Moment-based angular difference estimation between two tomographic projections in 2D and 3D

International audienceThis paper introduces a new method for estimating the angular difference between two tomographic projections belonging to a set of projections taken at unknown directions in 2D and 3D. Our method relies on the projection neighbor selection in projection moment space, the calculation of the angular differences between these neighboring projections using moment properties and a projection moment neighborhood graph. The accuracy and the robustness of our method are shown on a test database including fifty 2D and 3D gray-level images at different resolutions and with different levels of noise

Analysis of Tomographic Reconstruction of 2D Images using the Distribution of Unknown Projection Angles

It is well known that a band-limited signal can be reconstructed from its uniformly spaced samples if the sampling rate is sufficiently high. More recently, it has been proved that one can reconstruct a 1D band-limited signal even if the exact sample locations are unknown, but given just the distribution of the sample locations and their ordering in 1D. In this work, we extend the analytical bounds on the reconstruction error in such scenarios for quasi-bandlimited signals. We also prove that the method for such a reconstruction is resilient to a certain proportion of errors in the specification of the sample location ordering. We then express the problem of tomographic reconstruction of 2D images from 1D Radon projections under unknown angles with known angle distribution, as a special case for reconstruction of quasi-bandlimited signals from samples at unknown locations with known distribution. Building upon our theoretical background, we present asymptotic bounds for 2D quasi-bandlimited image reconstruction from 1D Radon projections in the unknown angles setting, which commonly occurs in cryo-electron microscopy (cryo-EM). To the best of our knowledge, this is the first piece of work to perform such an analysis for 2D cryo-EM, even though the associated reconstruction algorithms have been known for a long time

Diffraction tomography with Fourier ptychography

This paper presents a technique to image the complex index of refraction of a sample across three dimensions. The only required hardware is a standard microscope and an array of LEDs. The method, termed Fourier ptychographic tomography (FPT), first captures a sequence of intensity-only images of a sample under angularly varying illumination. Then, using principles from ptychography and diffraction tomography, it computationally solves for the sample structure in three dimensions. The experimental microscope demonstrates a lateral spatial resolution of 0.39 μm and an axial resolution of 3.7 μm at the Nyquist–Shannon sampling limit (0.54 and 5.0 μm at the Sparrow limit, respectively) across a total imaging depth of 110 μm. Unlike competing methods, this technique quantitatively measures the volumetric refractive index of primarily transparent and contiguous sample features without the need for interferometry or any moving parts. Wide field-of-view reconstructions of thick biological specimens suggest potential applications in pathology and developmental biology

Master of Science

thesisMineral identification is an extremely important topic in metallurgical engineering, and rare earth particle identification grows increasingly important as national and global demand increases. Due to the small concentration wherein they are usually found in the Florida phosphate industry, particle identification methods often overlook, miscount, and do not adequately describe the rare earth particles in sample streams. In this regard, dual energy radiography followed by X-ray tomography is used to quantitatively identify rare earth particles and to establish their characteristics in selected samples. It is hypothesized that by combining these two methods, better data can be gathered to make an accurate accounting of the parts per million concentration of the minerals and that time can be saved by employing both processes instead of only using X-ray tomography, which would be one procedure for mineral identification and liberation analysis. To verify that the proposed methodology does as claimed, it was used to identify rare earth particles in three sample streams provided by the Florida Industrial and Phosphate Research Institute (FIPR). Each sample was separated by size, prepared, then scanned by dual energy radiography, thresholded, and prepared and scanned by high resolution X-ray microtomography. The results were then analyzed. Based on the final digital 3D reconstruction of the samples, it was concluded that this methodology was indeed faster and more time efficient than only X-ray tomography. It was also concluded that some additional data could be gathered from the preconcentration of the X-ray tomography samples caused by preliminary dual energy radiography, but that data were dependent on the sample stream and not guaranteed for every sample scanned using this method. Therefore, it was finally concluded that the proposed methodology was time beneficial and that the potential additional data that could be gathered made this process worth exploring for future projects, especially if they involved identification of trace particles concentrated on a small, parts per million scale

On Wiener type filters in SPECT

International audienceFor 2D data with Poisson noise we give explicit formulas for the optimal space-invariant Wiener type filter with some a priori geometric restrictions on the window function. We show that, under some natural geometric condition, this restrictedly optimal Wiener type filter admits a very efficient approximation by an approximately optimal filter with unknown object power spectrum. Generalizations to the case of some more general noise model are also given. Proceeding from these results we (a) explain, in particular, an efficiency of some well-known "1D" approximately optimal space-invariant Wiener type filtering scheme with unknown object power spectrum in single-photon emission computed tomography (SPECT) and positron emission tomography (PET) imaging based on the classical FBP algorithm or its iterative use and (b) propose also an efficient 2D approximately optimal space-invariant Wiener type filter with unknown object power spectrum for SPECT imaging based on the generalized FBP algorithm (implementing the explicit formula for the nonuniform attenuation correction) and/or the classical FBP algorithm (used iteratively). An efficient space-variant version of the latter 2D filter is also announced. Numerical examples illustrating the aforementioned results in the framework of simulated SPECT imaging are given

