Three-dimensional contrast transfer functions in propagation-based tomography

A single-step method is developed for three-dimensional reconstruction of the spatial distribution of complex refractive index in weakly scattering objects from multiple planar transmission images. The images are collected using coherent or partially-coherent illumination at a range of incident directions in the Fresnel region after free-space propagation from the object to the detector. The method is based on the contrast transfer function formalism extended to the cases of partially-coherent illumination and strongly absorbing samples. The proposed tomographic methods can be used for 3D reconstruction of internal structure of objects with X-rays, electrons and other forms of radiation and matter waves. Compared to related previously published methods for propagation-based phase-contrast tomography, the results reported in the present paper can be applied to a wider range of imaging conditions and can be also advantageous in terms of computational efficiency and robustness with respect to noise

A feasibility study of X-ray phase-contrast mammographic tomography at the Imaging and Medical beamline of the Australian Synchrotron

Results are presented of a recent experiment at the Imaging and Medical beamline of the Australian Synchrotron intended to contribute to the implementation of low-dose high-sensitivity three-dimensional mammographic phase-contrast imaging, initially at synchrotrons and subsequently in hospitals and medical imaging clinics. The effect of such imaging parameters as X-ray energy, source size, detector resolution, sample-to-detector distance, scanning and data processing strategies in the case of propagation-based phase-contrast computed tomography (CT) have been tested, quantified, evaluated and optimized using a plastic phantom simulating relevant breast-tissue characteristics. Analysis of the data collected using a Hamamatsu CMOS Flat Panel Sensor, with a pixel size of 100 μm, revealed the presence of propagation-based phase contrast and demonstrated significant improvement of the quality of phase-contrast CT imaging compared with conventional (absorption-based) CT, at medically acceptable radiation doses

Imaging Breast Microcalcifications Using Dark-Field Signal in Propagation-Based Phase-Contrast Tomography

Breast microcalcifications are an important primary radiological indicator of breast cancer. However, microcalcification classification and diagnosis may be still challenging for radiologists due to limitations of the standard 2D mammography technique, including spatial and contrast resolution. In this study, we propose an approach to improve the detection of microcalcifications in propagation-based phase-contrast X-ray computed tomography of breast tissues. Five fresh mastectomies containing microcalcifications were scanned at different X-ray energies and radiation doses using synchrotron radiation. Both bright-field (i.e. conventional phase-retrieved images) and dark-field images were extracted from the same data sets using different image processing methods. A quantitative analysis was performed in terms of visibility and contrast-to-noise ratio of microcalcifications. The results show that while the signal-to-noise and the contrast-to-noise ratios are lower, the visibility of the microcalcifications is more than two times higher in the dark-field images compared to the bright-field images. Dark-field images have also provided more accurate information about the size and shape of the microcalcifications

Evaluation of Spatial Resolution and Noise Sensitivity of sLORETA Method for EEG Source Localization Using Low-Density Headsets

Electroencephalography (EEG) has enjoyed considerable attention over the pastcentury and has been applied for diagnosis of epilepsy, stroke, traumatic braininjury and other disorders where 3D localization of electrical activity in thebrain is potentially of great diagnostic value. In this study we evaluate theprecision and accuracy of spatial localization of electrical activity in thebrain delivered by a popular reconstruction technique sLORETA applied to EEGdata collected by two commonly used low-density headsets with 14 and 19measurement channels, respectively. Numerical experiments were performed for arealistic head model obtained by segmentation of MRI images. The EEG sourcelocalization study was conducted with a simulated single active dipole, as wellas with two spatially separated simultaneously active dipoles, as a function ofdipole positions across the neocortex, with several different noise levels inthe EEG signals registered on the scalp. The results indicate that while thereconstruction accuracy and precision of the sLORETA method are consistentlyhigh in the case of a single active dipole, even with the low-resolution EEGconfigurations considered in the present study, successful localization is muchmore problematic in the case of two simultaneously active dipoles. Thequantitative analysis of the width of the reconstructed distributions of theelectrical activity allows us to specify the lower bound for the spatialresolution of the sLORETA-based 3D source localization in the considered cases

Fast three-dimensional phase retrieval in propagation-based x-ray tomography

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

Noise-resolution uncertainty principle in classical and quantum systems

We show that the width of an arbitrary function and the width of the distribution of its values cannot be made arbitrarily small simultaneously. In the case of ergodic stochastic processes, an ensuing uncertainty relationship is then demonstrated for the product of correlation length and variance. A closely related uncertainty principle is also established for the average degree of fourth-order coherence and the spatial width of modes of bosonic quantum fields. However, it is shown that, in the case of stochastic and quantum observables, certain non-classical states with sub-Poissonian statistics, such as for example photon number squeezed states in quantum optics, can overcome the "classical" noise-resolution uncertainty limit. This uncertainty relationship, which is fundamentally different from the Heisenberg and related uncertainty principles, can define an upper limit for the information capacity of communication and imaging systems. It is expected to be useful in a variety of problems in classical and quantum optics and imaging

On noise-resolution uncertainty in quantum field theory

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

Phase-contrast clinical breast CT: Optimization of imaging setups and reconstruction workflows

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

X-ray Phase-Contrast Computed Tomography for Soft Tissue Imaging at the Imaging and Medical Beamline (IMBL) of the Australian Synchrotron

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