Image reconstruction in low-field MRI: A super-resolution approach

The quality of magnetic resonance images produced by conventional MRI scanners is guaranteed by the strength and homogeneity of the magnetic field. However, the superconducting magnets required to produce such a field make MRI scanners large and expensive and hence inaccessible to a large number of people in developing countries. Our partners are developing low-cost, portable MRI scanners that do not depend on superconducting magnets. In these scanners, the signal-to-noise ratio will be significantly lower due to the lower magnetic field strength. Additionally, inhomogeneities will be present, which means that the traditional way of obtaining the image, by inverse Fourier Transform, is no longer feasible. In this research, image reconstruction is done using an ill-posed system of equations of the form Ax = y, where A is the reconstruction matrix and x and y are vectors containing the image pixel values and the measured signals, respectively. Three different regularization techniques are considered, with total variation yielding the best results. Two methods for solving the regularized least-squares problem are considered: CGLS and CGNE. For the types of problems we are dealing with, CGNE is outperformed by CGLS: CGLS requires a lower number of iterations to converge and the computational cost per iteration is lower. The main focus of this research is on super-resolution: reconstructing a high resolution image from one or several low resolution images. Due to the low signal-to-noise ratios that are expected in the low-field MRI prototypes, it might be better to reconstruct images of a low resolution, and using these, create high resolution images, instead of opting for a direct high resolution reconstruction. In order to test this, the signal generation in a Halbach array based MRI scanner is simulated. Our simulations show that for very low (<1.5-2) signal-to-noise ratios, super-resolution can yield better results than direct high resolution reconstruction. Data obtained in a 7 T MRI scanner is used to validate our reconstruction model. Due to the type of gradient used and the low number of measurements in this experiment, the amount of available information is very limited. This makes it challenging to produce an image of good quality. However, in our final image, out of the four water bottles in the phantom, the three largest ones are clearly visible.Electrical Engineering, Mathematics and Computer ScienceDelft Institute of Applied Mathematic

Spin swap and exchange coupling in a quantum dot array

Quantum TransportApplied Mathematics/Applied PhysicsApplied Science

Image Reconstruction for Low-Field MRI

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...Numerical Analysi

Inversion of incomplete spectral data using support information with an application to magnetic resonance imaging

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.Numerical AnalysisImPhys/Medical ImagingCircuits and System

CG Variants for General-Form Regularization with an Application to Low-Field MRI

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.Green Open Access added to TU Delft Institutional Repository ‘You share, we take care!’ – Taverne project https://www.openaccess.nl/en/you-share-we-take-care Otherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public.Numerical AnalysisCircuits and System

Conjugate gradient variants for ℓ _p -regularized image reconstruction in low-field MRI

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. Numerical AnalysisCircuits and System

Low-field magnetic resonance imaging using multiplicative regularization

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.Numerical AnalysisCircuits and System

Description of a low-field MRI scanner based on permanent magnets

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.Numerical AnalysisEMSD EEMCS Project engineersCircuits and System

Deep learning-based single image super-resolution for low-field MR brain images

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.Numerical AnalysisCircuits and System

Machine learning for image analysis in the cervical spine: Systematic review of the available models and methods

Numerical AnalysisTera-Hertz SensingPattern Recognition and Bioinformatic