Selecting Optimal Sampling Rate for Stable Super-Resolution

2025/02/10 by Nuha Diab, Diab, Nuha
Computer Science · Engineering · #15A18 #15A22 #42A70 #Advanced Image Processing Techniques #FOS: Computer and information sciences #FOS: Mathematics #Image Processing Techniques and Applications #Information Theory (cs.IT) #Numerical Analysis (math.NA) #Optical Systems and Laser Technology

paper · pdf · doi:10.48550/arxiv.2502.06673

openalex publication_date 2025/02/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We investigate the recovery of nodes and amplitudes from noisy frequency samples in spike train signals, also known as the super-resolution (SR) problem. When the node separation falls below the Rayleigh limit, the problem becomes ill-conditioned. Admissible sampling rates, or decimation parameters, improve the conditioning of the SR problem, enabling more accurate recovery. We propose an efficient preprocessing method to identify the optimal sampling rate, significantly enhancing the performance of SR techniques.

Related

• Decimated Prony's Method for Stable Super-resolution
• Super-Resolution from Noisy Data
• Super-resolution with Binary Priors: Theory and Algorithms
• An Algorithm for Exact Super-resolution and Phase Retrieval
• Towards a Theory of Stable Super-Resolution: Model-Based Formulation and Stability Analysis