Parallel Magnetic Resonance Imaging as Approximation in a Reproducing Kernel Hilbert Space

In Magnetic Resonance Imaging (MRI) data samples are collected in the spatial frequency domain (k-space), typically by time-consuming line-by-line scanning on a Cartesian grid. Scans can be accelerated by simultaneous acquisition of data using multiple receivers (parallel imaging), and by using more efficient non-Cartesian sampling schemes. As shown here, reconstruction from samples at arbitrary locations can be understood as approximation of vector-valued functions from the acquired samples and formulated using a Reproducing Kernel Hilbert Space (RKHS) with a matrix-valued kernel defined by the spatial sensitivities of the receive coils. This establishes a formal connection between approximation theory and parallel imaging. Theoretical tools from approximation theory can then be used to understand reconstruction in k-space and to extend the analysis of the effects of samples selection beyond the traditional g-factor noise analysis to both noise amplification and approximation errors. This is demonstrated with numerical examples.Comment: 28 pages, 7 figure

Extraction of Structural Metrics from Crossing Fiber Models

Diffusion MRI (dMRI) measurements allow us to infer the microstructural properties of white matter and to reconstruct fiber pathways in-vivo. High angular diffusion imaging (HARDI) allows for the creation of more and more complex local models connecting the microstructure to the measured signal. One of the challenges is the derivation of meaningful metrics describing the underlying structure from the local models. The aim hereby is to increase the specificity of the widely used metric fractional anisotropy (FA) by using the additional information contained within the HARDI data. A local model which is connected directly to the underlying microstructure through the model of a single fiber population is spherical deconvolution. It produces a fiber orientation density function (fODF), which can often be interpreted as superposition of multiple peaks, each associated to one relatively coherent fiber population (bundle). Parameterizing these peaks one is able to disentangle and characterize these bundles. In this work, the fODF peaks are approximated by Bingham distributions, capturing first and second order statistics of the fiber orientations, from which metrics for the parametric quantification of fiber bundles are derived. Meaningful relationships between these measures and the underlying microstructural properties are proposed. The focus lies on metrics derived directly from properties of the Bingham distribution, such as peak length, peak direction, peak spread, integral over the peak, as well as a metric derived from the comparison of the largest peaks, which probes the complexity of the underlying microstructure. These metrics are compared to the conventionally used fractional anisotropy (FA) and it is shown how they may help to increase the specificity of the characterization of microstructural properties. Visualization of the micro-structural arrangement is another application of dMRI. This is done by using tractography to propagate the fiber layout, extracted from the local model, in each voxel. In practice most tractography algorithms use little of the additional information gained from HARDI based local models aside from the reconstructed fiber bundle directions. In this work an approach to tractography based on the Bingham parameterization of the fODF is introduced. For each of the fiber populations present in a voxel the diffusion signal and tensor are computed. Then tensor deflection tractography is performed. This allows incorporating the complete bundle information, performing local interpolation as well as using multiple directions per voxel for generating tracts. Another aspect of this work is the investigation of the spherical harmonic representation which is used most commonly for the fODF by means of the parameters derived from the Bingham distribution fit. Here a strong connection between the approximation errors in the spherical representation of the Dirac delta function and the distribution of crossing angles recovered from the fODF was discovered. The final aspect of this work is the application of the metrics derived from the Bingham fit to a number of fetal datasets for quantifying the brain’s development. This is done by introducing the Gini-coefficient as a metric describing the brain’s age

Development and analysis of Magnetic Resonance Imaging acquisition and reconstruction methods for functional and structural investigation of cardiac and lung tissues.

