Direct 3D Tomographic Reconstruction and Phase-Retrieval of Far-Field Coherent Diffraction Patterns

We present an alternative numerical reconstruction algorithm for direct tomographic reconstruction of a sample refractive indices from the measured intensities of its far-field coherent diffraction patterns. We formulate the well-known phase-retrieval problem in ptychography in a tomographic framework which allows for simultaneous reconstruction of the illumination function and the sample refractive indices in three dimensions. Our iterative reconstruction algorithm is based on the Levenberg-Marquardt algorithm. We demonstrate the performance of our proposed method with simulation studies

Isotropic inverse-problem approach for two-dimensional phase unwrapping

In this paper, we propose a new technique for two-dimensional phase unwrapping. The unwrapped phase is found as the solution of an inverse problem that consists in the minimization of an energy functional. The latter includes a weighted data-fidelity term that favors sparsity in the error between the true and wrapped phase differences, as well as a regularizer based on higher-order total-variation. One desirable feature of our method is its rotation invariance, which allows it to unwrap a much larger class of images compared to the state of the art. We demonstrate the effectiveness of our method through several experiments on simulated and real data obtained through the tomographic phase microscope. The proposed method can enhance the applicability and outreach of techniques that rely on quantitative phase evaluation

Hemodynamic Measurement Using Four-Dimensional Phase-Contrast MRI: Quantification of Hemodynamic Parameters and Clinical Applications

Recent improvements have been made to the use of time-resolved, three-dimensional phase-contrast (PC) magnetic resonance imaging (MRI), which is also named four-dimensional (4D) PC-MRI or 4D flow MRI, in the investigation of spatial and temporal variations in hemodynamic features in cardiovascular blood flow. The present article reviews the principle and analytical procedures of 4D PC-MRI. Various fluid dynamic biomarkers for possible clinical usage are also described, including wall shear stress, turbulent kinetic energy, and relative pressure. Lastly, this article provides an overview of the clinical applications of 4D PC-MRI in various cardiovascular regions.113Ysciescopuskc

Investigating the accuracy and precision of TE‐dependent versus multi‐echo QSM using Laplacian‐based methods at 3 T

Purpose: Multi‐echo gradient‐recalled echo acquisitions for QSM enable optimizing the SNR for several tissue types through multi‐echo (TE) combination or investigating temporal variations in the susceptibility (potentially reflecting tissue microstructure) by calculating one QSM image at each TE (TE‐dependent QSM). In contrast with multi‐echo QSM, applying Laplacian‐based methods (LBMs) for phase unwrapping and background field removal to single TEs could introduce nonlinear temporal variations (independent of tissue microstructure) into the measured susceptibility. Here, we aimed to compare the effect of LBMs on the QSM susceptibilities in TE‐dependent versus multi‐echo QSM. Methods: TE–dependent recalled echo data simulated in a numerical head phantom and gradient‐recalled echo images acquired at 3 T in 10 healthy volunteers. Several QSM pipelines were tested, including four distinct LBMs: sophisticated harmonic artifact reduction for phase data (SHARP), variable‐radius sophisticated harmonic artifact reduction for phase data (V‐SHARP), Laplacian boundary value background field removal (LBV), and one‐step total generalized variation (TGV). Results from distinct pipelines were compared using visual inspection, summary statistics of susceptibility in deep gray matter/white matter/venous regions of interest, and, in the healthy volunteers, regional susceptibility bias analysis and nonparametric tests. Results: Multi‐echo versus TE‐dependent QSM had higher regional accuracy, especially in high‐susceptibility regions and at shorter TEs. Everywhere except in the veins, a processing pipeline incorporating TGV provided the most temporally stable TE‐dependent QSM results with an accuracy similar to multi‐echo QSM. Conclusions: For TE‐dependent QSM, carefully choosing LBMs can minimize the introduction of LBM‐related nonlinear temporal susceptibility variations

Advanced satellite radar interferometry for small-scale surface deformation detection

