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A method is proposed for high-resolution, three-dimensional reconstruction of internal structure of objects from planar transmission images. The described approach can be used with any form of radiation or matter waves, in principle, provided that the depth of field is smaller than the thickness of the sample. The physical optics basis for the method is elucidated and the reconstruction algorithm is presented in detail. A simulated example demonstrates an application of the method to three-dimensional electron transmission imaging of a nanoparticle under realistic radiation dose and spatial resolution constraints. It is envisaged that the method can be applicable in high-resolution transmission electron microscopy, soft X-ray microscopy, ultrasound imaging and other areas., 20 pages, 5 figures

The Imaging and Medical Beamline (IMBL) is a superconducting multipole wiggler-based beamline at the 3 GeV Australian Synchrotron operated by the Australian Nuclear Science and Technology Organisation (ANSTO). The beamline delivers hard X-rays in the 25–120 keV energy range and offers the potential for a range of biomedical X-ray applications, including radiotherapy and medical imaging experiments. One of the imaging modalities available at IMBL is propagation-based X-ray phase-contrast computed tomography (PCT). PCT produces superior results when imaging low-density materials such as soft tissue (e.g., breast mastectomies) and has the potential to be developed into a valuable medical imaging tool. We anticipate that PCT will be utilized for medical breast imaging in the near future with the advantage that it could provide better contrast than conventional X-ray absorption imaging. The unique properties of synchrotron X-ray sources such as high coherence, energy tunability, and high brightness are particularly well-suited for generating PCT data using very short exposure times on the order of less than 1 min. The coherence of synchrotron radiation allows for phase-contrast imaging with superior sensitivity to small differences in soft-tissue density. Here we also compare the results of PCT using two different detectors, as these unique source characteristics need to be complemented with a highly efficient detector. Moreover, the application of phase retrieval for PCT image reconstruction enables the use of noisier images, potentially significantly reducing the total dose received by patients during acquisition. This work is part of ongoing research into innovative tomographic methods aimed at the introduction of 3D X-ray medical imaging at the IMBL to improve the detection and diagnosis of breast cancer. Major progress in this area at the IMBL includes the characterization of a large number of mastectomy samples, both normal and cancerous, which have been scanned at clinically acceptable radiation dose levels and evaluated by expert radiologists with respect to both image quality and cancer diagnosis.

It has been argued that in atomic-resolution transmission electron microscopy (TEM) of sparse weakly scattering structures, such as small biological molecules, multiple electron scattering usually has only a small effect, while the in-molecule Fresnel diffraction can be significant due to the intrinsically shallow depth of focus. These facts suggest that the three-dimensional reconstruction of such structures from defocus image series collected at multiple rotational orientations of a molecule can be effectively performed for each atom separately, using the incoherent first Born approximation. The corresponding reconstruction method, termed here Differential Holographic Tomography, is developed theoretically and demonstrated computationally on several numerical models of biological molecules. It is shown that the method is capable of accurate reconstruction of the locations of atoms in a molecule from TEM data collected at a small number of random orientations of the molecule, with one or more defocus images per orientation. Possible applications to cryogenic electron microscopy and other areas are briefly discussed., 32 pages, 8 figures, version 5c (a few typos have been found in the previous version and fixed in the current version)

A method for extracting the dark-field signal in propagation-based phase-contrast imaging is proposed. In the case of objects consisting predominantly of a single material, or several different materials with similar ratios of the real decrement to the imaginary part of the complex refractive index, the proposed method requires a single image for extraction of the dark-field signal in two-dimensional projection imaging. In the case of three-dimensional tomographic imaging, the method needs only one image to be collected at each projection angle. Initial examples using simulated and experimental data indicate that this method can improve visualization of small sharp features inside a larger object, e.g. the visualization of microcalcifications in propagation-based x-ray breast cancer imaging. It is suggested that the proposed approach may be useful in other forms of biomedical imaging, where it can help one to obtain additional small-angle scattering information without increasing the radiation dose to the sample.

Signal-to-noise ratio, spatial resolution and information capacity of tomographic coherent diffractive imaging are investigated; the results are expected to be useful for the design and analysis of synchrotron and XFEL-based diffractive imaging experiments., It is shown that the average signal-to-noise ratio (SNR) in the three-dimensional electron-density distribution of a sample reconstructed by coherent diffractive imaging cannot exceed twice the square root of the ratio of the mean total number of scattered photons detected during the scan and the number of spatially resolved voxels in the reconstructed volume. This result leads to an upper bound on Shannon’s information capacity of this imaging method by specifying the maximum number of distinguishable density distributions within the reconstructed volume when the radiation dose delivered to the sample and the spatial resolution are both fixed. If the spatially averaged SNR in the reconstructed electron density is fixed instead, the radiation dose is shown to be proportional to the third or fourth power of the spatial resolution, depending on the sampling of the three-dimensional diffraction space and the scattering power of the sample.

