# Signal Reconstruction using Blind Super-resolution with Arbitrary Sampling

## TL;DR

This paper introduces a novel semi-definite programming approach using Prolate Spheroidal Wave Functions for blind super-resolution of sparse signals, enabling spike localization without magnitude recovery, and demonstrates its effectiveness through numerical simulations.

## Contribution

It presents a new SDP formulation leveraging PSWFs for blind super-resolution that localizes spikes without needing magnitude information, advancing prior methods.

## Key findings

- Effective spike localization without magnitude recovery.
- Outperforms recent related methods in simulations.
- Applicable to arbitrary sampling schemes.

## Abstract

In this paper the problem of blind super-resolution of sparse signals using arbitrary sampling scheme and atomic lift is discussed. After comprehensive description on blind superresolution problem, it is shown that using Prolate Spheroidal Wave Functions (PSWFs), it is possible to derive a new SemiDefinite Program (SDP) for the blind super-resolution problem. Unlike the previous results, the newly proposed SDP can localize spikes without magnitude recovery. Several numerical simulations were conducted to compare the performance of the proposed method with the recent related research.