论文标题
非convex块 - sparse压缩感应的高阶块RIP
The high-order block RIP for non-convex block-sparse compressed sensing
论文作者
论文摘要
本文集中于块 - 宽带信号的恢复，这不仅是稀疏的，而且从线性测量中，非零元素也被逐渐成熟到某些块（簇）（群集），而不是在整个向量上进行任意分布。我们基于块RIP建立高阶足够条件，以确保通过混合$ l_2/l_p $最小化方法在无噪声案例中确切恢复每个块$ s $ s-sparse信号，并且在存在噪声的情况下信号不是准确地块 - sparse的情况下，稳定而强大的恢复。此外，获得了必要数量的随机高斯测量值的下限，以使该条件具有压倒性的概率。此外，进行的数值实验证明了该算法的性能。
This paper concentrates on the recovery of block-sparse signals, which is not only sparse but also nonzero elements are arrayed into some blocks (clusters) rather than being arbitrary distributed all over the vector, from linear measurements. We establish high-order sufficient conditions based on block RIP to ensure the exact recovery of every block $s$-sparse signal in the noiseless case via mixed $l_2/l_p$ minimization method, and the stable and robust recovery in the case that signals are not accurately block-sparse in the presence of noise. Additionally, a lower bound on necessary number of random Gaussian measurements is gained for the condition to be true with overwhelming probability. Furthermore, the numerical experiments conducted demonstrate the performance of the proposed algorithm.
