Accuracy of reconstruction of spike-trains with two near-colliding nodes

2017/01/05 by Andrey Akinshin, Gil Goldman, Akinshin, Andrey +5
Engineering · Medicine · Physics and Astronomy · #Advanced MRI Techniques and Applications #Atomic and Subatomic Physics Research #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Photoacoustic and Ultrasonic Imaging

paper · pdf · doi:10.48550/arxiv.1701.01482

openalex publication_date 2017/01/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider a signal reconstruction problem for signals F of the form F(x)=∑_j=1^da_jδ(x-x_j), from their moments m_k(F)=∫ x^kF(x)dx. We assume m_k(F) to be known for k=0,1,…,N, with an absolute error not exceeding ε> 0. We study the "geometry of error amplification" in reconstruction of F from m_k(F), in situations where two neighboring nodes x_i and x_i+1 near-collide, i.e x_i+1-x_i=h ≪ 1. We show that the error amplification is governed by certain algebraic curves S_F,i, in the parameter space of signals F, along which the first three moments m₀,m₁,m₂ remain constant.

Related

• Geometry of error amplification in solving Prony system with\n near-colliding nodes
• On algebraic properties of low rank approximations of Prony systems
• Accuracy of noisy Spike-Train Reconstruction: a Singularity Theory point of view
• Accuracy of spike-train Fourier reconstruction for colliding nodes
• Prony Scenarios and Error Amplification in a Noisy Spike-Train Reconstruction