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.
