Ab initio compressive phase retrieval

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.

7 pages, 4 figures, presented at the XXI IUCr Congress, Aug. 2008, Osaka Japan

References in corpus (5)

• X-ray image reconstruction from a diffraction pattern alone
• A unified evaluation of iterative projection algorithms for phase retrieval
• Three-dimensional coherent X-ray diffraction imaging of a ceramic nanofoam: determination of structural deformation mechanisms
• Phase retrieval and saddle-point optimization
• Ab initio structure solution by charge flipping

Cited by in corpus (4)

• Compressive Phase Retrieval via Generalized Approximate Message Passing
• Phase Retrieval with Random Phase Illumination
• Phase retrieval from single biomolecule diffraction pattern
• A general framework for denoising phaseless diffraction measurements