Team, Visitors, External Collaborators
Overall Objectives
Research Program
Application Domains
Highlights of the Year
New Software and Platforms
New Results
Bilateral Contracts and Grants with Industry
Partnerships and Cooperations
XML PDF e-pub
PDF e-Pub

Section: New Results

Axis 2: Multi-kernel unmixing and super-resolution using the Modified Matrix Pencil method

Participant: Hemant Tyagi.

Consider L groups of point sources or spike trains, with the lth group represented by xl(t). For a function g:RR, let gl(t)=g(t/μl) denote a point spread function with scale μl>0, and with μ1<<μL. With y(t)=l=1L(glxl)(t), our goal is to recover the source parameters given samples of y, or given the Fourier samples of y. This problem is a generalization of the usual super-resolution setup wherein L=1; we call this the multi-kernel unmixing super-resolution problem. Assuming access to Fourier samples of y, we derive an algorithm for this problem for estimating the source parameters of each group, along with precise non-asymptotic guarantees. Our approach involves estimating the group parameters sequentially in the order of increasing scale parameters, i.e., from group 1 to L. In particular, the estimation process at stage 1lL involves (i) carefully sampling the tail of the Fourier transform of y, (ii) a deflation step wherein we subtract the contribution of the groups processed thus far from the obtained Fourier samples, and (iii) applying Moitra's modified Matrix Pencil method on a deconvolved version of the samples in (ii).

This is joint work with Stephane Chretien (National Physical Laboratory, UK & Alan Turing Institute, London) and was mostly done while Hemant Tyagi was affiliated to the Alan Turing Institute. It is currently under revision in an international journal and is available as a preprint [56].