Each year, hundreds of thousands of infants develop hydrocephalus ("water on the brain"). This is a disease that, if untreated, leads to brain damage and ultimately death. The prevalence of hydrocephalus is relatively high in children living in the Global South (in sub-Saharan countries, for example), but access to advanced imaging technology is usually limited in countries belonging to the Global South. This is especially problematic for hydrocephalus, since magnetic resonance imaging often is the diagnostic tool of choice for this disease, but MRI scanners are essentially out of reach due to their cost, size, and stringent infrastructure demands. Therefore, the introduction of an inexpensive, portable, low-field MRI scanner is clinically relevant. An interdisciplinary team of researchers at the Leiden University Medical Center, Pennsylvania State University, Mbarara University of Science and Technology and Delft University of Technology has been working on the development of such low-fieldMRI scanners, with the first goal being to aid in the diagnosis of hydrocephalus in infants in sub-Saharan Africa. Within this project, several prototypes and various dedicated image reconstruction techniques have been developed. This dissertation focuses on the latter. High-field MRI scanners have very strong and homogeneous static magnetic background fields, due to the superconducting magnets they are equipped with. To significantly reduce production costs, the low-field scanners considered in this work use permanent magnets to realize their static background fields. Obviously, such background fields are much weaker than in a high-field MRI scanner, leading to measured signals with a significantly lower signal-to-noise ratio, since this ratio scales with the magnitude of the background field. For spatial encoding (i.e., to distinguish what part of the signal originates from what part of the body or object inside the scanner), high-field scanners depend on gradient coils which superimpose a linearly varying magnetic field on the background field. The first prototype we consider does not have any gradient coils. Instead, spatial encoding is carried out by making use of the inhomogeneities in the static magnetic background field. Due to the nonbijective nature of the field, a single measurement does not yield enough information for a reconstruction. However, by carrying out several measurements and rotating the field between subsequent measurements, image reconstruction should be possible. The second prototype follows the design of high-field scannersmore closely: it was designed such that the static magnetic field is as homogeneous as possible and the scanner is equipped with three gradient coils to allow for spatial encoding in three directions. In this case, the relationship between signal and image can be described by a Fourier Transform...@en

Low-field MRI scanners are significantly less expensive than their high-field counterparts, which gives them the potential to make MRI technology more accessible all around the world. In general, images acquired using low-field MRI scanners tend to be of a relatively low resolution, as signal-to-noise ratios are lower. The aim of this work is to improve the resolution of these images. To this end, we present a deep learning-based approach to transform low-resolution low-field MR images into high-resolution ones. A convolutional neural network was trained to carry out single image super-resolution reconstruction using pairs of noisy low-resolution images and their noise-free high-resolution counterparts, which were obtained from the publicly available NYU fastMRI database. This network was subsequently applied to noisy images acquired using a low-field MRI scanner. The trained convolutional network yielded sharp super-resolution images in which most of the high-frequency components were recovered. In conclusion, we showed that a deep learning-based approach has great potential when it comes to increasing the resolution of low-field MR images.

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In this paper we present a magnetic resonance imaging (MRI) technique that is based on multiplicative regularization. Instead of adding a regularizing objective function to a data fidelity term, we multiply by such a regularizing function. By following this approach, no regularization parameter needs to be determined for each new data set that is acquired. Reconstructions are obtained by iteratively updating the images using short-term conjugate gradient-type update formulas and Polak-Ribière update directions. We show that the algorithm can be used as an image reconstruction algorithm and as a denoising algorithm. We illustrate the performance of the algorithm on two-dimensional simulated low-field MR data that is corrupted by noise and on three-dimensional measured data obtained from a low-field MR scanner. Our reconstruction results show that the algorithm effectively suppresses noise and produces accurate reconstructions even for low-field MR signals with a low signal-to-noise ratio.

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In an earlier paper, we generalized the CGME (Conjugate Gradient Minimal Error) algorithm to the ℓ₂-regularized weighted least-squares problem. Here, we use this Generalized CGME method to reconstruct images from actual signals measured using a low-field MRI scanner. We analyze the convergence of both GCGME and the classical Generalized Conjugate Gradient Least Squares (GCGLS) method for the simple case when a Laplace operator is used as a regularizer and indicate when GCGME is to be preferred in terms of convergence speed. We also consider a more complicated ℓ₁-penalty in a compressed sensing framework.

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In this paper we discuss an imaging method when the object has known support and its spatial Fourier transform is only known on a certain k-space undersampled pattern. The simple conjugate gradient least squares algorithm applied to the corresponding truncated Fourier transform equation produces reconstructions that are basically of a similar quality as reconstructions obtained by solving a standard compressed sensing problem in which support information is not taken into account. Connections with previous one-dimensional approaches are highlighted and the performance of the method for two-and three-dimensional simulated and measured incomplete spectral data sets is illustrated. Possible extensions of the method are also briefly discussed.

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More than 6,000 infants develop hydrocephalus in East Africa every year. Magnetic Resonance Imaging is the preferred technique to diagnose hydrocephalus. In countries such as Uganda, MRI is unaffordable at even major referral hospitals. In order to provide a sustainable diagnostic tool we are developing an inexpensive and easy-to-use MRI system that yields images of sufficient quality to diagnose hydrocephalus. This paper describes our first prototype of such a scanner. We explain the lessons that we have learned from this prototype and how we used these to come up with an improved design. We also describe a dataset that has been obtained with this scanner that will be made publically available.@en

We consider the MRI physics in a low-field MRI scanner, in which permanent magnets are used to generate a magnetic field in the millitesla range. A model describing the relationship between measured signal and image is derived, resulting in an ill-posed inverse problem. In order to solve it, a regularization penalty is added to the least-squares minimization problem. We generalize the conjugate gradient minimal error (CGME) algorithm to the weighted and regularized least-squares problem. Analysis of the convergence of generalized CGME (GCGME) and the classical generalized conjugate gradient least squares (GCGLS) shows that GCGME can be expected to converge faster for ill-conditioned regularization matrices. The ℓ _p-regularized problem is solved using iterative reweighted least squares for p= 1 and p=12, with both cases leading to an increasingly ill-conditioned regularization matrix. Numerical results show that GCGME needs a significantly lower number of iterations to converge than GCGLS.

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We generalize the CGME (Conjugate Gradient Minimal Error) algo-rithm to the weighted and regularized least squares problem. Analysis ofthe convergence of generalized CGME and CGLS shows that CGMEcanbe expected to perform better for ill-conditioned regularization matrices.Two different types of regularization are considered: anℓ1penalty andanℓ2penalty. Theℓ1problem is solved using Iterative Reweighted LeastSquares, which leads to an ill-conditioned regularizationmatrix. The twomethods are applied in a low-field MRI framework. The MRI physics ina low-field scanner are simulated to generate a noisy signal.When anℓ1penalty is used and iterative reweighted least squares isemployed, GCGLS needs significantly more iterations to converge thanGCGME. GCGME has a regularizing effect that leads to fewer artifactsin our simulations. This effect seems to be stronger when a lower numberof CG iterations is used. These two observations indicate that GCGMEis a very promising alternative to GCGLS. @en

Inexpensive MRI scanners based on permanent magnets present a promising diagnostic tool for developing countries. An ill-posed system of equations has to be solved in order to obtain an image. Due to the low signal-to-noise ratio, direct attempts at generating high resolution images yield poor results. In this research, super-resolution reconstruction is considered as an alternative. By first obtaining low resolution images and then applying super-resolution, high resolution images of better quality can be obtained.@en