CIF: Small: Soft Inference under Structured Sparsity

CIF：小：结构化稀疏下的软推理

• 批准号: 1018368
• 负责人: Philip Schniter
• 金额: $ 42.3万
• 依托单位: Ohio State University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2010
• 资助国家: 美国
• 起止时间: 2010-10-01 至 2015-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1018368&HistoricalAwards=false
• 关键词: CIF; Small; Soft; Inference; under

In recent years, it has come to light that many signal estimation and detection problems in engineering, science, and statistics are significantly aided by modeling the signal as sparse in some basis.By now, a relatively comprehensive theory has been constructed for such signal models, yielding algorithms that give provably good performance even when sampling far below the Nyquist rate.The structure of real-world signals often goes beyond simple sparsity, though.For example, the wavelet coefficients of natural scenes are not only sparse, but also show persistence across scales of the wavelet tree.Recent investigations of structure within sparsity show that it can be exploited to yield gains in estimation performance, though existing results are somewhat limited.For example, existing approaches strive to find only the single "best"estimate, whereas many applications would like to know the set of all reasonable estimates along with relative confidence values, i.e., "soft" estimates.This research investigates soft inference strategies leveraging a statistical modeling framework based on hidden state variables.Here, e.g., using binary states would facilitate a sparse signal model, and using Markov structures on the binary states would facilitate structured sparsity.In particular, this research investigates iterative and sequential Bayesian approaches to soft inference, building on state-of-the-art algorithms used in noncoherent communication receivers that go by the name of "turbo equalization" and "sphere decoding."This research also investigates fundamental issues in communication over sparse fading channels.While existing approaches have focused on the problem of find the "best"sparse channel estimate for subsequent use in a coherent decoding algorithm, communication theory instead prescribes a decoding metric based on model-averaging of soft sparse channel estimates.

近年来，在工程、科学和统计学中，许多信号估计和检测问题都需要在一定的基础上将信号建模为稀疏信号，目前已经建立了较为完善的信号模型理论，产生算法，即使在采样率远低于奈奎斯特速率时也能提供可证明的良好性能。然而，世界信号往往超越简单的稀疏性。例如，自然场景的小波系数不仅是稀疏的，而且在小波树的尺度上也表现出持续性。最近对稀疏性中的结构的研究表明，它可以被利用来产生估计性能的增益，尽管现有的结果有些有限。例如，现有的方法努力仅找到单个“最佳“估计，而许多应用想要知道所有合理估计的集合沿着相对置信度值，即，“软”估计。这项研究调查利用基于隐藏状态变量的统计建模框架的软推理策略。在这里，例如，使用二进制状态将有助于稀疏信号模型，并使用马尔可夫结构的二进制状态将有助于结构化sparsity.In特别是，本研究探讨迭代和顺序贝叶斯方法的软推理，国家的最先进的算法，用于非相干通信接收机的名称为“涡轮均衡”和“球解码”。本研究还探讨了稀疏衰落信道通信中的基本问题。虽然现有的方法都集中在找到“最佳“稀疏信道估计的问题，以供随后在相干解码算法中使用，通信理论，而不是规定一个基于软稀疏信道估计的模型平均的解码度量。