique(0<q≤1).We propose a new null space property,referred to as block D-NSPq,which is based on the dictionary D.We establish that matrices adhering to the block D-NSPq condition are both necessary and sufficient for the exact recovery of block sparse signals via l2/lq-synthesis.Additionally,this condition is essential for the stable recovery of signals that are block-compressible with respect to D.This D-NSPq property is identified as the first complete condition for successful signal recovery using l2/lq-synthesis.Furthermore,we assess the theoretical efficacy of the l2/lq-synthesis method under conditions of measurement noise.关键词
压缩感知/组稀疏/l2/lq-综合法/零空间性质Key words
Compressed sensing/block sparse/l2/lq-synthesis method/null space property分类
数学引用本文复制引用
吴焚供,钟澎洪,覃跃海..框架下组稀疏非凸压缩感知问题:零空间性质与l2/lq(0<q≤1)-综合法[J].中山大学学报（自然科学版）（中英文）,2025,64(3):173-182,10.基金项目
Supported by The Featured Innovation Projects of the General University of Guangdong Province(2023KTSCX096) （2023KTSCX096）
The Special Projects in Key Areas of Guangdong Province(ZDZX1088) （ZDZX1088）
Research Team Project of Guangdong University of Education(2024KYCXTD018) （2024KYCXTD018）
