Abstract

Due to the physical nature of wave propagation and diffraction, there is a fundamental diffraction barrier in optical imaging systems which is called the diffraction limit or resolution limit. Rayleigh investigated this problem and formulated the well-known Rayleigh limit. However, the Rayleigh limit is empirical and only considers the resolving ability of the human visual system. On the other hand, resolving sources separated below the Rayleigh limit to achieve so-called “super-resolution” has been demonstrated in many experiments.
In this talk, we will propose a new concept “computational resolution limit” which reveals the fundamental limits in super-resolving the number and locations of point sources from a data-processing point of view. We will quantitatively characterize the computational resolution limits by the signal-to-noise ratio, the sparsity of sources, and the cutoff frequency of the imaging system. We will introduce several super-resolution algorithms that achieve the optimal resolution limit. Recent progress in both the theoretical generalization and practical applications of our results will also be discussed.