# Image Quality Improvement and Memory-Saving in a Permanent-Magnet-Array-Based MRI System
## 1 Introduction  
Magnetic resonance imaging (MRI) is a popular imaging modality for diagnosis and therapies. It shows the best soft tissue contrast and has no ionizing radiation. However, a conventional MRI system has been extremely expensive (approaching 1 million USD per Tesla (T) of the main magnetic field (\(\mathbf{B_{0}}\)-field)), which significantly limits its accessibility. Moreover, it requires a large space to site. The bulkiness of an MRI scanner prevents this imaging modality from being available to \"point-of-care\" and timely diagnosis, e.g., those in an ambulance, a field medical tent, or an intensive care unit (ICU). To this end, instead of using a superconducting magnet for a full body which requires a sophisticated and costly cooling system to maintain a superconducting state, body-part-dedicated permanent magnetarray (PMA) is drawing more and more attention to be used as a source to supply \(\mathbf{B_{0}}\)-field [1; 2; 3; 4; 5; 6] because of its low cost, no energy consumption, small footprint, and light weight. In the linear MRI system such as those for Cartesian or radial imaging, it requires both a highly homogeneous \(\mathbf{B_{0}}\) and a linear gradient field to ensure image quality and to avoid aliasing. When a PMA is used to supply such a \(\mathbf{B_{0}}\)-field, either the field of view (FoV) becomes small to guarantee a relatively high field strength and the homogeneity, or the field strength is lowered at a relatively large FoV. Such an MRI system is called PMA-based system in this content. In the former case when the VoF is compromised, a C-shaped permanent magnet array is scaled down to a table-top size, the FoV has to shrink to 1.3 cm and elliptic area with the lengths of the axes of 2 cm to have a homogeneity of 20 ppm at an average \(\mathbf{B_{0}}\)-field of 0.22 T [7] or an circular area with a diameter not exceeding 10 mm (with a homogeneity 10 ppm at an average field strength of 0.47 T) [8], which are not practical to image most body parts. With a similar approach, a C-shaped magnet was designed to scan a tree branch (a diameter of spherical volume(DSV) of 30 mm, average \(\mathbf{B_{0}}\) of 0.3 T, 60 ppm) [9] and a wrist (a DSV of 10 cm, average \(\mathbf{B_{0}}\) of 0.2 T, 50 ppm) [10]. In the other situation when the field strength is compromised while keeping a relatively large VoF, a table-top Halbach array with a diameter (outer) of 44.2 cm and a length of 49 cm was designed to supply an average magnetic field of 50.64 mT within a DSV of 20 cm for head imaging with a homogeneity of 433 ppm. Due to the high requirements on \(\mathbf{B_{0}}\) homogeneity, in a PMA-based MRI system, it is difficult to design a magnet array with a high field strength and a large FoV simultaneously. One of the solutions is to use the inhomogeneous field generated by a PMA as gradients for image encoding [11]. With the relaxed requirements on inhomogeneity, the FoV can be larger with a higher field strength. Examples for head imaging are reported in the literature, e.g., a DSV of 20 mm with an average field strength of around 80 mT and a homogeneity of 13,670 ppm [3; 12], a diameter of 20 mm in a 2D VoF with an average field strength of 167 mT and a homogeneity of 32,511 ppm [5] and an average field strength of 132 mT and a homogeneity of 151,840 ppm [6]. The field distribution that has a pattern and is used for signal encoding is a spatial encoding magnetic (SEM) field which was originally named for PatLoc (**Parallel** imaging technique using **Localized gradients**) imaging [13]. The pattern of an SEM in a PMA-based MRI system is determined by the configurations of the magnet arrays, and are usually not linear, for example, it is quadrupolar in [3; 4], concentric in [5], and monotonic along a single direction (close to linear) in [6; 12]. When an MRI system is targeted to in-time and on-site imaging, such as that in an ambulance, besides a reduced size/footprint, the quality and speed of image reconstruction, and the corresponding required computer memory are critical.