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.

真实信号通常是稀疏的，因为它们通过使用适当的基数具有紧凑的表示。值得注意的例子是可以通过各种压缩技术紧凑地表示和压缩的数字图像。稀疏性利用已被证明是用于获取、传输和存储高维信号的强大工具。值得注意的是，它允许从相对较少的测量中恢复整个信号。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，聚类或块稀疏系数），从而可以更有效地恢复信号。然而，当稀疏模式不规则或未知时，如何从几次测量中有效地恢复信号在很大程度上仍然是一个未知领域。这是该项目的第一个研究重点。同时，对于信号采集，实际系统通常采用量化，将每个测量值转换为几个二进制位，以便于处理和存储。然而，大多数经典的稀疏信号恢复方法都忽略了量化的影响。直到最近，明确说明量化效果的稀疏信号重建/估计才开始受到关注，尽管大多数此类工作仅考虑启发式量化器。该项目的第二个研究重点是研究与量化相关的两个问题：（1）开发具有量化测量的有效信号恢复算法； (2)用于稀疏信号恢复的最佳量化器设计，特别是对于许多具有带宽/功率限制的传感系统所需的低速率量化的情况。该项目还有一个重要的教育部分，旨在为本科生和研究生提供综合研究经验和培训。该项目采取了多种方法来解决上述问题。首先，在聚类稀疏信号恢复方面，PI提出了一种新的贝叶斯学习框架，用于具有未知块稀疏结构的稀疏信号恢复。所提出的研究建立在一种新颖的贝叶斯分层模型的基础上，该模型涉及耦合超参数，以在不强加刚性块结构的情况下促进块稀疏性。基于所提出的模型，将开发一系列贝叶斯推理算法，同时考虑到计算效率和对噪声的鲁棒性。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的稀疏信号恢复算法的重建性能。所提出的方法包括顺序量化每个测量，使用过去的量化位来预测下一个要量化的样本，最后在预测值处进行阈值化。第三，在使用量化测量的重建算法的开发上，PI建议采用S形函数在重建信号和量化测量之间施加一致性约束，这与现有方法相比，具有降低计算复杂性和显着提高重建精度的优点。