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

研究了多通道卷积盲除混问题的新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问题出现在许多众所周知的信号处理和通信应用中；我们这个项目的目标之一是为解决这些问题提供一个统一的框架，该框架具有坚实的算法和理论基础。目标是提供MCBD的信息理论极限的基本分析，以及在这些极限或接近这些极限的可证明的性能保证下运行的可扩展算法。MCBD问题在机器学习领域的新应用也将被探索。特别是，研究人员将研究如何将MCBD问题的解作为训练深度卷积神经网络初始化的有效方法，以及解决与生成模型相关的逆问题。这项工作将结合经典的统计方法和基于现代优化技术的约束逆问题。特别令人感兴趣的是结构在使问题可识别方面所起的作用，以及在观测结果被噪声破坏时解决方案的稳定性。将考虑这种结构来自特定领域知识的场景，以及模型是数据驱动的场景。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等领域的应用中得到验证。所提出的研究与大规模MIMO通信的下一代阵列处理、物联网的设备对设备通信以及新型集成电路RF发射器直接相关。这项工作也可能为平行核磁共振成像开辟一个新的方向。研究活动将辅以新的研究生课程，重点关注下一代数据科学家的现代数学方法。

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.