Soft Recovery With General Atomic Norms

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 $A{v}_0$. 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 $v^{\ast }$. 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.

References in corpus (1)

• Image Separation using Wavelets and Shearlets

Cited by in corpus (2)

• Estimation of Angles of Arrival Through Superresolution -- A Soft Recovery Approach for General Antenna Geometries
• Thermal Source Localization Through Infinite-Dimensional Compressed Sensing