干扰环境下压缩感知：方法及应用

In recent years, Compressed sensing (CS) is one of the hottest research directions in the field of signal processing. In the traditional model of compressed sensing, in general, the random noises are taken into account. However, considering the structural corruption in the model can express the interfered environments in actual engineering more precisely and can simplfy the processing. This proposal wishes to research the theoretical methods in this kind of compressed sensing for corrupted cases. Also, the results of the research will be applied to some engineering fields. In light of engineering practice, this project will study the essential theory and key technology of compressed sensing in this corrupted environment. The research is mainly divided into the following aspects: according to the physical mechanism of interferences, various corruptions with some structures and practical meanings will be considered to construct the new models of compressed sensing that will be almost coincident with the engineering. For the corrupted models, the signal recovery algorithms will be studied. At same time, the recoverability of the algorithms will be discussed in the corrupted environments. Finally, some software package will be made based on our contribution and will be applied to some practices. In order to suppress the corruptions and noises, to reduce the number of the observed measurements, and to ensure the recovery reliably at the same time, in the research, some mathematical methods and machine learning methods will be used, such as the space correlation analysis, linear and nonlinear functional analysis, stochastic analysis, probability and statistics, numerical analysis, optimization theory, and sub-supervised or unsupervised learning methods. The proposal intends some influential achievements both in the essential theory and key technology with high performance.

压缩感知是近年来信号处理领域热门研究方向之一。传统压缩感知模型一般仅考虑随机噪声干扰，而同时考虑带有结构化干扰的模型更能具体反映工程实际，且能使处理变得简单。本项目针对此类有干扰环境下的压缩感知，探讨其理论方法，推动它在工程中的应用。 基于工程实际，本项目将研究干扰环境下的压缩感知基本理论与关键技术，主要包括以下几方面的内容：针对干扰的物理机制，研究各种具有工程意义的、有结构的干扰信号，建立新的符合实际的干扰压缩感知模型；针对所构造的干扰模型，研究相应的信号恢复算法；同时，针对新的干扰模型研究稀疏信号的可恢复性基本理论；基于这些研究，形成算法软件包，应用于实际工程。 为同时达到抗干扰、降低采样数与可靠恢复原信号的目的，在研究中将采用空间相关性分析、线性与非线性泛函分析、随机分析、概率统计、数值分析、最优化理论等数学方法和机器学习方法，以期在基本理论和高性能关键技术方面取得有影响力的成果。

压缩感知是一种新颖的信号采样方法，在低于传统奈奎斯特采样率的情况下，对具有一定稀疏特性的信号进行采样，而且在一些先决条件下能够从较少的采样信号中重构原信号。压缩感知的潜在应用相当广泛，例如，压缩感知雷达、压缩感知磁共振成像等等。但是在工程应用场景中干扰总是存在的，例如各种噪声的干扰必须考虑。不考虑干扰的研究成果无法实际应用。本项目主要内容是，在干扰环境下，研究压缩感知的方法、算法和应用中的关键问题。.研究成果，主要有：噪声干扰环境下，压缩感知中信号可恢复性的研究，信号恢复算法的研究，得到了保证原信号（或者其支撑）可恢复的新的理论结果，得到了与干扰相关的参数取法机理；对于不同的噪声干扰，给出了适用于通信信号处理、磁共振成像、图像处理等应用的实值及复值信号的恢复算法，成果中算法在速度、精度和鲁棒性能方面均已证实相对于传统算法具有优势。在应用方面针对射频探测信号处理、磁共振成像、图像处理、人脸识别、室内定位等问题展开研究取得了相应的能够抗干扰的算法，同时申请了相应的专利。