CIF:Small:Model-Based Blind Demixing for Signal Processing and Machine Learning

研究了多通道卷积盲解混(MCBD)问题的新的数值方法和支持理论，其中一组相互关联的时不变系统的响应仅通过观察它们的输出来估计。MCBD问题出现在信号处理和通信中的许多众所周知的应用中；我们这个项目的目标之一是提供一个具有坚实算法和理论基础的统一框架来解决这些问题。目标是提供对MCBD的信息理论限制的基本分析，以及在达到或接近这些限制时具有可证明的性能保证的可扩展算法。还将探索MCBD问题在机器学习领域的新应用。特别是，研究人员将研究如何将MCBD问题的解用作训练深度卷积神经网络的初始化和求解与产生式模型相关的逆问题的有效方法。这项工作将结合经典的统计方法和基于现代优化的约束逆问题的技术。尤其令人感兴趣的是，结构在使问题变得可识别以及在观测被噪声破坏时解的稳定性方面所起的作用。我们将考虑这种结构来自特定领域知识的场景，以及模型由数据驱动的场景。该项目开发的算法将在天文成像、神经成像、医学成像、地震成像、水下声学和深度学习的应用中进行验证。拟议的研究与用于大规模MIMO通信的下一代阵列处理、用于物联网的设备到设备通信以及新型集成电路射频发射机直接相关。这项工作也可能为并行MRI开辟一个新的方向。作为研究活动的补充，将为下一代数据科学家开设新的研究生课程，重点是现代数学方法。

The research centers on novel numerical methods and supporting theory for the multichannel convolutive blind demixing (MCBD) problem, where the responses for a set of inter-related time-invariant systems are estimated by observing only their outputs. The MCBD problem arises in many well-known applications in signal processing and communications; one of our goals for this project is to provide a unified framework for solving these problems that has a firm algorithmic and theoretical foundation. The goals are to provide a fundamental analysis of the information theoretic limits of MCBD, along with scalable algorithms that operate with provable performance guarantee at or near these limits. New applications of the MCBD problem will also be explored in the area of machine learning. In particular, the investigators will study how solutions to the MCBD problem can be used as an efficient method for both for the initialization in training deep convolutional neural networks, and for solving inverse problems associated with generative models.The work will combine classical statistical approaches and modern optimization-based techniques for constrained inverse problems. Of particular interest is the role that structure plays on making the problem identifiable, and on the stability of the solutions when the observations are corrupted by noise. Scenarios where this structure comes from domain-specific knowledge will be considered, along with scenarios where the model is data-driven. The algorithms developed in the project will be validated on applications in astronomical imaging, neuroimaging, medical imaging, seismic imaging, underwater acoustics, and deep learning. The proposed research has direct relevance to next-generation array processing for massive MIMO communications, device-to-device communication for the Internet-of-Things, and new integrated circuit RF transmitters. The work also may open a new direction in parallel MRI. The research activities will be complemented by new graduate courses focusing on modern mathematical methods for the next generation of data scientists.