Global Convergence of ESPRIT with Preconditioned First-Order Methods for Spike Deconvolution
Abstract
Spike deconvolution is the problem of recovering point sources from their convolution with a known point spread function, playing a fundamental role in many sensing and imaging applications. This paper proposes a novel approach combining ESPRIT with Preconditioned Gradient Descent (PGD) to estimate the amplitudes and locations of the point sources by a non-linear least squares. The preconditioning matrices are adaptively designed to account for variations in the learning process, ensuring a proven super-linear convergence rate. We provide local convergence guarantees for PGD and performance analysis of ESPRIT reconstruction, leading to global convergence guarantees for our method in one-dimensional settings with multiple snapshots, demonstrating its robustness and effectiveness. Numerical simulations corroborate the performance of the proposed approach for spike deconvolution.
Cite
@article{arxiv.2502.08035,
title = {Global Convergence of ESPRIT with Preconditioned First-Order Methods for Spike Deconvolution},
author = {Joseph Gabet and Meghna Kalra and Maxime Ferreira Da Costa and Kiryung Lee},
journal= {arXiv preprint arXiv:2502.08035},
year = {2025}
}