We propose a general framework to recover underlying images from noisy phaseless diffraction measurements based on the alternating directional method of multipliers and the plug-and-play technique. The algorithm consists of three-step iterations: (i) Solving a generalized least square problem with the maximum a posteriori (MAP) estimate of the noise, (ii) Gaussian denoising and (iii) updating the multipliers. The denoising step utilizes higher order filters such as total generalized variation and nonlocal sparsity based filters including nonlocal mean (NLM) and Block-matching and 3D filtering (BM3D) filters. The multipliers are updated by a symmetric technique to increase convergence speed. The proposed method with low computational complexity is provided with theoretical convergence guarantee, and it enables recovering images with sharp edges, clean background and repetitive features from noisy phaseless measurements. Numerous numerical experiments for Fourier phase retrieval (PR) as coded diffraction and ptychographic patterns are performed to verify the convergence and efficiency, showing that our proposed method outperforms the state-of-art PR algorithms without any regularization and those with total variational regularization.

Phaseless diffraction measurements recorded by CCD detectors are often affected by Poisson noise. In this paper, we propose a dictionary learning model by employing patches based sparsity in order to denoise such Poisson phaseless measurements. The model consists of three terms: (i) A representation term by an orthogonal dictionary, (ii) an L⁰ pseudo norm of the coefficient matrix, and (iii) a Kullback-Leibler divergence term to fit phaseless Poisson data. Fast alternating minimization method (AMM) and proximal alternating linearized minimization (PALM) are adopted to solve the proposed model, and especially the theoretical guarantee of the convergence of PALM is provided. The subproblems for these two algorithms both have fast solvers, and indeed, the solutions for the sparse coding and dictionary updating both have closed forms due to the orthogonality of learned dictionaries. Numerical experiments for phase retrieval using coded diffraction and ptychographic patterns are conducted to show the efficiency and robustness of proposed methods, which, by preserving texture features, produce visually and quantitatively improved restored images compared with other phase retrieval algorithms without regularization and local sparsity promoting algorithms.

Linear dichroism is an important tool to characterize the transmission matrix and determine the crystal or orbital orientation in a material. In order to achieve high-resolution mapping of transmission properties, the linear-dichroism scattering model in ptychographic imaging is introduced, and an efficient two-stage reconstruction algorithm is developed. Using the proposed algorithm on a uniaxial material, the dichroic transmission matrix can be recovered without an analyzer by using ptychography measurements with as few as three different polarization angles, with the help of an empty region to remove phase ambiguities.

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 ptychographic 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 el-ementwise operations. Numerically, the proposed algorithm outperforms state-of-the-art algorithms in both speed and image quality.

In order to determine the 3D structure of a thick sample, researchers have recently combined ptychography (for high resolution) and tomography (for 3D imaging) in a single experiment. 2-step methods are usually adopted for reconstruction, where the ptychography and tomography problems are often solved independently. In this paper, we provide a novel model and ADMM-based algorithm to jointly solve the ptychography-tomography problem iteratively, also employing total variation regularization. The proposed method permits large scan stepsizes for the ptychography experiment, requiring less measurements and being more robust to noise with respect to other strategies, while achieving higher reconstruction quality results.

Coherent ptychographic imaging experiments often discard the majority of the flux from a light source to define the coherence of the illumination. Even when the coherent flux is sufficient, the stability required during an exposure is another important limiting factor. Partial coherence analysis can considerably reduce these limitations. A partially coherent illumination can often be written as the superposition of a single coherent illumination convolved with a separable translational kernel. This article proposes the gradient decomposition of the probe (GDP), a model that exploits translational kernel separability, coupling the variances of the kernel with the transverse coherence. An efficient first-order splitting algorithm (GDP-ADMM) for solving the proposed nonlinear optimization problem is described. Numerical experiments demonstrate the effectiveness of the proposed method with Gaussian and binary kernel functions in fly-scan measurements. Remarkably, GDP-ADMM using nanoprobes produces satisfactory results even when the ratio between the kernel width and the beam size is more than one, or when the distance between successive acquisitions is twice as large as the beam width.

Spectroscopic ptychography is a powerful technique to determine the chemical composition of a sample with high spatial resolution. In spectro-ptychography, a sample is rastered through a focused X-ray beam with varying photon energy so that a series of phaseless diffraction data are recorded. Each chemical component in the material under investigation has a characteristic absorption and phase contrast as a function of photon energy. Using a dictionary formed by the set of contrast functions of each energy for each chemical component, it is possible to obtain the chemical composition of the material from high-resolution multi-spectral images. This paper presents SPA (spectroscopic ptychography with alternating direction method of multipliers), a novel algorithm to iteratively solve the spectroscopic blind ptychography problem. First, a nonlinear spectro-ptychography model based on Poisson maximum likelihood is designed, and then the proposed method is constructed on the basis of fast iterative splitting operators. SPA can be used to retrieve spectral contrast when considering either a known or an incomplete (partially known) dictionary of reference spectra. By coupling the redundancy across different spectral measurements, the proposed algorithm can achieve higher reconstruction quality when compared with standard state-of-the-art two-step methods. It is demonstrated how SPA can recover accurate chemical maps from Poisson-noised measurements, and its enhanced robustness when reconstructing reduced-redundancy ptychography data using large scanning step sizes is shown.

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.

Helical alignments within the hearts musculature have been speculated to be important in achieving physiological pumping efficiencies. Testing this possibility is difficult, however, because it is challenging to reproduce the fine spatial features and complex structures of the hearts musculature using current techniques. Here we report focused rotary jet spinning (FRJS), an additive manufacturing approach that enables rapid fabrication of micro/nanofiber scaffolds with programmable alignments in three-dimensional geometries. Seeding these scaffolds with cardiomyocytes enabled the biofabrication of tissue-engineered ventricles, with helically aligned models displaying more uniform deformations, greater apical shortening, and increased ejection fractions compared with circumferential alignments. The ability of FRJS to control fiber arrangements in three dimensions offers a streamlined approach to fabricating tissues and organs, with this work demonstrating how helical architectures contribute to cardiac performance.

Hydrogels are attractive materials for tissue engineering, but efforts to date have shown limited ability to produce the microstructural features necessary to promote cellular self-organization into hierarchical three-dimensional (3D) organ models. Here we develop a hydrogel ink containing prefabricated gelatin fibres to print 3D organ-level scaffolds that recapitulate the intra- and intercellular organization of the heart. The addition of prefabricated gelatin fibres to hydrogels enables the tailoring of the ink rheology, allowing for a controlled sol-gel transition to achieve precise printing of free-standing 3D structures without additional supporting materials. Shear-induced alignment of fibres during ink extrusion provides microscale geometric cues that promote the self-organization of cultured human cardiomyocytes into anisotropic muscular tissues in vitro. The resulting 3D-printed ventricle in vitro model exhibited biomimetic anisotropic electrophysiological and contractile properties.