自1-bit压缩感知问题提出以来，由于其广泛的工程应用，吸引了大量从事数据分析处理、工程领域、应用数学研究人员的兴趣，最终人们把这个1-bit压缩感知问题在理论上归结为两个数学模型（见申请书正文的（3）和（4）式）。其中第一个模型本质上是一个线性问题，而第二个模型却是一个非线性问题。本基金项目将对这两个数学模型进行理论与应用（算法）的研究，从理论上考虑解的分析性质。即，什么时候解是存在唯一的？对非唯一解如何给出其特征刻画？如何求解？等问题的分析，从而指导算法的改进，并进一步应用于诸如手写字识别、分割、脑信号处理等实际问题。

Since the conception of 1-bit compressive sensing had been proposed, there are a lot of peoples, such as date analyzer、engineer and mathematician, interested in it due to its widely applications. Now, the 1-bit compressive sensing has been attributed to two mathematical model in theory (see (3) and (4) in this proposal ). Essentially, the first model is linear model and the second is nonlinear. This proposal is focus on its theoretical research and application. In theory, we will investigate the solution of 1-bit compressive sensing and its analytical properties, such as when there exists unique solution? In addition, how to character these solutions? and how to find out these solutions? Moreover, we hope to improve the algorithm and apply it to handwritten character recognition、segmentation and brain signal processing.