稳健的一比特压缩感知方法及其应用

One-bit compressive sensing (1bit-CS) is a recently proposed method which can recover sparse signals from signs of the samplings. Since samplings' signs can be obtained by a compactor, which operates at low power and a high rate, 1bit-CS becomes very attractive. To further improve the performance of the existing 1bit-CS algorithms, especially for the robustness and sparseness, we in this project are aiming at: i) to statistically investigate the noise of 1bit-CS system and then to develop a new recovery algorithm; ii) to design robust 1bit-CS, for which the discussion is similar to the robustness for classification; iii) to enhance the sparsity via utilizing non-convex regularizations, for which fast algorithms are required; iv) to further consider mixed 1bit model that can acquire information from sensing system with saturation phenomenon; v) applying the proposed algorithm on X-ray computed tomography, for which saturation could occur due to over-exposure or low-dose.

一比特压缩感知是利用稀疏性从采样的符号中进行信号恢复的新型技术。由于采样上的便利性和广泛的应用前景，这一方法在近年来吸引了越来越多的关注。针对现有一比特压缩感知算法的恢复精度欠佳、稳健性不足等问题，本项目计划展开以下研究：1）通过对噪声和野值进行合理的统计建模，发展新型的信号恢复算法；2）借鉴分类问题中的稳健罚函数，构建稳健的一比特压缩感知方法；3）利用非凸正则化项增强算法的稀疏性，同时发展相应的快速求解策略；4）利用一比特压缩感知对符号信息的获取能力，设计信号恢复算法用以处理采样系统中的饱和现象；5）将所发展的算法应用于断层扫描图像的恢复，处理过曝光或低剂量照射造成的饱和现象。

本项目主要研究一比特压缩感知方法，针对其恢复精度和稳健性不足的问题设计相应的模型和算法，发展新型信号恢复方法以处理符号采样与连续采样混合的系统，并应用于计算机断层扫描重建问题中。研究工作主要取得了以下几个方面的成果：1）构建了稳健的一比特压缩感知方法；2）设计了适用于一比特压缩感知方法的非凸正则化项；3）提出了处理普通信号和一比特信号的混合一比特压缩感知方法；4）应用混合一比特压缩感知方法处理CT重建中的过曝光饱和及植入物遮挡问题。