On strong basins of attractions for non-convex sparse spike estimation: upper and lower bounds

DOI10.1007/s10851-023-01163-wMaRDI QIDQ6154437

Arthur Leclaire, Yann Traonmilin, Pierre-Jean Bénard, Jean-François Aujol

Publication date: 15 February 2024

Published in: Journal of Mathematical Imaging and Vision (Search for Journal in Brave)

zbMATH Keywords

super-resolutionnon-convex methodsoff-the-grid estimation

Mathematics Subject Classification ID

Nonconvex programming, global optimization (90C26) Computer graphics; computational geometry (digital and algorithmic aspects) (68U05) Image processing (compression, reconstruction, etc.) in information and communication theory (94A08)

Cites Work

• Super-resolution from noisy data
• Exact support recovery for sparse spikes deconvolution
• Statistical learning guarantees for compressive clustering and compressive mixture modeling
• Exact Solutions to Super Resolution on Semi-Algebraic Domains in Higher Dimensions
• Atomic Norm Denoising With Applications to Line Spectral Estimation
• High-Dimensional Probability
• The basins of attraction of the global minimizers of the non-convex sparse spike estimation problem
• The sliding Frank–Wolfe algorithm and its application to super-resolution microscopy
• Compressed Sensing Off the Grid
• Towards a Mathematical Theory of Super‐resolution
• Blind inverse problems with isolated spikes
• The basins of attraction of the global minimizers of non-convex inverse problems with low-dimensional models in infinite dimension