Towards a Mathematical Theory of Super-resolution

• Published in: Communications on pure and applied mathematics Vol. 67; no. 6; pp. 906 - 956
• Main Authors: Candès, Emmanuel J., Fernandez-Granda, Carlos
• Format: Journal Article
• Language: English
• Published: New York Blackwell Publishing Ltd 01.06.2014; John Wiley and Sons, Limited
• Subjects: Mathematical problems; Optimization; Theory

This paper develops a mathematical theory of super‐resolution. Broadly speaking, super‐resolution is the problem of recovering the fine details of an object—the high end of its spectrum—from coarse scale information only—from samples at the low end of the spectrum. Suppose we have many point sources...