Increasing interest in three-dimensional nanostructures adds impetus to electron microscopy techniques capable of imaging at or below the nanoscale in three dimensions. We present a reconstruction algorithm that takes as input a focal series of four-dimensional scanning transmission electron microscopy (4D-STEM) data. We apply the approach to a lead iridate, Pb$_2$Ir$_2$O$_7$, and yttrium-stabilized zirconia, Y$_{0.095}$Zr$_{0.905}$O$_2$, heterostructure from data acquired with the specimen in a single plan-view orientation, with the epitaxial layers stacked along the beam direction. We demonstrate that Pb–Ir atomic columns are visible in the uppermost layers of the reconstructed volume. We compare this approach to the alternative techniques of depth sectioning using differential phase contrast scanning transmission electron microscopy (DPC-STEM) and multislice ptychographic reconstruction.

In order to merge the advantages of the traditional compressed sensing (CS) methodology and the data-driven deep network scheme, this paper proposes a physical model-driven deep network, termed CS-Net, for solving target image reconstruction problems in through-the-wall radar imaging. The proposed method consists of two consequent steps. First, a learned convolutional neural network prior is introduced to replace the regularization term in the traditional iterative CS-based method to capture the redundancy of the radar echo signal. Moreover, the physical model of the radar signal is used in the data consistency layer to encourage consistency with the measurements. Second, the iterative CS optimization is unrolled to yield a deep learning network, where the weight, regularization parameter, and the other parameters are learnable. A quantity of training data enables the network to extract high-dimensional characteristics of the radar echo signal to reconstruct the spatial target image. Simulation results demonstrated that the proposed method can achieve accurate target image reconstruction and was superior to the traditional CS method, in terms of mean squared error and the target texture details.

This work examines the impact of the inverse chirp z-transform (ICZT) for frequency-to-time-domain conversion during image reconstruction of a pre-clinical radar-based breast microwave imaging system operating over 1–8 GHz. Two anthropomorphic breast phantoms were scanned with this system, and the delay-multiply-and-sum beamformer was used to reconstruct images of the phantoms, after using either the ICZT or the inverse discrete Fourier transform (IDFT) for frequency-to-time domain conversion. The contrast, localization error, and presence of artifacts in the reconstructions were compared. The use of the IDFT resulted in prominent ring artifacts that were not present when using the ICZT, and the use of the ICZT resulted in higher contrast between the tumor and clutter responses. In one of the phantoms, the tumor response was only visible in reconstructions that used the ICZT. The use of the ICZT evaluated with a time-step size of 11 ps resulted in the reduction of prominent artifacts present when using the IDFT and the successful identification of the tumor response in the reconstructed images.

Early detection of breast cancer is required to increase the chances of a successful treatment. However, current breast-imaging systems such as X-Ray mammography, breast ultrasound, and magnetic resonance imaging have technological limitations so that novel solutions are needed to address this major societal problem. The current paper considers ultra-wideband (UWB) microwave radiation in the frequency band from 1 to 9 GHz. Given by the non-ionizing nature of microwaves frequent check-ups are more feasible. In this work, we propose algorithms for qualitative and quantitative microwave breast imaging for a transmission-based UWB system. Based on numerical and experimental data, the performance of the algorithms has been investigated and compared. Finally, microwave images obtained during an initial patient study are discussed relative to corresponding X-ray images.

Electron tomography has become an essential tool for three-dimensional (3D) characterization of nanomaterials. In recent years, advances have been made in specimen preparation and mounting, acquisition geometries, and reconstruction algorithms. All of these components work together to optimize the resolution and clarity of an electron tomogram. However, one important component of the data-processing has received less attention: the 2D tilt series alignment. This is challenging for a number of reasons, namely because the nature of the data sets and the need to be coherently aligned over the full range of angles. An inaccurate alignment may be difficult to identify, yet can significantly limit the final 3D resolution. In this work, we present an improved center-of-mass alignment model that allows us to overcome discrepancies from unwanted objects that enter the imaging area throughout the tilt series. In particular, we develop an approach to overcome changes in the total mass upon rotation of the imaging area. We apply our approach to accurately recover small Pt nanoparticles embedded in a zeolite that may otherwise go undetected both in the 2D microscopy images and the 3D reconstruction. In addition to this, we highlight the particular effectiveness of the compressed sensing methods with this data set.

Multi-view images are acquired by a lensless compressive imaging architecture, which consists of an aperture assembly and multiple sensors. The aperture assembly consists of a two-dimensional array of aperture elements whose transmittance can be individually controlled to implement a compressive sensing matrix. For each transmittance pattern of the aperture assembly, each of the sensors takes a measurement. The measurement vectors from the multiple sensors represent multi-view images of the same scene. We present theoretical framework for multi-view reconstruction and experimental results for enhancing quality of image using compressive measurements from multiple sensors.

