压缩感知中噪声感知Lq最优化模型的统一恢复界估计
A unified recovery bound estimation for noise-aware Lq optimization model in compressed sensing
摘要：
本文给出了压缩感知中Lq（0 < q < 1）最优化模型的稳定恢复界的统一结果，该模型是一个线性系中存在噪声的约束Lq最小化问题.具体而言，不使用限制等距常数（RIC），我们证明了任何全局解决方案的噪声感知Lq最优化模型和理想的稀疏解的无噪声模型之间的误差是上界由一个常数乘以噪声水平，给定理想的解决方案的稀疏性是小于一定数量。引入了一个有趣的参数{gamma}，它表示差错向量的稀疏程度，并在我们的分析中起着重要的作用。此外，当γ > 2时，Lq（0 < q < 1）模型的恢复界比L1模型的恢复界小于，并且Lq（0 < q < 1）模型对理想解的稀疏性要求比L1模型的弱.
英文摘要：
In this letter, we present a unified result for the stable recovery bound of Lq(0 < q < 1) optimization model in compressed sensing, which is a constrained Lq minimization problem aware of the noise in a linear system. Specifically, without using the restricted isometry constant (RIC), we show that the error between any global solution of the noise-aware Lq optimization model and the ideal sparse solution of the noiseless model is upper bounded by a constant times the noise level,given that the sparsity of the ideal solution is smaller than a certain number. An interesting parameter {gamma} is introduced, which indicates the sparsity level of the error vector and plays an important role in our analysis. In addition, we show that when γ > 2, the recovery bound of the Lq (0 < q < 1) model is smaller than that of the L1 model, and the sparsity requirement of the ideal solution in the Lq(0 < q < 1) model is weaker than that of the L1 model.
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