Graduate Students Seminar

Speaker 1: Ahmad Mousavi

Title

Exact Vector Recovery with CP-admissible Constraints

Abstract

Inspired by constrained sparse signal recovery, we propose a constrained matching pursuit algorithm and develop conditions for exact vector recovery on constraint sets via this algorithm. We show that exact recovery via constrained matching pursuit not only depends on a measurement matrix but also critically relies on a constraint set. We thus identify an important class of constraint sets, called coordinate projection admissible set, or simply CP admissible sets. This class of sets includes the Euclidean space, the nonnegative orthant, and many others arising from various applications; analytic and geometric properties of these sets are established.  Moreover, by making use of cone properties and conic hull structure of CP admissible sets and constrained optimization techniques, we also provide sufficient conditions for uniform exact recovery on CP admissible sets in terms of the restricted isometry-like constant and the restricted orthogonality-like constant.

Speaker 2: Lillian Chow

Title

An Overview of "A Functional Approach to Deconvolve Neuroimaging Data"

Abstract

Dynamic Positron Emission Tomography (PET) Scan data is used in medical research to identify and investigate chemical changes within the human body. The deconvolution and analysis of the dynamic PET data currently rely on classic assumptions that the data can be modeled using linear first-order kinetics and compartmental analysis; however, there is strong biological and statistical evidence that questions the validity of these assumptions for neuroimaging data. In the paper, "A Functional Approach to Deconvolve Dynamic Neuroimaging Data", Ci-Ren Jiang, John A. D. Aston and Jane-Ling Wang propose a non-parametric method for the deconvolution of the data based on Functional Principal Component Analysis (FPCA). This proposed method does not rely on the classic assumptions and is computationally less intensive than other deconvolution methods. The FPCA method of deconvolution performs comparably with other common methods of deconvolution of neuroimaging data in both simulations and application to real data.

This presentation provides an overview of the classic assumptions, the issues with using these assumptions for neuroimaging data, and an overview of the FPCA method proposed in this paper.