The imaging of the lung and of the heart are often challenging in magnetic resonance due to the motion of the organs. In order to avoid motion artifacts it is possible to make the acquisition fast enough to fit in the breath-hold, or use some motion management methods in free breathing. A fast image acquisition can be obtained with non-Cartesian acquisition schemes, which require specialized reconstruction methods. In this work the least-squares non-uniform fast Fourier transform (LS-NUFFT) was compared to the standard gridding (GR) taking the direct summation method (DS) as reference. LS-NUFFT obtained lower root mean square error (RMSE), but heavier geometric information loss. The performance improvement of the LS-NUFFT was studied using three regularization methods. The truncated SVD reduced the RMSE of the simple regularization-free LS-NUFFT. Alternatively, the scan time can be shortened with some FOV reduction techniques. For cardiac imaging, the inner volume (IV) reduced-FOV selection was explored for the myocardial T2 mapping. The FOV reduction successfully avoided aliasing and provided a scan time reduction from about 23s to 15s. However, undesired stimulated echoes caused an overestimation in the T2 of about 20%. The effects of the inner volume excitation on the T2 mapping were described and clarified. Finally, motion management was explored for lung imaging in free-breathing, using a non-Cartesian acquisition trajectory. The rotating ultra-fast sequence (RUFIS) was demonstrated to be very suitable for the short T2* lung tissue. The respiratory motion was addressed with three methods: prospective triggering (PT), prospective gating (PG) and retrospective gating (RG). All methods were able to reconstruct a 3D high-resolution dataset. PG and RG could achieve 1.2 mm isotropic resolution in clinically reasonable scan time (~6min). The RG sequence could reconstruct multiple phases of the respiration cycle at cost of higher scan time

Reordering for Improved Constrained Reconstruction from Undersampled k-Space Data

Recently, there has been a significant interest in applying reconstruction techniques, like constrained reconstruction or compressed sampling methods, to undersampled k-space data in MRI. Here, we propose a novel reordering technique to improve these types of reconstruction methods. In this technique, the intensities of the signal estimate are reordered according to a preprocessing step when applying the constraints on the estimated solution within the iterative reconstruction. The ordering of the intensities is such that it makes the original artifact-free signal monotonic and thus minimizes the finite differences norm if the correct image is estimated; this ordering can be estimated based on the undersampled measured data. Theory and example applications of the method for accelerating myocardial perfusion imaging with respiratory motion and brain diffusion tensor imaging are presented

Finite element surface registration incorporating curvature, volume preservation, and statistical model information

We present a novel method for nonrigid registration of 3D surfaces and images. The method can be used to register surfaces by means of their distance images, or to register medical images directly. It is formulated as a minimization problem of a sum of several terms representing the desired properties of a registration result: smoothness, volume preservation, matching of the surface, its curvature, and possible other feature images, as well as consistency with previous registration results of similar objects, represented by a statistical deformation model. While most of these concepts are already known, we present a coherent continuous formulation of these constraints, including the statistical deformation model. This continuous formulation renders the registration method independent of its discretization. The finite element discretization we present is, while independent of the registration functional, the second main contribution of this paper. The local discontinuous Galerkin method has not previously been used in image registration, and it provides an efficient and general framework to discretize each of the terms of our functional. Computational efficiency and modest memory consumption are achieved thanks to parallelization and locally adaptive mesh refinement. This allows for the first time the use of otherwise prohibitively large 3D statistical deformation models

Learned Interferometric Imaging for the SPIDER Instrument

The Segmented Planar Imaging Detector for Electro-Optical Reconnaissance (SPIDER) is an optical interferometric imaging device that aims to offer an alternative to the large space telescope designs of today with reduced size, weight and power consumption. This is achieved through interferometric imaging. State-of-the-art methods for reconstructing images from interferometric measurements adopt proximal optimization techniques, which are computationally expensive and require handcrafted priors. In this work we present two data-driven approaches for reconstructing images from measurements made by the SPIDER instrument. These approaches use deep learning to learn prior information from training data, increasing the reconstruction quality, and significantly reducing the computation time required to recover images by orders of magnitude. Reconstruction time is reduced to ${\sim} 10$ milliseconds, opening up the possibility of real-time imaging with SPIDER for the first time. Furthermore, we show that these methods can also be applied in domains where training data is scarce, such as astronomical imaging, by leveraging transfer learning from domains where plenty of training data are available.Comment: 21 pages, 14 figure