Fixing Acceleration and Image Resolution Issues of Nuclear Magnetic Resonance

Lately, Magnetic Resonance scans have struggled with their own inherent limitations, such as spatial resolution as well as long examination times. A novel, rapid compressively-sensed magnetic resonance high-resolution image resolution algorithm is presented in this research paper. This technique addresses these two key issues by employing a highly-sparse sampling scheme and super-resolution reconstruction (SRR) method. Due to highly challenging requirements for the accuracy of diagnostic images registration, the presented technique exploits image priors, deblurring, parallel imaging, and a deformable human body motion analysis. Clinical trials as well as a phantom-based study have been conducted. It has been proven that the proposed algorithm can enhance image spatial resolution and reduce motion artefacts and scan times.


Introduction
Brain nuclear imaging has, in the last few years, become one of the most critical techniques to diagnose brain abnormalities. High-definition imaging with enough details has had its impact on medical imaging. As a result of these applications, the requirement for high quality visualisation is rapidly expanding. Yet, because of the constraints of inherent limitations of magnetic resonance imaging (MRI) scanners or issues related to the bandwidth in the transmission process, obtaining the high-definition head MR scans that meets the requirements for applications has been proving to be difficult. Efforts made to resolve this predicament have led to the improvement of developing studies in digital signal processing, especially in the field of image resolution enhancement. This area of interest has been especially has been researched in the latest years. The algorithm shown in this research paper enriches Iterative Back Projection (IBP) [1] and its improved version [2] in a few directions. It utilises a deformable image registration.
The SRR (Super-Resolution Image Reconstruction) has proven its worth in the field of various medical modalities [3][4][5]. Super Resolution Image Reconstruction is an example of an improperly modelled problem because of too-few low-resolution images. Numerous regularisation algorithms have been given to develop the inversion of this underdetermined problem. Freeman et al. [6] were the first to suggest that machine training procedures could be used to enhance the resolution of the frames.
By using the Markov random field (MRF), the authors defined the connection between the High-Resolution frame and the Low-Resolution frame. The preliminary estimate of the High-Resolution frame was accomplished by using interpolating polynomials. The missing upper frequencies of the High-Resolution frame were resolved using training technique and a preliminary estimate. Afterwards, the High-Resolution frame was calculated. Sun [7] has improved this technology by enhancing image features. The SR methods utilising the neural nets with convolution were proposed in the references [8,9]. This technique was employed in order to conduct single-multi-contrast SRR at the same time. It should examination charges. And, consequently, significant reduction of scanning times was a major reason for transplanting the CS to the field of Magnetic Resonance Imaging. Several researches have argued that the procedures such as k-t SPARSE, CS dynamic imaging [22] and k-t FOCUSS [29,30] images are compressible under a well-chosen sparsyfying transform. One of most important technological breakthroughs in medicine and healthcare was parallel imaging [22,31,32]. Currently, the majority of clinical scanners are loaded with parallel imaging methodology, and this way is the standard arrangement for numerous scanning schemes. It has been proven that scan time can be lowered by sampling a reduced number of phase encoding lines in frequency domain. Most modern clinical scanners collect input samples from several seperate receiver coil arrays [33].
