Parallel MRI is a fast imaging technique that enables the acquisition of highly resolved images in space or/and in time. The performance of parallel imaging strongly depends on the reconstruction algorithm, which can proceed either in the original k-space (GRAPPA, SMASH) or in the image domain (SENSE-like methods). To improve the performance of the widely used SENSE algorithm, 2D- or slice-specific regularization in the wavelet domain has been deeply investigated. In this paper, we extend this approach using 3D-wavelet representations in order to handle all slices together and address reconstruction artifacts which propagate across adjacent slices. The gain induced by such extension (3D-Unconstrained Wavelet Regularized -SENSE: 3D-UWR-SENSE) is validated on anatomical image reconstruction where no temporal acquisition is considered. Another important extension accounts for temporal correlations that exist between successive scans in functional MRI (fMRI). In addition to the case of 2D+t acquisition schemes addressed by some other methods like kt-FOCUSS, our approach allows us to deal with 3D+t acquisition schemes which are widely used in neuroimaging. The resulting 3D-UWR-SENSE and 4D-UWR-SENSE reconstruction schemes are fully unsupervised in the sense that all regularization parameters are estimated in the maximum likelihood sense on a reference scan. The gain induced by such extensions is illustrated on both anatomical and functional image reconstruction, and also measured in terms of statistical sensitivity for the 4D-UWR-SENSE approach during a fast event-related fMRI protocol. Our 4D-UWR-SENSE algorithm outperforms the SENSE reconstruction at the subject and group levels (15 subjects) for different contrasts of interest (eg, motor or computation tasks) and using different parallel acceleration factors (R=2 and R=4) on 2x2x3mm3 EPI images.
Parallel MRI is a fast imaging technique that enables the acquisition of highly resolved images in space. It relies on $k$-space undersampling and multiple receiver coils with complementary sensitivity profiles in order to reconstruct a full Field-Of-View (FOV) image. The performance of parallel imaging mainly depends on the reconstruction algorithm, which can proceed either in the original $k$-space (GRAPPA, SMASH) or in the image domain (SENSE-like methods). To improve the performance of the widely used SENSE algorithm, 2D- or slice-specific regularization in the wavelet domain has been effi…
We introduce WECS (Wavelet Energies Correlation Sreening), an unsupervised sparse procedure to detect spatio-temporal change points on multi-temporal SAR (POLSAR) images or even on sequences of very high resolution images. The procedure is based on wavelet approximation for the multi-temporal images, wavelet energy apportionment, and ultra-high dimensional correlation screening for the wavelet coefficients. We present two complimentary wavelet measures in order to detect sudden and/or cumulative changes, as well as for the case of stationary or non-stationary multi-temporal images. We show WEC…
Monash University（莫纳什大学）；Indian Institute of Technology Bombay（印度理工学院孟买分校）；IITB Monash Research Academy（IITB-莫纳什研究学院）；Swinburne University of Technology（斯威本科技大学）
The incoherence between measurement and sparsifying transform matrices and the restricted isometry property (RIP) of measurement matrix are two of the key factors in determining the performance of compressive sensing (CS). In CS-MRI, the randomly under-sampled Fourier matrix is used as the measurement matrix and the wavelet transform is usually used as sparsifying transform matrix. However, the incoherence between the randomly under-sampled Fourier matrix and the wavelet matrix is not optimal, which can deteriorate the performance of CS-MRI. Using the mathematical result that noiselets are max…
University of Bath（巴斯大学）；Imago7 foundation（Imago7基金会）；University of Edinburgh（爱丁堡大学）；GE Healthcare（GE医疗）；Technical University of Munich（慕尼黑工业大学）
We propose a dictionary-matching-free pipeline for multi-parametric quantitative MRI image computing. Our approach has two stages based on compressed sensing reconstruction and deep learned quantitative inference. The reconstruction phase is convex and incorporates efficient spatiotemporal regularisations within an accelerated iterative shrinkage algorithm. This minimises the under-sampling (aliasing) artefacts from aggressively short scan times. The learned quantitative inference phase is purely trained on physical simulations (Bloch equations) that are flexible for producing rich training sa…
