多面体块稀疏表示和非凸压缩感知

Block sparse representation of a polytope and non-convex compressed sensing

压缩感知(compressed sensing,CS)理论表明稀疏信号可以从欠定系统中被准确恢复,但在很多实际应用中,信号不一定有标准稀疏性而可能拥有一些其他的结构特点,典型的一种就是块稀疏信号,它的非零元仅在很少的一些块中出现.本文考虑从很少的线性测量中恢复块稀疏信号,并得到经混合l_(2)=l_(q)(0<q ≤1)最小化准确重构块稀疏信号时,测量矩阵需满足的充分条件,同时进一步给出带噪声时稳定恢复的紧性分析.

It is stated in compressed sensing(CS)that a sparse signal can be recovered accurately from the underdetermined system.While in many applications,real-world signals do not necessarily have standard sparsity,but exhibit additional structures.A typical one is the so-called block-sparse signal whose non-zero coefficients occur in a few blocks.In this paper,we consider recovering the block-sparse signal from very few linear measurements via mixed l_(2)/l_(q)(0<q≤1)norm minimization,and obtain the sufficient condition that the measurement matrix should satisfy.Furthermore,we give the sharp analysis of stable recovery in the noisy case.