6 papers
Characterization of the Basin of Convexity for Multi-Snapshot Spike Deconvolution via Variable Projection
Meghna Kalra, Maxime Ferreira Da Costa, Kiryung Lee
The problem of multi-snapshot spike deconvolution is studied, where the goal is to recover the locations of sparse impulses from their noisy convolution with a known point spread f…
Locally Near Optimal Piecewise Linear Regression in High Dimensions via Difference of Max-Affine Functions
Haitham Kanj, Kiryung Lee
This paper presents a parametric solution to piecewise linear regression through the Adaptive Block Gradient Descent (ABGD) algorithm. The heart of the method is the parametrizatio…
Global Convergence of ESPRIT with Preconditioned First-Order Methods for Spike Deconvolution
Joseph Gabet, Meghna Kalra, Maxime Ferreira Da Costa +1
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 app…
Sparse Max-Affine Regression
Haitham Kanj, Seonho Kim, Kiryung Lee
This paper presents Sparse Gradient Descent as a solution for variable selection in convex piecewise linear regression, where the model is given as the maximum of -affine functi…
Robust Phase Retrieval by Alternating Minimization
Seonho Kim, Kiryung Lee
We consider a least absolute deviation (LAD) approach to the robust phase retrieval problem that aims to recover a signal from its absolute measurements corrupted with sparse noise…
Small-Noise Sensitivity Analysis of Locating Pulses in the Presence of Adversarial Perturbation
Meghna Kalra, Maxime Ferreira Da Costa, Kiryung Lee
A fundamental small-noise sensitivity analysis of spike localization in the presence of adversarial perturbations and an arbitrary point spread function (PSF) is presented. The ana…