Unified Convex Optimization Approach to Super-Resolution Based on Localized Kernels

TL;DR

This paper introduces a unified convex optimization framework for super-resolution that leverages localized kernels to reconstruct fine details from coarse measurements, applicable to various engineering and physics problems.

Contribution

It presents a novel convex optimization method using localized kernels for super-resolution, connecting it to the stream of pulses problem.

Findings

Effective reconstruction of signals from coarse measurements

Unified approach applicable to multiple super-resolution scenarios

Theoretical guarantees for the interpolation method

Abstract

The problem of resolving the fine details of a signal from its coarse scale measurements or, as it is commonly referred to in the literature, the super-resolution problem arises naturally in engineering and physics in a variety of settings. We suggest a unified convex optimization approach for super-resolution. The key is the construction of an interpolating polynomial based on localized kernels. We also show that the localized kernels act as the connecting thread to another wide-spread problem of stream of pulses.