lp范数最小化问题下部分稀疏信号的稳定恢复

摘要

The problem of recovering a partially sparse signal stably from a given set of noisy linear measurements is studied via lp norm minimization method.A sufficient partial restricted p-isometry properties(p-RIP) condition is proposed and an error between the solution of the noisy lp minimization and the original signal needs to recover is obtained.Moreover,in the condition of no noise,a lower bound on the number of random Gaussian measurements is given to recover the partially sparse signal by lp minimization with high probability.%通过lp范数最小化模型,研究了在有噪音线性测量值下稳定恢复部分稀疏信号的问题.首先提出了恢复信号的充分条件:部分p-限制等距条件(p-RIP),并推导出此模型的最优解与要恢复的原始信号误差范围.最后在无噪音lp范数最小化问题模型下,计算出至少多少随机高斯测量值能够以高概率恢复部分稀疏信号.