Adhesions are an important cause of chronic pain following abdominal surgery. Recent developments in abdominal cine-MRI have enabled the non-invasive diagnosis of adhesions. Adhesions are identified on cine-MRI by the absence of sliding motion during movement. Diagnosis and mapping of adhesions improves the management of patients with pain. Detection of abdominal adhesions on cine-MRI is challenging from both a radiological and deep learning perspective. We focus on classifying presence or absence of adhesions in sagittal abdominal cine-MRI series. We experimented with spatio-temporal deep lea…
In this paper offers a simple and lossless compression method for compression of medical images. Method is based on wavelet decomposition of the medical images followed by the correlation analysis of coefficients. The correlation analyses are the basis of prediction equation for each sub band. Predictor variable selection is performed through coefficient graphic method to avoid multicollinearity problem and to achieve high prediction accuracy and compression rate. The method is applied on MRI and CT images. Results show that the proposed approach gives a high compression rate for MRI and CT im…
DUN-SRE: Deep Unrolling Network with Spatiotemporal Rotation Equivariance for Dynamic MRI Reconstruction
University of Nottingham Ningbo China（诺丁汉大学宁波校区）；Shenzhen Institute of Advanced Technology, Chinese Academy of Sciences（深圳先进技术研究院）；School of Mathematics and Statistics, Xi’an Jiaotong University（西安交通大学数学与统计学院）
Spatiotemporal implicit neural representation for unsupervised dynamic MRI reconstruction
School of Biomedical Engineering, Shanghai Jiao Tong University, Shanghai, China（上海交通大学生物医学工程学院）；School of Information Science and Technology, ShanghaiTech University, Shanghai, China（上海科技大学信息科学与技术学院）；iHuman Institute, Shanghaitech University, Shanghai, China（上海科技大学iHuman研究所）
Spatio-Temporal Mixture-of-Modality-Experts Diffusion for Quantitative DCE-MRI Synthesis from Incomplete MR Sequences
Interdisciplinary Program in Cancer Biology, Seoul National University College of Medicine（首尔大学医学院癌症生物学跨学科项目）；Department of Radiology, Seoul National University Hospital（首尔大学医院放射科）；Department of Radiology, Seoul National University College of Medicine（首尔大学医学院放射科）；Healthcare AI Research Institute, Seoul National University Hospital（首尔大学医院医疗人工智能研究所）
Technical University of Munich（慕尼黑工业大学）；GE Global Research（通用电气全球研发中心）；Harvard Medical School（哈佛医学院）
Perfusion-weighted magnetic resonance imaging (MRI) is an imaging technique that allows one to measure tissue perfusion in an organ of interest through the injection of an intravascular paramagnetic contrast agent (CA). Due to a preference for high temporal and spatial resolution in many applications, this modality could significantly benefit from accelerated data acquisitions. In this paper, we specifically address the problem of reconstructing perfusion MR image series from a subset of k-space data. Our proposed approach is motivated by the observation that temporal variations (dynamics) in …
Studies of functional MRI data are increasingly concerned with the estimation of differences in spatio-temporal networks across groups of subjects or experimental conditions. Unsupervised clustering and independent component analysis (ICA) have been used to identify such spatio-temporal networks. While these approaches have been useful for estimating these networks at the subject-level, comparisons over groups or experimental conditions require further methodological development. In this paper, we tackle this problem by showing how self-organizing maps (SOMs) can be compared within a Frechean …
We propose a new computer aided detection framework for tumours acquired on DCE-MRI (Dynamic Contrast Enhanced Magnetic Resonance Imaging) series on small animals. In this approach we consider DCE-MRI series as multivariate images. A full multivariate segmentation method based on dimensionality reduction, noise filtering, supervised classification and stochastic watershed is explained and tested on several data sets. The two main key-points introduced in this paper are noise reduction preserving contours and spatio temporal segmentation by stochastic watershed. Noise reduction is performed in …
Charité - Universitätsmedizin Berlin（柏林夏里特医学院）；Berlin Institute of Health（柏林健康研究所）；Physikalisch-Technische Bundesanstalt (PTB)（德国联邦物理技术研究院（PTB））；King’s College London（伦敦国王学院）
In this work we reduce undersampling artefacts in two-dimensional ($2D$) golden-angle radial cine cardiac MRI by applying a modified version of the U-net. We train the network on $2D$ spatio-temporal slices which are previously extracted from the image sequences. We compare our approach to two $2D$ and a $3D$ Deep Learning-based post processing methods and to three iterative reconstruction methods for dynamic cardiac MRI. Our method outperforms the $2D$ spatially trained U-net and the $2D$ spatio-temporal U-net. Compared to the $3D$ spatio-temporal U-net, our method delivers comparable results…
