Ptychography has risen as a reference X-ray imaging technique: it achieves resolutions of one billionth of a meter, macroscopic field of view, or the capability to retrieve chemical or magnetic contrast, among other features. A ptychographyic reconstruction is normally formulated as a blind phase retrieval problem, where both the image (sample) and the probe (illumination) have to be recovered from phaseless measured data. In this article we address a nonlinear least squares model for the blind ptychography problem with constraints on the image and the probe by maximum likelihood estimation of the Poisson noise model. We formulate a variant model that incorporates the information of phaseless measurements of the probe to eliminate possible artifacts. Next, we propose a generalized alternating direction method of multipliers designed for the proposed nonconvex models with convergence guarantee under mild conditions, where their subproblems can be solved by fast element-wise operations. Numerically, the proposed algorithm outperforms state-of-the-art algorithms in both speed and image quality.

Ptychographic imaging is a powerful means of imaging beyond the resolution limits of typical x-ray optics. Recovering images from raw ptychographic data, however, requires the solution of an inverse problem, namely, phase retrieval. Phase retrieval algorithms are computationally expensive, which precludes real-time imaging. In this work, we propose PtychoNN, an approach to solve the ptychography data inversion problem based on a deep convolutional neural network. We demonstrate how the proposed method can be used to predict real-space structure and phase at each scan point solely from the corresponding far-field diffraction data. Our results demonstrate the practical application of machine learning to recover high fidelity amplitude and phase contrast images of a real sample hundreds of times faster than current ptychography reconstruction packages. Furthermore, by overcoming the constraints of iterative model-based methods, we can significantly relax sampling constraints on data acquisition while still producing an excellent image of the sample. Besides drastically accelerating acquisition and analysis, this capability has profound implications for the imaging of dose sensitive, dynamic, and extremely voluminous samples.

The analysis of chemical states and morphology in nanomaterials is central to many areas of science. We address this need with an ultrahigh-resolution scanning transmission soft x-ray microscope. Our instrument provides multiple analysis tools in a compact assembly and can achieve few-nanometer spatial resolution and high chemical sensitivity via x-ray ptychography and conventional scanning microscopy. A novel scanning mechanism, coupled to advanced x-ray detectors, a high-brightness x-ray source, and high-performance computing for analysis provide a revolutionary step forward in terms of imaging speed and resolution. We present x-ray microscopy with 8-nm full-period spatial resolution and use this capability in conjunction with operando sample environments and cryogenic imaging, which are now routinely available. Our multimodal approach will find wide use across many fields of science and facilitate correlative analysis of materials with other types of probes.

The success of ptychographic imaging experiments strongly depends on achieving high signal-to-noise ratio. This is particularly important in nanoscale imaging experiments when diffraction signals are very weak and the experiments are accompanied by significant parasitic scattering (background), outliers or correlated noise sources. It is also critical when rare events such as cosmic rays, or bad frames caused by electronic glitches or shutter timing malfunction take place. In this paper, we propose a novel iterative algorithm with rigorous analysis that exploits the direct forward model for parasitic noise and sample smoothness to achieve a thorough characterization and removal of structured and random noise. We present a formal description of the proposed algorithm and prove its convergence under mild conditions. Numerical experiments from simulations and real data (both soft and hard X-ray beamlines) demonstrate that the proposed algorithms produce better results when compared to state-of-the-art methods.

Abstract-The release of the CUDA Kepler architecture in March 2012 has provided Nvidia GPUs with a larger register memory space and instructions for the communication of registers among threads. This facilitates a new programming strategy that utilizes registers for data sharing and reusing in detriment of the shared memory. Such a programming strategy can significantly improve the performance of applications that reuse data heavily. This paper presents a register-based implementation of the Discrete Wavelet Transform (DWT), the prevailing data decorrelation technique in the field of image coding. Experimental results indicate that the proposed method is, at least, four times faster than the best GPU implementation of the DWT found in the literature. Furthermore, theoretical analysis coincide with experimental tests in proving that the execution times achieved by the proposed implementation are close to the GPU's performance limits.