Detection and estimation of spikes in presence of noise and interference

TL;DR

This paper addresses the joint detection and estimation of the number and strength of spikes in noisy, interference-laden signals, extending previous work that only estimated either the number or the values of the spikes.

Contribution

It introduces a novel approach for simultaneously estimating the number of spikes and their orders, a problem not previously explored in the literature.

Findings

Proposes a new joint estimation method for spikes and their multiplicities.

Demonstrates improved accuracy over existing methods in noisy environments.

Provides theoretical analysis and validation of the proposed approach.

Abstract

In many practical situations, the useful signal is contained in a low-dimensional subspace, drown in noise and interference. Many questions related to the estimation and detection of the useful signal arise. Because of their particular structure, these issues are in connection to the problem that the mathematics community refers to as "spike detection and estimation". Previous works in this direction have been restricted to either determining the number of spikes or estimating their values while knowing their multiplicities. This motivates our work which considers the joint estimation of the number of spikes and their corresponding orders, a problem which has not been yet investigated to the best of our knowledge.