脉冲噪声下的稀疏重建与低秩逼近算法研究

In recent years, sparse reconstruction and low-rank approximation in low-dimensional measurement space have been receiving considerable interest in the thrust of information science, which has been widely used in signal processing, wireless communications, and machine learning, etc. However, most of the existing approaches for sparse reconstruction and low-rank approximation rest upon the assumption of Gaussian background noise, and cannot be applicable to the impulse noise environment, and the associated performance will be severely degraded in the presence of impulsive noise. ..This project aims at designing low computational complexity and high accuracy algorithms for sparse reconstruction and low-rank approximation from the low-dimensional data in impulse noise environment, mainly based on the block Majorization Minimization (MM) and generalized approximate message passing (GAMP). In terms of sparse reconstruction, we respectively design a joint signal recovery algorithm by using the greedy block MM principle and a joint signal recovery algorithm with group sparsity via the GAMP inference. In terms of low-rank approximation, by leveraging the matrix factorization method and combing with the parallel block MM principle and the GAMP approach, we propose some novel algorithms for the asymmetric and symmetric low-rank matrix decomposition approximation for fending against the impulse noise. The algorithms studied in this project are oriented to the practical application background, and has important theoretical significance and engineering importance.

近年来，低维测量空间中的稀疏重建与低秩逼近已成为信息领域发展极为迅猛的一个研究热点，已广泛应用于信号处理、无线通信及机器学习等领域。然而，现有大多数稀疏重建与低秩逼近算法都是基于高斯背景噪声展开分析的，对实际系统中广泛存在的非高斯脉冲噪声并不适用甚至性能严重下降。..本项目将以被脉冲噪声污染的低维测量数据为对象，以低计算复杂度及高准确度为目标，以块优化最小化和广义近似消息传递为技术基础，设计对脉冲噪声具有鲁棒性的稀疏重建与低秩逼近算法。在稀疏重建方面，拟研究基于贪婪块优化最小化的联合稀疏信号恢复和广义近似消息传递的结构化联合信号恢复算法。在低秩逼近方面，借助矩阵因子分解思想，并结合并行块优化最小化及广义近似消息传递，研究适用于脉冲噪声的非对称和对称低秩矩阵分解逼近算法。本课题研究的算法以实际应用背景为导向，具有重要的理论研究意义和工程应用价值。

稀疏重建与低秩逼近已广泛地应用于信号处理、无线通信及机器学习等领域，高效、鲁棒及可扩展的稀疏重构与低秩逼近算法是实现其应用的前提条件。本青年基金项目主要研究稀疏重建与低秩逼近算法及其应用，取得的主要研究进展包括：1）提出了一种基于马尔科夫-消息传递的聚类稀疏重建算法，并应用于大规模多输入多输出无线通信系统的超分辨信道估计；2）针对块稀疏信号的压缩感知重建问题，提出一种基于方差状态传播的迭代近似消息传递算法；3）针对脉冲噪声下的双线性矩阵分解及非负对称矩阵分解，提出了基于块优化最小化的鲁棒快速低秩逼近算法；4）提出了一种基于广义近似消息传递的仿射双线性矩阵分解算法，用于解决智能反射面辅助的大规模MIMO系统的级联信道估计问题；5）提出了一种基于广义近似消息传递的三线性矩阵分解算法，并用于解决智能反射面辅助的大规模MIMO系统的半盲级联信道估计问题。项目在研期间，课题组共发表5篇IEEE期刊论文，其中1篇期刊论文入选为ESI高被引和热点论文；申请中国发明专利3项，授权1项；完成既定任务。