一种基于CGLS和LSQR的联合优化的匹配追踪算法

A Matching Pursuit Algorithm of Jointing Optimization Based on CGLS and LSQR

在压缩感知理论中,设计好的稀疏重构算法是一个比较重要,同时也是一个具有挑战性的问题.稀疏重构的基本目标是用较少的数据样本,通过解一个优化问题完成信号或者图像重构.关于稀疏重构过程,一个重要的研究方向是在数据受噪声干扰的情况下,如何高效快速地重建原信号.本文提出了基于共轭梯度最小二乘法(Conjugate gradient least squares,CGLS)和最小二乘QR分解(Least squares QR,LSQR)的联合优化的匹配追踪算法.该算法采用Alpha散度来测量CGLS和LSQR之间的离散度(差异度),并通过离散度来选择最优的解序列.实验分析表明基于CGLS和LSQR的联合优化的匹配追踪算法在压缩采样的信号受噪声干扰情况下具有较好的恢复能力.

For compressed sensing theory, to design a good sparse reconstruction algorithm is a challenge. The basic purpose of sparse reconstruction is to implement the signal or image reconstruction by solving optimization problem on the condition of fewer data samples. For the sparse reconstruction, an important aspect is how to reconstruct original signal when data is contaminated by noise. In this article, we present a matching pursuit algorithm, in which the conjugate gradient least squares（CGLS） method combines the least squares QR（LSQR） method to solve the optimization. This algorithm uses alpha divergence to measure dispersion between CGLS and LSQR, then selects optimization solution sequence in light of the dispersion. Experiment shows that the matching pursuit algorithm has excellent reconstruction performance when the signal of compressed sampling is contaminated.