A mathematical theory of computational resolution limit in one dimension

Understand

Given an image generated by the convolution of point sources with a band-limited function, the deconvolution problem is to reconstruct the source number, positions, and amplitudes.

• This problem arises from many important applications in imaging and signal processing.
• It is well-known that it is impossible to resolve the sources when they are close enough in practice.
• Rayleigh investigated this problem and formulated a resolution limit, the so-called Rayleigh limit, for the case of two sources with identical amplitudes.