To evaluate and compare the image quality of propagation-based phase-contrast computed tomography (PB-CT) using synchrotron radiation and conventional cone-beam breast computed tomography (CBBCT) based on various radiological image quality criteria. Eight excised breast tissue samples of various sizes and containing different lesion types were scanned using PB-CT at a synchrotron facility and using CBBCT at a university-affiliated breast imaging centre. PB-CT scans were performed at two different mean glandular dose (MGD) levels: standard (5.8 mGy) and low (1.5 mGy), for comparison with CBBCT scans at the standard MGD (5.8 mGy). Image quality assessment was carried out using six quality criteria and six independent medical imaging experts in a reading room with mammography workstations. The interobserver agreement between readers was evaluated using intraclass correlation coefficient (ICC), and image quality was compared between the two breast imaging modalities using the area under the visual grading characteristic curve (AUCVGC). Interobserver agreement between the readers showed moderate reliability for five image criteria (ICC: ranging from 0.488 to 0.633) and low reliability for one criterion (image noise) (ICC 0.307). For five image quality criteria (overall quality, perceptible contrast, lesion sharpness, normal tissue interfaces, and calcification visibility), both standard-dose PB-CT images (AUCVGC 0.958 to 1, p ≤ .05) and low dose PB-CT images (AUCVGC 0.785 to 0.834, p ≤ .05) were of significantly higher image quality than standard-dose CBBCT images. Synchrotron-based PB-CT can achieve a significantly higher radiological image quality at a substantially lower radiation dose compared with conventional CBBCT. • PB-CT using synchrotron radiation results in higher image quality than conventional CBBCT for breast imaging. • PB-CT using synchrotron radiation requires a lower radiation dose than conventional CBBCT for breast imaging. • PB-CT can help clinicians diagnose patients with breast cancer.

In this study we demonstrate the first direct comparison between synchrotron x-ray propagation-based CT (PB-CT) and cone-beam breast-CT (CB-CT) on human mastectomy specimens (N = 12) including different benign and malignant lesions. The image quality and diagnostic power of the obtained data sets were compared and judged by two independent expert radiologists. Two cases are presented in detail in this paper including a comparison with the corresponding histological evaluation. Results indicate that with PB-CT it is possible to increase the level of contrast-to-noise ratio (CNR) keeping the same level of dose used for the CB-CT or achieve the same level of CNR reached by CB-CT at a lower level of dose. In other words, PB-CT can achieve a higher diagnostic potential compared to the commercial breast-CT system while also delivering a considerably lower mean glandular dose. Therefore, we believe that PB-CT technique, if translated to a clinical setting, could have a significant impact in improving breast cancer diagnosis.

The following paper describes a method for three-dimensional (3D) reconstruction of multi-material objects based on propagation-based X-ray phase-contrast tomography (PB-CT) with phase retrieval using the homogenous form of the Transport-of-Intensity equation (TIE-Hom). Unlike conventional PB-CT algorithms that perform phase retrieval of individual projections, the described post-reconstruction phase-retrieval method is applied in 3D to a localised region of the CT-reconstructed volume. We demonstrate via numerical simulations the accuracy and noise characteristics of the method under a variety of experimental conditions, comparing it to both conventional absorption tomography and two-dimensional (2D) TIE-Hom phase retrieval applied to projection images. The results indicate that the 3D post-reconstruction method generally achieves a modest improvement in noise suppression over existing PB-CT methods. It is also shown that potentially large computational gains over projection-based phase retrieval for multi-material samples are possible. In particular, constraining phase retrieval to a localised 3D region of interest reduces the overall computational cost and eliminates the need for multiple CT reconstructions and global 2D phase retrieval operations for each material within the sample., 23 pages, 8 figures

Rationale and Objectives This study employs clinical/radiological evaluation in establishing the optimum imaging conditions for breast cancer imaging using the X-ray propagation-based phase-contrast tomography. Materials and Methods Two series of experiments were conducted and in total 161 synchrotron-based computed tomography (CT) reconstructions of one breast mastectomy specimen were produced at different imaging conditions. Imaging factors include sample-to-detector distance, X-ray energy, CT reconstruction method, phase retrieval algorithm applied to the CT projection images and maximum intensity projection. Observers including breast radiologists and medical imaging experts compared the quality of the reconstructed images with reference images approximating the conventional (absorption) CT. Various radiological image quality attributes in a visual grading analysis design were used for the radiological assessments. Results The results show that the application of the longest achievable sample-to-detector distance (9.31 m), the lowest employed X-ray energy (32 keV), the full phase retrieval, and the maximum intensity projection can significantly improve the radiological quality of the image. Several combinations of imaging variables resulted in images with very high-quality scores. Conclusion The results of the present study will support future experimental and clinical attempts to further optimize this innovative approach to breast cancer imaging.

