Signal Recovery with Unknown Clustered Sparsity and Quantization

具有未知聚类稀疏性和量化的信号恢复

• 批准号: 1408182
• 负责人: Hongbin Li
• 金额: $ 29.5万
• 依托单位: Stevens Institute of Technology
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2014
• 资助国家: 美国
• 起止时间: 2014-08-01 至 2018-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1408182&HistoricalAwards=false
• 关键词: Signal; Recovery; Unknown; Clustered; Sparsity

Real-word signals are often sparse in that they have compact representation by using proper bases. Notable examples are digital images which can be compactly represented and compressed via various compression techniques. Sparsity exploitation has proven a powerful tool for the acquisition, transmission, and storage of high-dimensional signals. Remarkably, it allows recovering the entire signal from relatively few measurements. Many sparse signals such as images, audio and video signals also exhibit some sparsity pattern (e.g., clustered or block sparse coefficients) that admits more efficient signal recovery. However, when the sparsity pattern is irregular or unknown, how to efficiently recover the signal from a few measurements is still largely an uncharted territory. This is the first research thrust pursued in this project. Meanwhile, for signal acquisition, practical systems usually employ quantization which converts each measurement into a few binary bits to facilitate processing and storage. The effect of quantization, however, was neglected by most classical sparse signal recovery methods. Only recently, sparse signal reconstruction/estimation which explicitly accounts for the effect of quantization started to receive attention, although most such works just considered heuristic quantizers. A second research thrust of this project examines two problems related to quantization: (1) development of efficient signal recovery algorithms with quantized measurements; and (2) optimum quantizer design for sparse signal recovery, in particular for the case of low-rate quantization which is required in many sensing systems that have bandwidth/power constraints. This project also has a significant educational component aimed to provide integrated research experience and training for undergraduate and graduate students. This project takes several approaches to address the above problems. First, on clustered sparse signal recovery, the PI proposes a new Bayesian learning framework for sparse signal recovery with unknown block sparsity structure. The proposed research builds on a novel Bayesian hierarchical model involving coupled hyperparameters to promote block sparsity without imposing rigid block structures. Based on the proposed models, a range of Bayesian inference algorithms are to be developed, taking into account of computational efficiency and robustness to noise. Second, on low-rate quantizer design, the PI proposes an adaptive quantization approach to enhance the reconstruction performance of sparse signal recovery algorithms taking quantized measurements. The proposed approach involves sequentially quantizing each measurement, using past quantized bits to predict the next sample to be quantized, and finally thresholding at the predicted value. Third, on the development of reconstruction algorithms using quantized measurements, the PI proposes to employ a sigmoid function to impose a consistency constraint between the reconstructed signal and the quantized measurements, which is shown to offer the benefit of computational complexity reduction and significant reconstruction accuracy improvement over existing methods.

现实信号通常很少，因为它们通过使用适当的基础具有紧凑的表示形式。值得注意的例子是数字图像，可以通过各种压缩技术紧凑和压缩。稀疏性开发已证明是一种强大的工具，用于获取，传输和存储高维信号。值得注意的是，它允许从相对较少的测量值中恢复整个信号。许多稀疏信号（例如图像，音频和视频信号）也表现出一些稀疏模式（例如，聚类或阻止稀疏系数），这些模式可以接收更有效的信号恢复。但是，当稀疏性模式不规则或未知时，如何从几个测量中有效恢复信号仍然很大程度上是一个未知的领域。这是该项目中首次提出的研究。同时，对于信号获取，实用系统通常采用量化，将每个测量值转换为一些二进制位以促进处理和存储。但是，大多数经典的稀疏信号恢复方法忽略了量化的效果。直到最近，明确解释量化效果的稀疏信号重建/估计才开始受到关注，尽管大多数这样的工作只是被认为是启发式量化器。该项目的第二项研究作用研究了与量化有关的两个问题：（1）通过量化测量的有效信号回收算法的开发； （2）用于稀疏信号恢复的最佳量化设计，特别是对于具有带宽/功率约束的许多传感系统所需的情况。该项目还具有重要的教育部分，旨在为本科生和研究生提供综合的研究经验和培训。该项目采用了几种方法来解决上述问题。首先，在聚类的稀疏信号恢复上，PI提出了一个新的贝叶斯学习框架，用于稀疏信号恢复，具有未知的块稀疏结构。拟议的研究建立在一个新型的贝叶斯分层模型的基础上，该模型涉及耦合的超参数，以促进块稀疏性而不施加刚性块结构。根据提出的模型，考虑到计算效率和噪声鲁棒性，将开发一系列贝叶斯推理算法。其次，在低速率量化器设计上，PI提出了一种自适应量化方法，以增强采用量化测量值的稀疏信号回收算法的重建性能。所提出的方法涉及使用过去的量化位依次量化每个测量值，以预测要量化的下一个样品，最后以预测值进行阈值。第三，关于使用量化测量值的重建算法的开发，PI提议采用Sigmoid函数来在重建信号和量化测量值之间施加一致性约束，这证明可以提供计算复杂性降低和显着重构准确性改善现有方法的好处。