1-比特压缩感知的理论与算法研究

Compressive sensing has become an active research area in the field of applied and computational harmonic analysis. It has been widely used in signal acquisition and processing, medical imaging, machine learning and many other fields. The classical compressive sensing theory is developed based on the assumption that the sensing data has infinite precision. However, the sensing data is inevitably quantized in practice. An extreme quantization method is only recording the sign of the sensing data. This kind of problem is called 1-bit compressive sensing. In this project we study 1-bit compressive sensing problems, including the signal reconstruction theory and algorithms. In the theory part of this project, our goal is establishing a new mathematical model for 1-bit compressive sensing and prove it can reconstruct the sparse signal with less sensing data and is robust to noise. Moreover, we anticipate developing fast algorithms for 1-bit compressive sensing signal reconstruction and analyzing the convergence of the proposed algorithms.

压缩感知是应用与计算调和分析中比较活跃的一个研究领域，在信号采集与处理、医学成像、机器学习等方面得到广泛应用。经典的压缩感知理论是建立在感知数据具有无穷精度的基础之上。然而实际中，感知数据需要量化存储，其中一种极端的量化方式为仅保留感知数据的符号。该问题称为1-比特压缩感知问题。本项目研究1-比特压缩感知的理论与算法。在理论方面，希望建立新的1-比特压缩感知的数学模型，并证明该模型可以用更少的感知数据去重构原始稀疏信号，并且对噪声具有稳健性。在算法方面，希望发展1-比特压缩感知重构信号的快速算法，且证明算法的收敛性及收敛速率。

压缩感知是应用与计算调和分析中比较活跃的一个研究领域，在信号采集与处理、医学成像、机器学习等方面得到广泛应用。经典的压缩感知理论是建立在感知数据具有无穷精度的基础之上。然而实际中，感知数据需要量化存储，其中一种极端的量化方式为仅保留感知数据的符号。该问题称为1-比特压缩感知问题。本项目研究1-比特压缩感知的理论与算法。在理论方面，希望建立新的1-比特压缩感知的数学模型，研究其优化模型的理论、算法，并将其应用到模式识别中。