Indirect high resolution electron microscopy using one of several possible data-set geometries offers advantages over conventional high-resolution imaging in enabling the recovery of the complex wavefunction at the specimen exit plane and simultaneously eliminating the aberrations present in the objective lens. This article discusses results obtained using this method from structures formed by inorganic materials confined within the bores of carbon nanotubes. Such materials are shown to be atomically regulated due to their confinement, leading to integral layer architectures that we have termed “Feynman crystals.” These one-dimensional (1D) crystals also show a wide range of structural deviations from the bulk, including unexpected lattice distortions, and in some cases entirely new forms have been observed.

Improvements in instrumentation and image processing techniques mean that methods involving reconstruction of focal or beam-tilt series of images are now realizing the promise they have long offered. This indirect approach recovers both the phase and the modulus of the specimen exit plane wave function and can extend the interpretable resolution. However, such reconstructions require the a posteriori determination of the objective lens aberrations, including the actual beam tilt, defocus, and twofold and threefold astigmatism. In this review, we outline the theory behind exit plane wavefunction reconstruction and describe methods for the accurate and automated determination of the required coefficients of the wave aberration function. Finally, recent applications of indirect reconstruction in the structural analysis of complex oxides are presented.

Cone-beam X-ray microtomography attracts increasing attention due to its applications in biomedical sciences, material engineering, and industrial nondestructive evaluation. Rapid volumetric image reconstruction is highly desirable in all these areas for prompt visualization and analysis of complex structures of interest. In this article, we reformulate a generalized Feldkamp cone-beam image reconstruction algorithm, utilize curved voxels and mapping tables, improve the reconstruction efficiency by an order of magnitude relative to a direct implementation of the standard algorithm, and demonstrate the feasibility with numerical simulation and experiments using a prototype cone-beam X-ray microtomographic system. Our fast algorithm reconstructs a 256-voxel cube from 100 projections within 2 min on an Intel Pentium II® 233 MHz personal computer, produces satisfactory image quality, and can be further accelerated using special hardware and/or parallel processing techniques.

The vault complex is a ubiquitous 13-MDa ribonucleoprotein assembly, composed of three proteins (TEP1, 240 kDa; VPARP, 193 kDa; and MVP, 100 kDa) that are highly conserved in eukaryotes and an untranslated RNA (vRNA). The vault has been shown to affect multidrug resistance in cancer cells, and one particular component, MVP, is thought to play a role in the transport of drug from the nucleus. To locate the position of the vRNA, vaults were treated with RNases, and cryo-electron microscopy (cryo-EM) was performed on the resulting complexes. Using single-particle reconstruction techniques, 3,476 particle images were combined to generate a 22-Å-resolution structure. Difference mapping between the RNase-treated vault and the previously calculated intact vault reconstructions reveals the vRNA to be at the ends of the vault caps. In this position, the vRNA may interact with both the interior and exterior environments of the vault. The finding of a 16-fold density ring at the top of the cap has allowed modeling of the WD40 repeat domain of the vault TEP1 protein within the cryo-EM vault density. Both stoichiometric considerations and the finding of higher resolution for the computationally selected and refined “barrel only” images indicate a possible symmetry mismatch between the barrel and the caps. The molecular architecture of the complex is emerging, with 96 copies of MVP composing the eightfold symmetric barrel, and the vRNA together with one copy of TEP1 and four predicted copies of VPARP comprising each cap.

Lucy's algorithm is applied to iterative blind deconvolution method. This new approach enables to reconstruct a greatly extended object from one speckle frame and to reinforce image domain constraints. A greatly extended object makes speckle images flow over detecting surface. Lucy's algorithm is accommodated to handle such an image and built into iterative blind deconvolution methods. Computer simulation and observational data analyses are conducted and the effectiveness of the proposed methods are exemplified.

A technique for reconstructing diffraction-limited image of an object from speckle images without reference star is applied to both simulated and real data. The object spectrum is estimated by blind deconvolution using the power spectrum of the speckle images and the phase is restored from the bispectrum.

In an optical interferometer, the delay lines compensate the optical path difference between the different arms of the interferometer, so that the interference patterns, which contain the information, can be observed. Thanks to the phase closure technics, the phase information can be extracted, despite the random phase shifts introduced by the atmospheric turbulence. As we used the redundant spacing calibration to reconstruct an image, the telescopes of the interferometer have to be arranged according to a given iterative procedure. The advantage of this technics is to enable the reconstruction of an image without any a priori knowledge on the object. But this implies constraints on the configurations of the telescopes array, and therefore on the offsets and on the kinematics of the delay lines. Their motion have been studied to define the future layout of the 3 telescopes optical interferometer of the Calern's Observatory (CHARON III project) and also to define the operational procedure.

A new method to reconstruct the phase of bidimensional interferograms, obtained through pupil-plane interferometry is presented. We compute the average complex phasor components of the cross-spectrum on a data set to reconstruct the original unperturbed phase. We present preliminary results on simulated images which visibility phases are distorted using a model of atmospheric perturbed wavefronts.