Phase-contrast X-ray imaging can improve the visibility of weakly absorbing objects (e.g. soft tissues) by an order of magnitude or more compared to conventional radiographs. Combining phase retrieval with computed tomography (CT) can increase the signal-to-noise ratio (SNR) by up to two orders of magnitude over conventional CT at the same radiation dose, without loss of image quality. Our experiments reveal that as the radiation dose decreases, the relative improvement in SNR increases. We show that this enhancement can be traded for a reduction in dose greater than the square of the gain in SNR. Upon reducing the dose 300 fold, the phase-retrieved SNR was still up to 9.6 ± 0.2 times larger than the absorption contrast data with spatial resolution in the tens of microns. We show that this theoretically reveals the potential for dose reduction factors in the tens of thousands without loss in image quality, which would have a profound impact on medical and industrial imaging applications.

An uncertainty inequality is presented that establishes a lower limit for the product of the variance of the time-averaged intensity of a mode of a quantized electromagnetic field and the degree of its spatial localization. The lower limit is determined by the vacuum fluctuations within the volume corresponding to the width of the mode. This result also leads to a generalized form of the Heisenberg uncertainty principle for boson fields in which the lower limit for the product of uncertainties in the spatial and momentum localization of a mode is equal to the product of Planck’s constant and a dimensionless functional which reflects the joint signal-to-noise ratio of the position and momentum of vacuum fluctuations in the region of the phase space occupied by the mode. Experimental X-ray synchrotron measurements provide an initial verification of the proposed theory in the case of Poisson statistics.

We present the outcomes of combined feasibility studies carried out at Elettra and Australian Synchrotron to evaluate novel protocols for threedimensional (3D) mammographic phase contrast imaging. A custom designed plastic phantom and some tissue samples have been studied at diverse resolution scales and experimental conditions. Several computed tomography (CT) reconstruction algorithms with different pre-processing and post-processing steps have been considered. Special attention was paid to the effect of phase retrieval on the diagnostic value of the reconstructed images. The images were quantitatively evaluated using objective quality indices in comparison with subjective assessments performed by three experienced radiologists and one pathologist. We show that the propagation-based phase-contrast imaging (PBI) leads to substantial improvement to the contrast-to-noise and to the intrinsic quality of the reconstructed CT images compared with conventional techniques as well as to an important reduction of the delivered doses, thus opening the way to clinical implementations.

Localizing the sources of electrical activity in the brain from electroencephalographic (EEG) data is an important tool for noninvasive study of brain dynamics. Generally, the source localization process involves a high‐dimensional inverse problem that has an infinite number of solutions and thus requires additional constraints to be considered to have a unique solution. In this article, we propose a novel method for EEG source localization. The proposed method is based on dividing the cerebral cortex of the brain into a finite number of “functional zones” which correspond to unitary functional areas in the brain. To specify the sparsity profile of human brain activity more concisely, the proposed approach considers grouping of the electrical current dipoles inside each of the functional zones. In this article, we investigate the use of Brodmann's areas as the functional zones while sparse Bayesian learning is used to perform sparse approximation. Numerical experiments are conducted on a realistic head model obtained from segmentation of MRI images of the head and includes four major compartments namely scalp, skull, cerebrospinal fluid (CSF), and brain with relative conductivity values. Three different electrode setups are tested in the numerical experiments. The results demonstrate that the proposed approach is quite promising in solving the EEG source localization problem. In a noiseless environment with 71 electrodes, the proposed method was found to accurately locate up to 6 simultaneously active sources with accuracy >70%.

We report the results of a systematic study of phase-contrast x-ray computed tomography in the propagation-based and analyser-based modes using specially designed phantoms and excised breast tissue samples. The study is aimed at the quantitative evaluation and subsequent optimization, with respect to detection of small tumours in breast tissue, of the effects of phase contrast and phase retrieval on key imaging parameters, such as spatial resolution, contrast-to-noise ratio, x-ray dose and a recently proposed ‘intrinsic quality’ characteristic which combines the image noise with the spatial resolution. We demonstrate that some of the methods evaluated in this work lead to substantial (more than 20-fold) improvement in the contrast-to-noise and intrinsic quality of the reconstructed tomographic images compared with conventional techniques, with the measured characteristics being in good agreement with the corresponding theoretical estimations. This improvement also corresponds to an approximately 400-fold reduction in the x-ray dose, compared with conventional absorption-based tomography, without a loss in the imaging quality. The results of this study confirm and quantify the significant potential benefits achievable in three-dimensional mammography using x-ray phase-contrast imaging and phase-retrieval techniques.

Quantitative phase retrieval is experimentally demonstrated using the Inverse Compton Scattering X-ray source available at the Accelerator Test Facility (ATF) in the Brookhaven National Laboratory. Phase-contrast images are collected using in-line geometry, with a single X-ray pulse of approximate duration of one picosecond. The projected thickness of homogeneous samples of various polymers is recovered quantitatively from the time-averaged intensity of transmitted X-rays. The data are in good agreement with the expectations showing that ATF Inverse Compton Scattering source is suitable for performing phase-sensitive quantitative X-ray imaging on the picosecond scale. The method shows promise for quantitative imaging of fast dynamic phenomena.