CIF: Small: Soft Inference under Structured Sparsity

近年来，工程、科学和统计学中的许多信号估计和检测问题都可以通过在某些基础上将信号建模为稀疏而得到极大的帮助。到目前为止，已经为这种信号模型构建了一个相对全面的理论，产生的算法即使在采样率远低于奈奎斯特率时也能提供良好的性能。然而，现实世界信号的结构往往超出了简单的稀疏性。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表现出持久性。最近对稀疏性结构的研究表明，尽管现有的结果有些有限，但它可以用来提高估计性能。例如，现有的方法努力只找到单一的“最佳”估计，而许多应用程序希望知道所有合理估计的集合以及相对置信度值，即“软”估计。本研究利用基于隐状态变量的统计建模框架研究软推理策略。在这里，例如，使用二进制状态将有利于稀疏信号模型，并且在二进制状态上使用马尔可夫结构将有利于结构化稀疏性。特别地，本研究探讨了迭代和顺序贝叶斯方法的软推理，建立在最先进的算法在非相干通信接收器中使用的“涡轮均衡”和“球体解码”。本研究还探讨了稀疏衰落信道通信的基本问题。虽然现有的方法集中在寻找“最佳”稀疏信道估计的问题上，以便在相干译码算法中后续使用，但通信理论却规定了基于软稀疏信道估计的模型平均的译码度量。

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.