Ab initio compressive phase retrieval

TL;DR

This paper introduces an algorithm for phase retrieval that leverages the compressibility of natural objects, enabling imaging without prior information, applicable across various diffraction and scattering techniques.

Contribution

The novel algorithm reconstructs images from diffraction data by exploiting object compressibility, removing the need for prior size or atomic information.

Findings

Successfully reconstructs images without prior object information

Applicable to multiple diffraction and scattering techniques

Demonstrates robustness in various imaging scenarios

Abstract

Any object on earth has two fundamental properties: it is finite, and it is made of atoms. Structural information about an object can be obtained from diffraction amplitude measurements that account for either one of these traits. Nyquist-sampling of the Fourier amplitudes is sufficient to image single particles of finite size at any resolution. Atomic resolution data is routinely used to image molecules replicated in a crystal structure. Here we report an algorithm that requires neither information, but uses the fact that an image of a natural object is compressible. Intended applications include tomographic diffractive imaging, crystallography, powder diffraction, small angle x-ray scattering and random Fourier amplitude measurements.