Parallel imaging procedures utilise properties of these coil arrays to isolate aliased pixels in the image domain or to estimate missing k-space data exploiting knowledge of neighbouring k-space locations. Several approaches to the parallel imaging methods have been proposed [26,34]. The most prominent examples include SENSE, GRAPPA, and SPIRiT. They were all successfully applied in clinical practice. These procedures can be modified to consider irregular sampling schemes. Non-Cartesian sampling schemes deliver several valuable properties, that is, the appearance of incoherent aliasing artefacts. The latest improvements in concurrent multi-slice imaging are proposed, which utilise parallel imaging to separate images of numerous slices that have been obtained at the same time. Parallel imaging can also be applied to quicken three dimensional MRI, in which an adjacent volume is scanned rather than sequential slices. Another category of phase-constrained parallel imaging procedure makes use of both image magnitude and phase to improve reconstruction performance. Nevertheless, the robustness of compressively sensed MRI scanning procedures is still technically challenging. Numerous authors have noted that the pulse sequence is supposed to be wisely implemented to overcome any tendency of inconsistency, such as image resolution, number of frames/slices, contrast-to-noise ratio (CNR), and field of view. Meanwhile, other authors have proposed parallel imaging methods for handling dynamic Magnetic Resonance. In this way the techniques and methods which show the most effectiveness with certain types of procedures such as TSENSE and TGRAPPA [19] have been presented. They have proven their usefulness to capture 3-4 slices per heartbeat with relevant temporal and spatial resolution for diagnostic use, utilising commercially obtainable radiofrequency (RF) coil arrays. To enhance image resolution as well as the field of view, more complex and intricate methods are needed to achieve higher acceleration rates. Examples of this include procedures such as SENSE, GRAPPA and k-t-blast [35][36][37] to ensure the precision of exploiting spatiotemporal correlations in the dynamic Magnetic Resonance Imaging data either alone or in combination with coil sensitivity information. Such data sampling, as expect, gives rise, to reducing data overlapping, which delivers high acceleration rates. The most significant disadvantage is the need of dynamic learning data to set up an aliasing pattern in the frequency domain, which minimises the resulting acceleration rate. In opposite to these techniques, the CS framework relies on the assumption that a sparsely sampled frame in a known transform domain can be calculated using randomly undersampled k-space data [38] and does not need any training data.

The Proposed Algorithm
Most SRR algorithms incline to produce similar results because of oversimplified motion trajectories which do not display real biological behaviour. This is crucial in all instances of patient motion within an image, such as respiratory, heart motion, circulation, and other potentially misregistration-causing artefacts. A deformable, groupwise non-rigid image registration method for motion compensation is utilised in the algorithm being presented in this paper [39,40].
Medical image processing has experienced a variety of difficulties in the past including distortion removal, spatial resolution and examination times [41,42]. Mathematically speaking, all these aspects lead to forming a cost function, which is crucial to get accurate and better predictions.This registration algorithm had proven its competency in the Computed Tomography [43], PET/MRI as well as DW-MRI fields. The proposed SRR algorithm concurrently uses High-Resolution sparsity priors, deformable motion registration parameters as well as the MAP (maximum a posteriori) for blur estimation. The proposed SRR algorithm minimises [39,40] the cost function consisting of the HR input image Γ H , motion fields {w i }, noise level {θ i } as well blur kernel B. The algorithm gets started with using an initial guess which yields convergence to a solution, see the pseudocode below and Figures 2 and 3. Input: set of Low-resolution input Magnetic Resonance Scans /each is reconstructed from a compressively sensed k-space's blade.
1. high-resolution estimate produced by → the submethod, see Enhance the high-resolution estimate Γ n H e. Repeat steps a-d until convergence, see Figure 3 Output: high-resolution Magnetic Scan. The procedure performs image upscaling regarding the motion fields to produce a current HR image estimate. The proposed algorithm utilises a smooth kernel, which blurs the resulting image. The image is subsampled and noised to form the set of observed low-resolution images. This iterative technique is continued until the solution converges towards values that change by less than some specified tolerance threshold between successive iterations [7]. The proposed SRR algorithm can be expressed in the following way: Note that the Γ n,0 L represents the estimated reference initial guess related to n-th set of "compressed" PROPELLER blades, Γ n,j L is the i-th obtained LR frame with regard to degradation parameters, Γ n L is HR estimate, ∇ is the gradient operator,Γ n H is the n-th HR image estimate D, B, w i denote the down-sampling, blur kernel, deformable image registration vectors, individually. To be able to employ gradient optimisation we need to replace L1 norms with their differentiable approximations.
It should be noted that the deformable motion estimation is a prominent example of a highly nonconvex optimisation problem, which is associated with several conditions that must be satisfied [44]. Moreover, this process is highly ill-conditioned tending to sensitivity regarding measurements and model errors. The motion estimation algorithm adopted in this paper is globally optimal deformable registration. That algorithm avoids using continuous optimisation because it may be prone to local minima. To overcome this advantage, discrete optimisation was applied. The frame grid is modelled as a minimum spanning tree. Instead of using gradients to find a global optimum of the cost function, it can be found rapidly using dynamic programming, which enforces the smoothness of the deformations.
