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.

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.

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.

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.

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.