Structure-Aware Non-Uniform Samplers for Compressive Parameter Estimation
报告摘要：With technological advances in sensing and computation, ever-increasing amounts of data are beingacquired every day. Modern signal processing techniques such as compressed sensing havesuccessfully utilized the parsimonious representations of data (in terms of sparsity and low rank) toenable efficient/optimal compression for signal reconstruction with provable guarantees. However, theultimate goal in many inference problems is to estimate certain physically meaningful parameters ofinterest from compressive measurements without having to recover the original data. In this talk, I will show how to optimally exploit the geometry of the physical measurement model andcorrelation priors on the unknown signal (alongside other forms of parsimony) to enable reliableinference from compressed measurements. In particular, I will present my work on two interrelatedtopics. (1) Toeplitz covariance matrix compression: I will show how to exploit T oeplitz structure withdeterministic samplers and achieve optimal sample complexity. I will also present an efficient samplingand analysis framework for estimating low rank Toeplitz covariance matrices. (2) Sparse supportrecovery with correlation information: My talk will show how correlation-aware support recovery ispossible in the regime where there are fewer measurements than the support size. Iwill also discuss asimple hard-thresholding support recovery algorithm. For both topics, I will highlight the role of sparsearray in breaking the sample complexity barriers in previous compressed sensing literature. I will-conclude with my vision to exploit statistical priors in the problems of array signal processing,super-resolution imaging, and high-dimensional data compression, 报告人简介：Heng Qiao is a Ph.D. Candidate in Electrical and Computer Engineering at the University ofCalifornia, San Diego. He received a B.E. in Electronic Engineering from Tsinghua University, Beijingin 2012, and a M.S. in Electrical Engineering from the University of Maryland, College Park in 2016.At UCSD, he is the recipient of a Qualcomm Fellow-Mentor-Advisor Fellowship (2018) and theShannon Graduate Fellowship (2019). His work on co-array interpolation received the Best StudentPaper Award (First Place) at IEE ICASSP 2017 in New Orleans, USA. His research interests includestatistical signal processing for high-dimensional data, sensor array processing, high-resolutionimaging, and optimization.