The Markov Random Field (MRF) labelling is used to perform discrete optimisation, see Figure 4. In the algorithm adopted in this paper a spanning tree with minimum total edge costs is derived. The nodes i ∈ P refer to pixels (or group of pixels) and for each node, a collection of hidden, and corresponding to the motion fields, labels are expressed as The algorithm, more specifically, the energy function to be optimised consists of two terms: that is, the data cost S and the pair-wise regularisation cost R(w l i , w m i ) for all the nodes l − s associated with the nodes m − s: The cost function shown above estimates the inter-pixel correlation of a pair of images being compared. Specifically, this term does not depend on the displacements of its neighbours.
The κ refers to a weighting parameter, which controls the influence of the regularisation term. The first component in Equation (2) denotes the data term; the second one is the regularisation term.

Results
In the experimental studies, all the raw data signals are appropriately compressed with the sampling rates: 25%, 40% and 60% of the fully sampled k-spaces.
In order to measure the performance of the proposed algorithm, both laboratory phantom studies and an in-vivo assessment were performed. The purpose of the experiment was to compare the effectiveness of various ways of obtaining a compressively-sensed input. In a study of the effects of various compressedsensing ratio on test performance, the test performance of the proposed Super-Resolution Image Reconstruction method was tested. Moreover, several MRI k-space sampling patterns have been compared. Figures 5-22 show the achieved results. It must be emphasised that combining Compressed Sensing with Hermitian symmetry property, as well as Partial Fourier allows the shortening of k-space filling when compared to the different k-space sampling schemes, see Figure 1.   [45], E: Enhanced deep residual networks for single image super-resolution [14], F: Image super-resolution using very deep residual channel attention networks [16], G: Residual dense network for image super-resolution [15], H: super-resolution with proposed sampling scheme and motion compensation (the proposed algorithm). Compression ratio is 50%. Please see Table 1 for the PSNR values at other compression ratios.   [14], F: Image super-resolution using very deep residual channel attention networks [16], G: Residual dense network for image super-resolution [15], H: superresolution with proposed sampling scheme and motion compensation (the proposed algorithm). Compression ratio is 50%. Please see Table 2 for the PSNR values at other compression ratios.   [14], F: Image super-resolution using very deep residual channel attention networks [16], G: Residual dense network for image super-resolution [15], H: super-resolution with proposed sampling scheme and motion compensation (the proposed algorithm). Compression ratio is 50%. Please see Table 3 for the PSNR values at other compression ratios.   Table 4 for the PSNR values at other compression ratios.      Table 6 illustrated). Table 6. Stats of the IEM metrics for Figure 7 at different CS ratio.        It must be emphasised that combining Compressed Sensing with Hermitian symmetry property, as well as Partial Fourier allows the shortening of k-space filling when compared to the different k-space sampling schemes. This paper focuses on fusing the super-resolution image reconstruction with k-space sparse sampling of MRI scanners. Moreover, the phantom studies were concentrated on the inverse problems of compressed sensing for MRI, see Figure 9. In this part of the experiment the Shepp-Logan phantom data Figures 6 and 22 were reconstructed from sets of sparse projections. To model the sparsity, PROPELLER blades have been sensitively compressed with 30 and twelve radial lines in frequency domain as well as reconstruction from reduced-angle projections, with a contracted subset of 50 projections within a 90-degree aperture. The unmodified PROPELLER sampling scheme has been compared with the proposed one, see Figure 23. Furthermore, the ground truth MR images meshes were warped using nonrigid, deformable transformations. Lastly, Gaussian blur kernel and noise and downsampling were applied to such processed images to simulate real MR images.

