Our recent work on a precise high-dimensional analysis of subspace learning algorithms from subsampled measurements will appear at the SPARS workshop as an oral presentation. (Full paper with technical details will soon follow.)

Finding the sparse representation of a signal in an overcomplete dictionary has attracted a lot of attention over the past years. In our paper, we analyze the probabilistic average-case performance of ProSparse, a new polynomial complexity algorithm that solves the sparse representation problem when the underlying dictionary is the union of a Vandermonde matrix and a banded matrix. Closed-form expressions for the exact success probabilities of ProSparse are given. We also analyze the success probabilities in the high-...

Estimating low-rank positive-semidefinite (PSD) matrices from symmetric rank-one measurements is of great importance in many applications, such as high-dimensional data processing, quantum state tomography, and phase retrieval. When the rank is known a priori, this problem can be regarded as solving a system of quadratic equations of a low-dimensional subspace. In a recent paper, we develop a...

Starting from Jan. 1, 2016, I am an Associate Professor of Electrical Engineering at Harvard SEAS.