Yakov Nesterets

Refracting Röntgen’s rays: Propagation-based x-ray phase contrast for biomedical imaging

Absorption-contrast x-ray imaging serves to visualize the variation in x-ray attenuation within the volume of a given sample, whereas phase contrast allows one to visualize variations in x-ray refractive index. The former imaging mechanism has been well known and widely utilized since the time of Rontgen’s Nobel prize winning work, whereas the latter mechanism—sought for, but not found, by Rontgen himself—has laid the foundation for a revolution in x-ray imaging which is the central topic of this review. We consider the physical imaging mechanisms underlying both absorption contrast and phase contrast, together with the associated inverse problem of how one may obtain quantitative two- or three-dimensional information regarding a sample, given one or more phase-contrast images of the same. Practical questions are considered, regarding optimized phase-contrast imaging geometries as a function of detector resolution, source size, x-ray spectrum, and dose. Experimental examples pertaining to biomedical appli...

Some simple rules for contrast, signal-to-noise and resolution in in-line x-ray phase-contrast imaging

Simple analytical expressions are derived for the spatial resolution, contrast and signal-to-noise in X-ray projection images of a generic phase edge. The obtained expressions take into account the maximum phase shift generated by the sample and the sharpness of the edge, as well as such parameters of the imaging set-up as the wavelength spectrum and the size of the incoherent source, the source-to-object and object-to-detector distances and the detector resolution. Different asymptotic behavior of the expressions in the cases of large and small Fresnel numbers is demonstrated. The analytical expressions are compared with the results of numerical simulations using Kirchhoff diffraction theory, as well as with experimental X-ray measurements.

Toolbox for advanced x-ray image processing

A software system has been developed for high-performance Computed Tomography (CT) reconstruction, simulation and other X-ray image processing tasks utilizing remote computer clusters optionally equipped with multiple Graphics Processing Units (GPUs). The system has a streamlined Graphical User Interface for interaction with the cluster. Apart from extensive functionality related to X-ray CT in plane-wave and cone-beam forms, the software includes multiple functions for X-ray phase retrieval and simulation of phase-contrast imaging (propagation-based, analyzer crystal based and Talbot interferometry). Other features include several methods for image deconvolution, simulation of various phase-contrast microscopy modes (Zernike, Schlieren, Nomarski, dark-field, interferometry, etc.) and a large number of conventional image processing operations (such as FFT, algebraic and geometrical transformations, pixel value manipulations, simulated image noise, various filters, etc.). The architectural design of the system is described, as well as the two-level parallelization of the most computationally-intensive modules utilizing both the multiple CPU cores and multiple GPUs available in a local PC or a remote computer cluster. Finally, some results about the current system performance are presented. This system can potentially serve as a basis for a flexible toolbox for X-ray image analysis and simulation, that can efficiently utilize modern multi-processor hardware for advanced scientific computations.

Noise propagation in x-ray phase-contrast imaging and computed tomography

Three phase-retrieval algorithms, based on the transport-of-intensity equation and on the contrast transfer function for propagation-based imaging, and on the linearized geometrical optics approximation for analyser-based imaging, are investigated. The algorithms are compared in terms of their effect on propagation of noise from projection images to the corresponding phase-retrieved images and further to the computed tomography (CT) images/slices of a monomorphous object reconstructed using filtered backprojection algorithm. The comparison is carried out in terms of an integral noise characteristic, the variance, as well as in terms of a simple figure-of-merit, i.e. signal-to-noise ratio per unit dose. A gain factor is introduced that quantitatively characterizes the effect of phase retrieval on the variance of noise in the reconstructed projection images and in the axial slices of the object. Simple analytical expressions are derived for the gain factor and the signal-to-noise ratio, which indicate that the application of phase-retrieval algorithms can increase these parameters by up to two orders of magnitude compared to raw projection images and conventional CT, thus allowing significant improvement in the image quality and/or reduction of the x-ray dose delivered to the patient.

Analysis and interpretation of the first monochromatic X-ray tomography data collected at the Australian Synchrotron Imaging and Medical beamline.

The first monochromatic X-ray tomography experiments conducted at the Imaging and Medical beamline of the Australian Synchrotron are reported. The sample was a phantom comprising nylon line, Al wire and finer Cu wire twisted together. Data sets were collected at four different X-ray energies. In order to quantitatively account for the experimental values obtained for the Hounsfield (or CT) number, it was necessary to consider various issues including the point-spread function for the X-ray imaging system and harmonic contamination of the X-ray beam. The analysis and interpretation of the data includes detailed considerations of the resolution and efficiency of the CCD detector, calculations of the X-ray spectrum prior to monochromatization, allowance for the response of the double-crystal Si monochromator used (via X-ray dynamical theory), as well as a thorough assessment of the role of X-ray phase-contrast effects. Computer simulations relating to the tomography experiments also provide valuable insights into these important issues. It was found that a significant discrepancy between theory and experiment for the Cu wire could be largely resolved in terms of the effect of the point-spread function. The findings of this study are important in respect of any attempts to extract quantitative information from X-ray tomography data, across a wide range of disciplines, including materials and life sciences.

Accuracy and precision of reconstruction of complex refractive index in near-field single-distance propagation-based phase-contrast tomography

We investigate the quantitative accuracy and noise sensitivity of reconstruction of the 3D distribution of complex refractive index, n(r)=1−δ(r)+iβ(r), in samples containing materials with different refractive indices using propagation-based phase-contrast computed tomography (PB-CT). Our present study is limited to the case of parallel-beam geometry with monochromatic synchrotron radiation, but can be readily extended to cone-beam CT and partially coherent polychromatic X-rays at least in the case of weakly absorbing samples. We demonstrate that, except for regions near the interfaces between distinct materials, the distribution of imaginary part of the refractive index, β(r), can be accurately reconstructed from a single projection image per view angle using phase retrieval based on the so-called homogeneous version of the Transport of Intensity equation (TIE-Hom) in combination with conventional CT reconstruction. In contrast, the accuracy of reconstruction of δ(r) depends strongly on the choice of the...

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.

Investigation of the imaging quality of synchrotron-based phase-contrast mammographic tomography

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.

A method for local deconvolution

A new method for deconvolution of one-dimensional and multidimensional data is suggested. The proposed algorithm is local in the sense that the deconvolved data at a given point depend only on the value of the experimental data and their derivatives at the same point. In a regularized version of the algorithm the deconvolution is constructed iteratively with the help of an approximate deconvolution operator that requires only the low-order derivatives of the data and low-order integral moments of the point-spread function. This algorithm is expected to be particularly useful in applications in which only partial knowledge of the point-spread function is available. We tested and compared the proposed method with some of the popular deconvolution algorithms using simulated data with various levels of noise.

Coherent and diffuse X-ray scattering in crystals modulated by a surface acoustic wave

Equations describing the coherent and diffuse scattering in a crystal modulated by a surface acoustic wave (SAW) are derived using the dynamical X-ray diffraction theory. The effect of depth attenuation of the Rayleigh surface wave amplitude on the crystal rocking curve profiles is investigated. Results of the numerical simulation of the dynamical diffraction in a mosaic crystal modulated by a SAW, taking into account a block size distribution, are presented. It is shown that the diffuse scattering is distributed in the reciprocal space not only in the vicinity of the main diffraction peak but also about the satellite diffraction peaks, and this distribution depends on the size fluctuations of the crystal defects. Theoretical reciprocal space maps and rocking curves are compared with the corresponding experimental results.