Searching with iterated maps Elser, V; Rankenburg, I; Thibault, P
Proceedings of the National Academy of Sciences - PNAS,
01/2007, Letnik:
104, Številka:
2
Journal Article
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In many problems that require extensive searching, the solution can be described as satisfying two competing constraints, where satisfying each independently does not pose a challenge. As an ...alternative to tree-based and stochastic searching, for these problems we propose using an iterated map built from the projections to the two constraint sets. Algorithms of this kind have been the method of choice in a large variety of signal-processing applications; we show here that the scope of these algorithms is surprisingly broad, with applications as diverse as protein folding and Sudoku.
An information theoretic criterion for the feasibility of reconstructing diffraction signals from noisy tomographs, when the positions of the tomographs within the signal are unknown, is derived. For ...shot-noise limited data, the number of detected photons per tomograph for successful reconstruction is much smaller than previously believed necessary, growing only logarithmically with the number of contrast elements of the diffracting object. Reconstruction up to the theoretic criterion is demonstrated on simulated data with an algorithm that combines the expectation-maximization (EM) principle with constraints arising from the band-limited nature of the signal.
Intense femtosecond x-ray pulses from free-electron laser sources allow the imaging of individual particles in a single shot. Early experiments at the Linac Coherent Light Source (LCLS) have led to ...rapid progress in the field and, so far, coherent diffractive images have been recorded from biological specimens, aerosols, and quantum systems with a few-tens-of-nanometers resolution. In March 2014, LCLS held a workshop to discuss the scientific and technical challenges for reaching the ultimate goal of atomic resolution with single-shot coherent diffractive imaging. This paper summarizes the workshop findings and presents the roadmap toward reaching atomic resolution, 3D imaging at free-electron laser sources.
We reconstructed the 3D Fourier intensity distribution of monodisperse prolate nanoparticles using single-shot 2D coherent diffraction patterns collected at DESY's FLASH facility when a bright, ...coherent, ultrafast x-ray pulse intercepted individual particles of random, unmeasured orientations. This first experimental demonstration of cryptotomography extended the expansion-maximization-compression framework to accommodate unmeasured fluctuations in photon fluence and loss of data due to saturation or background scatter. This work is an important step towards realizing single-shot diffraction imaging of single biomolecules.
New sources and detectors are allowing scientists to look at matter with finer spatial and temporal resolutions. These experiments can produce data that are a series of severely Poisson limited ...snap-shots of randomly oriented samples. An extreme case of this is destructive imaging of single particles with an x-ray free-electron laser – many frames are needed for a reconstruction, but there is no a priori information associated with the frames about particle orientation. We use Cornell's Pixel Array Detectors (PADs) to examine the practical limits of an expectation maximization (EM) algorithm designed to deal with extremely low-fluence data, having just a few photons per frame. We demonstrate image reconstruction of a high-contrast sample using hundreds of thousands of randomly oriented frames with an average x-ray photon occupancy as low as 2.5 photons per frame. Practical aspects of reducing low-fluence data, such as thresholding and noise limits, will be discussed for high- and low-contrast samples; and data collected in the presence of significant background signal.
A computational method has been developed for generating graphitic carbon structures on an arbitrary smooth surface and with a given number of carbon rings. Using both periodic and random surfaces ...for constraint, many extended graphitic carbon structures have been generated. The energy relative to graphite and the bulk elastic properties have been calculated. Like their periodic counterparts, the random structures are found to be exceptionally stable. Their radial distribution functions match closely those of films of amorphous carbon grown on NaCl substrates from sublimated graphite. (Author)
We have used the method of x-ray diffraction microscopy to image the complex-valued exit wave of an intact and unstained yeast cell. The images of the freeze-dried cell, obtained by using 750-eV ...x-rays from different angular orientations, portray several of the cell's major internal components to 30-nm resolution. The good agreement among the independently recovered structures demonstrates the accuracy of the imaging technique. To obtain the best possible reconstructions, we have implemented procedures for handling noisy and incomplete diffraction data, and we propose a method for determining the reconstructed resolution. This work represents a previously uncharacterized application of x-ray diffraction microscopy to a specimen of this complexity and provides confidence in the feasibility of the ultimate goal of imaging biological specimens at 10-nm resolution in three dimensions.
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