Synthetic aperture radar interferometry (InSAR) is a technique that enables generation of Digital Elevation Models (DEMs) and detection of surface motion at the centimetre level using radar signals transmitted from a satellite or an aeroplane. Deformation observations can be performed due to the fact that surface motion, caused by natural and human activities, generates a local phase shift in the resultant interferogram. The magnitude of surface deformation can be estimated directly as a fraction of the wavelength of the transmitted signal. Moreover, differential InSAR (DInSAR) eliminates the phase signal caused by relief to yield a differential interferogram in which the signature of surface deformation can be seen. Although InSAR applications are well established, the improvement of the interferometry technique and the quality of its products is highly desirable to further enhance its capabilities. The application of InSAR encounters problems due to noise in the interferometric phase measurement, caused by a number of decorrelation factors. In addition, the interferogram contains biases owing to satellite orbit errors and atmospheric heterogeneity These factors dramatically reduce the stlectiveness of radar interferometry in many applications, and, in particular, compromise detection and analysis of small-scale spatial deformations. The research presented in this thesis aim to apply radar interferometry processing to detect small-scale surface deformations, improve the quality of the interferometry products, determine the minimum and maximum detectable deformation gradient and enhance the analysis of the interferometric phase image. The quality of DEM and displacement maps can be improved by various methods at different processing levels. One of the methods is filtering of the interferometric phase.However, while filtering reduces noise in the interferogram, it does not necessarily enhance or recover the signal. Furthermore, the impact of the filter can significantly change the structure of the interferogram. A new adaptive radar interferogram filter has been developed and is presented herein. The filter is based on a modification to the Goldstein radar interferogram filter making the filter parameter dependent on coherence so that incoherent areas are filtered more than coherent areas. This modification minimises the loss of signal while still reducing the level of noise. A methodology leading to the creation of a functional model for determining minimum and maximum detectable deformation gradient, in terms of the coherence value, has been developed. The sets of representative deformation models have been simulated and the associated phase from these models has been introduced to real SAR data acquired by ERS-1/2 satellites. A number of cases of surface motion with varying magnitudes and spatial extent have been simulated. In each case, the resultant surface deformation has been compared with the 'true' surface deformation as defined by the deformation model. Based on those observations, the functional model has been developed. Finally, the extended analysis of the interferometric phase image using a wavelet approach is presented. The ability of a continuous wavelet transform to reveal the content of the wrapped phase interferogram, such as (i) discontinuities, (ii) extent of the deformation signal, and (iii) the magnitude of the deformation signal is examined. The results presented represent a preliminary study revealing the wavelet method as a promising technique for interferometric phase image analysis

Doctor of Philosophy

dissertationMagnetic resonance guided high intensity focused ultrasound (MRgHIFU) is a promising minimal invasive thermal therapy for the treatment of breast cancer. This study develops techniques for determining the tissue parameters - tissue types and perfusion rate - that influence the local temperature during HIFU thermotherapy procedures. For optimal treatment planning for each individual patient, a 3D volumetric breast tissue segmentation scheme based on the hierarchical support vector machine (SVM) algorithm was developed to automatically segment breast tissues into fat, fibroglandular tissue, skin and lesions. Compared with fuzzy c-mean and conventional SVM algorithm, the presented technique offers tissue classification performance with the highest accuracy. The consistency of the segmentation results along both the sagittal and axial orientations indicates the stability of the proposed segmentation routine. Accurate knowledge of the internal anatomy of the breast can be utilized in the ultrasound beam simulation for the treatment planning of MRgHIFU therapy. Completely noninvasive MRI techniques were developed for visualizing blood vessels and determining perfusion rate to assist in the MRgHIFU therapy. Two-point Dixon fat-water separation was achieved using a 3D dual-echo SSFP sequence for breast vessel imaging. The performances of the fat-water separation with various readout gradient designs were evaluated on a water-oil phantom, ex vivo pork sample and in vivo breast imaging. Results suggested that using a dual-echo SSFP readout with bipolar readout gradient polarity, blood vasculature could be successfully visualized through the thin-slab maximum intensity projection SSFP water-only images. For determining the perfusion rate, we presented a novel imaging pulse sequence design consisting of a single arterial spin labeling (ASL) magnetization preparation followed by Look-Locker-like image readouts. This flow quantification technique was examined through simulation, in vitro and in vivo experiments. Experimental results from a hemodialyzer when fitted with a Bloch-equation-based model provide flow measurements that are consistent with ground truth velocities. With these tissue properties, it is possible to compensate for the dissipative effects of the flowing blood and ultimately improve the efficacy of the MRgHIFU therapies. Complete noninvasiveness of these techniques allows multiple measurements before, during and after the treatment, without the limitation of washout of the injected contrast agent

Estudo das técnicas de processamento de imagem dedicadas ao tratamento dos mapas de fase

As técnicas ópticas, em conjunto com as ferramentas de processamento digital de imagem, têm encontrado um interesse cada vez maior na investigação laboratorial. No âmbito da mecânica experimental, as técnicas ópticas de interferometria Speckle são utilizadas para a medição do campo de deslocamentos de estruturas sob solicitação. A informação é gravada na forma de mapas de fase, os quais estão contaminados por ruído de Speckle e apresentam descontinuidades na fase. Estes deverão ser posteriormente tratados por ferramentas dedicadas de processamento de imagem de forma a eliminar o ruído sem destruir a informação de fase. Neste trabalho descrevem-se as principais técnicas de processamento de imagem dedicadas à análise de padrões de interferometria Speckle, como são, por exemplo, as técnicas de filtragem de fase e de padrões de intensidade, métodos de desembrulhar da fase. A partir de simulações numéricas é realizada uma análise comparativa da eficácia e robustez de diversas técnicas na remoção do ruído e eliminação das descontinuidades de fase. A partir pela minimização do valor eficaz do erro são determinados os parâmetros óptimos de cada técnica

Mathematics and Algorithms in Tomography

This is the eighth Oberwolfach conference on the mathematics of tomography. Modalities represented at the workshop included X-ray tomography, sonar, radar, seismic imaging, ultrasound, electron microscopy, impedance imaging, photoacoustic tomography, elastography, vector tomography, and texture analysis