Year: 2017
Type: preprint
Abstract: This paper describes a dual certificate condition on a linear measurement operator $A$ (defined on a Hilbert space $\mathcal{H}$ and having finite-dimensional range) which guarantees that an atomic norm minimization, in a certain sense, will be able to approximately recover a structured signal $v_0 \in \mathcal{H}$ from measurements $Av_0$. Put very streamlined, the condition implies that peaks in a sparse decomposition of $v_0$ are close the the support of the atomic decomposition of the solution $v^*$. The condition applies in a relatively general context - in particular, the space $\mathcal{H}$ can be infinite-dimensional. The abstract framework is applied to several concrete examples, one example being super-resolution. In this process, several novel results which are interesting on its own are obtained.
Source: arXiv (Cornell University)
Author: Flinth, Axel
Institution: Technische Universität Berlin
Language: English
Subfield: Computational Mechanics
Field: Engineering
Domain: Physical Sciences
Open Access status: green
Funder: Deutsche Forschungsgemeinschaft
Awards: G3622883762, G6000301443, G6712660282
OpenAlex ID: W2612326314