Convex relaxations of spectral sparsity for robust super-resolution and line spectrum estimation

Yuejie Chi

doi:10.1117/12.2270060

24 August 2017 Convex relaxations of spectral sparsity for robust super-resolution and line spectrum estimation

Yuejie Chi

Proceedings Volume 10394, Wavelets and Sparsity XVII; 103941G (2017) https://doi.org/10.1117/12.2270060
Event: SPIE Optical Engineering + Applications, 2017, San Diego, California, United States

Abstract

We consider recovering the amplitudes and locations of spikes in a point source signal from its low-pass spectrum that may suffer from missing data and arbitrary outliers. We first review and provide a unified view of several recently proposed convex relaxations that characterize and capitalize the spectral sparsity of the point source signal without discretization under the framework of atomic norms. Next we propose a new algorithm when the spikes are known a priori to be positive, motivated by applications such as neural spike sorting and fluorescence microscopy imaging. Numerical experiments are provided to demonstrate the effectiveness of the proposed approach.

Citation Download Citation

Yuejie Chi "Convex relaxations of spectral sparsity for robust super-resolution and line spectrum estimation", Proc. SPIE 10394, Wavelets and Sparsity XVII, 103941G (24 August 2017); https://doi.org/10.1117/12.2270060

ACCESS THE FULL ARTICLE

INSTITUTIONAL
Select your institution to access the SPIE Digital Library.

SELECT YOUR INSTITUTION

PERSONAL
Sign in with your SPIE account to access your personal subscriptions or to use specific features such as save to my library, sign up for alerts, save searches, etc.

PERSONAL SIGN IN

No SPIE Account? Create one

PURCHASE THIS CONTENT

SUBSCRIBE TO DIGITAL LIBRARY

50 downloads per 1-year subscription

Members: $195

Non-members: $335 ADD TO CART

25 downloads per 1 - year subscription

Members: $145

Non-members: $250 ADD TO CART

PURCHASE SINGLE ARTICLE

Includes PDF, HTML & Video, when available