Discussion
For over nearly two decades, SR procedures have effectively been exploited to enhance the spatial resolution of diagnostic images after k-spaces data are collected, thus making the doctor's diagnosis easier. The variety of applications and methods has grown ever since, especially in the MRI modality, exposing the interest of the community to such post-processing. MRI, CT, PET and hybrid techniques are still suffering from insufficient spatial resolution, contrast issues, visual noise scattering and blurring produced by motion artefacts. These underlying issues can lead to problems in identifying abnormalities. Reducing scanning time is a serious challenge for many medical imaging techniques. Compressed Sensing (CS) theory delivers an appealing framework to address this inconvenience since it provides theoretical guarantees on the reconstruction of sparse signals by projection on a low dimensional linear subspace. Numerous adjustments here are presented and proven to be efficient for enhancing MRI spatial resolution while reducing acquisition lengths. The proposed technique minimises artefacts produced by highly sparse data, even in the influence of misregistration artefacts. In order to expedite the process of k-space filling and enhance spatial resolution, the algorithm combines several sub-techniques, that is, compressive-sensing, Poisson Disc sampling and Partial Fourier with SR technique. This combination allowed for improving both image definition and time consumption. Furthermore, improved upper frequencies provides better edge delineation. The proposed algorithm can be directly implemented to MR scanners without any hardware modifications. Moreover, it has been proven that the implemented technique produces enhanced and sharper shapes. It really minimises the risk of misdiagnosis. The financial aspects in healthcare must be addressed and sufficient value to all participants are supposed to justify their use. Apart from enhancing the spatial resolution, this technique can be useful in addressing misregistration issues. Phantom-based studies as well in-vivo experiments have proven to be successful in reducing examination time. The achieved results show an improvement of definition and readability of the MR images, see . The techniques used to identify abnormalities that are claimed to be potentially malignant or pre-malignant expose a higher capability to spot them due to the improved image quality parameters. Furthermore, the achievements have been validated by PSNR and IEM metrics [45] that can measure medical image quality with great competence. In more extended studies numerous scanning techniques were investigated. The proposed algorithm has been compared with SENSE, GRAPPA as well as unmodified PROPELLER. Despite reasonable results achieved using competitive algorithms, the proposed algorithms offered the shortest scanning time, see Table 7. In order to get a quantitative assessment, the peak signal-to-noise ratio (PSNR) and the mean absolute error (MAE) have been utilised. Both the smaller MAE or higher PSNR confirmed robustness of the applied algorithm. All the most commonly applied image quality metrics, including the IEM, confirmed the weight of the results. The proposed algorithm was compared with 4 state-of-the-art SRRs: Non-Rigid Multi-Modal 3D Medical Image Registration Based on Foveated Modality Independent Neighbourhood Descriptor [45], Residual dense network for image super-resolution [15], Enhanced deep residual networks for single image super-resolution [14] and Image super-resolution using very deep residual channel attention networks [16]. L1-cost regularisation is applied to learn the nets of the following procedures-Enhanced deep residual networks for single image super-resolution, Residual dense network for image super-resolution and Image super-resolution using very deep residual channel attention networks. The compressively-sensed, Super-Resolution images have achieved the highest IEM values [46]. it is obvious to see that the compression ratios highly affect the PSNR scores (see Tables 1-18). It is worth being underlined that satisfying results occurred for halved sampling spaces. The mean PSNR and IEM values are used to compare the results. Each simulation was run N = 100 times. The signed rank test was applied to all the image quality metrics to verify if the null hypothesis that the central tendency of the difference was zero at numerous acceleration rates. All the statistical tests were performed using The R Project for Statistical Computing, see . A separate group t-student's test was conducted in order to compare the PSNR mean scores between 2 seperate sets, with a paired t-test. The significance test, Student's t-test was carried out on the PSNR and are found that the probability validates the method's performance. The results are exposed in Tables 1-19. The achieved p-values have proven high statistical significance.Future research will be concentrated on testing competitive solutions which operate using Discrete Shearlet Transform because of its ability to be a good candidate for MRI sparse sampling. Presently, the algorithm is being validated via testing using DW-MRI/PET scanners.  Funding: This research received no external funding.

Conflicts of Interest:
The author declares no conflict of interest. In the past five years, I have not received reimbursements, fees, funding, or any salaries from any organisation that may in any way gain or lose financially from the publication of this manuscript. I do not hold any stocks or shares in an organisation that may in any way gain or lose financially from the publication of this manuscript. I do not hold and I am not currently applying for any patents relating to the content of the manuscript. I do not have any other financial competing interests.