Fast Microwave Tomography Algorithm for Breast Cancer Imaging

Microwave tomography has shown promise for breast cancer imaging. The microwaves are harmless to body tissues, which makes microwave tomography a safe adjuvant screening to mammography. Although many clinical studies have shown the effectiveness of regular screening for the detection of breast cancer, the anatomy of the breast and its critical tissues challenge the identification and diagnosis of tumors in this region. Detection of tumors in the breast is more challenging in heterogeneously dense and extremely dense breasts, and microwave tomography has the potential to be effective in such cases. The sensitivity of microwaves to various breast tissues and the comfort and safety of the screening method have made microwave tomography an attractive imaging technique. Despite the need for an alternative screening technique, microwave tomography has not yet been introduced as a screening modality in regular health care, and is still subject to research. The main obstacles are imperfect hardware systems and inefficient imaging algorithms. The immense computational costs for the image reconstruction algorithm present a crucial challenge. 2D imaging algorithms are proposed to reduce the amount of hardware resources required and the imaging time. Although 2D microwave tomography algorithms are computationally less expensive, few imaging groups have been successful in integrating the acquired 3D data into the 2D tomography algorithms for clinical applications. The microwave tomography algorithms include two main computation problems: the forward problem and the inverse problem. The first part of this thesis focuses on a new fast forward solver, the 2D discrete dipole approximation (DDA), which is formulated and modeled. The effect of frequency, sampling number, target size, and contrast on the accuracy of the solver are studied. Additionally, the 2D DDA time efficiency and computation time as a single forward solver are investigated.\ua0 The second part of this thesis focuses on the inverse problem. This portion of the algorithm is based on a log-magnitude and phase transformation optimization problem and is formulated as the Gauss-Newton iterative algorithm. The synthetic data from a finite-element-based solver (COMSOL Multiphysics) and the experimental data acquired from the breast imaging system at Chalmers University of Technology are used to evaluate the DDA-based image reconstruction algorithm. The investigations of modeling and computational complexity show that the 2D DDA is a fast and accurate forward solver that can be embedded in tomography algorithms to produce images in seconds. The successful development and implementation in this thesis of 2D tomographic breast imaging with acceptable accuracy and high computational cost efficiency has provided significant savings in time and in-use memory and is a dramatic improvement over previous implementations

Characterization of tissue properties on the sub-micron scale in human bone by means of synchrotron radiation CT

Gesunder humaner Knochen unterliegt einem permanenten Umbau, um sich den mechanischen Anforderungen anzupassen, Mikrofrakturen zu reparieren und das Mineraliengleichgewicht zu erhalten. Dieser Umbauprozess wird durch Osteoblasten- und Osteoklastenaktivität realisiert, den knochenbildenden bzw. knochenresorbierenden Zellen. Gesteuert wird dieser Prozess durch Osteozyten, dessen Netzwerk mechanosensorische Fähigkeiten zugesprochen werden. Bisphosphonate (BP), hemmen die Osteoklastenaktivität und erhöhen somit die Knochenumsatzzeit. Im ersten Teil dieser Arbeit wurden morphologische Eigenschaften der Osteozyten-Lakunen (OL) in humanem Knochen mittels Synchrotron-µCT untersucht. Dabei wurden sowohl gesunde als auch mit BP behandelte Spender verglichen. Anschließend haben wir Synchrotron-Nano-CT in Kombination mit Phasenkontrast angewandt, um unsere Untersuchungen auf die Morphologie des lakuno-kanalikulären Netzwerkes (LKN) und die Gewebeeigenschaften in der Umgebung des LKN auszuweiten. Wir nahmen an, dass der sekundäre Mineralisierungsprozess mittels eines Diffusionsprozesses durch die Grenzfläche der extrazellulären Flüssigkeit im LKN stattfindet, was zu Gradienten der Massendichte in der Umgebung des LKN führen sollte. Unsere Untersuchungen haben gezeigt, dass sowohl in der Umgebung der OL als auch der Kanäle Massendichtegradienten existieren. Daraus schließen wir, dass der Mineralienaustausch zwischen der extrazellulären Flüssigkeit und der mineralisierten Matrix an der gesamten Oberfläche des LKN stattfindet. Wir schätzten, dass die Kapazität, unter Berücksichtigung des gesamten LKN, Mineralien auszutauschen etwa eine Größenordnung höher ist, gegenüber der Annahme, dass der Austausch lediglich an den Grenzflächen der OL stattfindet. Zukünftige Studien sollten nicht nur die peri-LKN Gewebeeigenschaften während der sekundären Mineralisierung untersuchen, sondern auch Schwankungen der Mineralienkonzentration bei hohen Kalziumanforderungen des Körpers berücksichtigen.Under healthy conditions human bone undergoes permanent remodeling to adjust to mechanical demands, to repair micro-cracks and to maintain mineral homeostasis. This process of remodeling is performed by osteoblasts and osteoclasts: bone-forming and bone-resorbing cells. The activity of osteoclasts and osteoblasts is triggered by osteocytes, the most frequently occurring type of bone cell, via mechanosensation processes. Bisphosphonates (BP) prescribed during treatment for osteoporosis or bone metastasis inhibit osteoclast activity and thus decrease the bone turnover. In this work, the distribution and morphology of osteocyte lacunae of human cortical jaw bone was investigated in 3D, and a comparison between healthy and BP-treated donors was performed using synchrotron radiation (SR) µCT. In a second approach, we used SR nano-CT with phase contrast to investigate the morphology of the canalicular network and the bone tissue properties in the vicinity of the lacuna-canalicular network of human jaw bone, originating from both healthy subjects and patients treated with BPs. We hypothesized that secondary mineralization takes place via a diffusion process through the fluid-matrix interface at both the lacunar and the canalicular surfaces. This should result in mass density gradients with respect to the distance to the pore boundary. Such mass density gradients were indeed observed at both lacunar and canalicular interfaces. We concluded that mineral exchange between extracellular fluid and mineralized matrix occurs at all bone surfaces, including the canaliculi. Our data suggested that the capacity of the pore network to exchange mineral with the bone matrix would increase by one order of magnitude if the canalicular surface is taken into account. However, more studies should be performed, targeting not only the changes of tissue properties during secondary mineralization, but also during fluctuations of mineral concentration in periods of high mineral demand