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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.
When x-rays penetrate soft matter, their phase changes more rapidly than their amplitude. In- terference effects visible with high brightness sources creates higher contrast, edge enhanced images. When the object is piecewise smooth (made of big bloc
In the compressive phase retrieval problem, or phaseless compressed sensing, or compressed sensing from intensity only measurements, the goal is to reconstruct a sparse or approximately $k$-sparse vector $x in mathbb{R}^n$ given access to $y= |Phi x|
Ultrafast nanocrystallography has the potential to revolutionize biology by enabling structural elucidation of proteins for which it is possible to grow crystals with 10 or fewer unit cells on the side. The success of nanocrystallography depends on r
Available simulation methods, suitable to describe solid-solid phase transitions occurring upon increasing of presssure and/or temperature, are based on empirical interatomic potentials: this restriction reduces the predictive power, and thus the gen
In this work we consider the problem of reconstruction of a signal from the magnitude of its Fourier transform, also known as phase retrieval. The problem arises in many areas of astronomy, crystallography, optics, and coherent diffraction imaging (C