Friedrich-Alexander-University Erlangen-Nuremberg（埃尔朗根-纽伦堡弗里德里希-亚历山大大学）；University of Leeds（利兹大学）
Quantitative assessment of cardiac left ventricle (LV) morphology is essential to assess cardiac function and improve the diagnosis of different cardiovascular diseases. In current clinical practice, LV quantification depends on the measurement of myocardial shape indices, which is usually achieved by manual contouring of the endo- and epicardial. However, this process subjected to inter and intra-observer variability, and it is a time-consuming and tedious task. In this paper, we propose a spatio-temporal multi-task learning approach to obtain a complete set of measurements quantifying cardia…
We propose to learn a probabilistic motion model from a sequence of images. Besides spatio-temporal registration, our method offers to predict motion from a limited number of frames, useful for temporal super-resolution. The model is based on a probabilistic latent space and a novel temporal dropout training scheme. This enables simulation and interpolation of realistic motion patterns given only one or any subset of frames of a sequence. The encoded motion also allows to be transported from one subject to another without the need of inter-subject registration. An unsupervised generative defor…
Instituto de Telecomunicações（电信研究所）；Universidade da Beira Interior（贝拉内格罗大学）
Segmentation of skeletal muscles in Magnetic Resonance Images (MRI) is essential for the study of muscle physiology and diagnosis of muscular pathologies. However, manual segmentation of large MRI volumes is a time-consuming task. The state-of-the-art on algorithms for muscle segmentation in MRI is still not very extensive and is somewhat database-dependent. In this paper, an automated segmentation method based on AdaBoost classification of local texture features is presented. The texture descriptor consists of the Histogram of Oriented Gradients (HOG), Wavelet-based features, and a set of sta…
A Latent ODE Approach to Spatiotemporal Modeling of Cine Cardiac MRI
Swiss Data Science Center, EPFL and ETH Zürich（瑞士数据科学中心，EPFL 和 ETH 苏黎世）；Diagnostic and Interventional Radiology, University Hospital Zürich（诊断与介入放射学，苏黎世大学医院）；Institute for Biomedical Engineering, University and ETH Zürich（生物医学工程研究所，苏黎世大学和 ETH 苏黎世）；Biomedical Informatics Group, ETH Zürich（生物医学信息学小组，ETH 苏黎世）；Division of Preventive Medicine, Brigham and Women’s Hospital / Harvard Medical School（预防医学部，布莱根妇女医院/哈佛医学院）
We present a robust method to correct for motion and deformations for in-utero volumetric MRI time series. Spatio-temporal analysis of dynamic MRI requires robust alignment across time in the presence of substantial and unpredictable motion. We make a Markov assumption on the nature of deformations to take advantage of the temporal structure in the image data. Forward message passing in the corresponding hidden Markov model (HMM) yields an estimation algorithm that only has to account for relatively small motion between consecutive frames. We demonstrate the utility of the temporal model by sh…
We present a video compressive sensing framework, termed kt-CSLDS, to accelerate the image acquisition process of dynamic magnetic resonance imaging (MRI). We are inspired by a state-of-the-art model for video compressive sensing that utilizes a linear dynamical system (LDS) to model the motion manifold. Given compressive measurements, the state sequence of an LDS can be first estimated using system identification techniques. We then reconstruct the observation matrix using a joint structured sparsity assumption. In particular, we minimize an objective function with a mixture of wavelet sparsi…
University of Bath（巴斯大学）；Technical University of Munich（慕尼黑工业大学）；GE Healthcare（通用电气医疗集团）；Technische Hochschule Ingolstadt（英戈尔施塔特应用技术大学）
Current spatiotemporal deep learning approaches to Magnetic Resonance Fingerprinting (MRF) build artefact-removal models customised to a particular k-space subsampling pattern which is used for fast (compressed) acquisition. This may not be useful when the acquisition process is unknown during training of the deep learning model and/or changes during testing time. This paper proposes an iterative deep learning plug-and-play reconstruction approach to MRF which is adaptive to the forward acquisition process. Spatiotemporal image priors are learned by an image denoiser i.e. a Convolutional Neura…
Comprehending the interplay between spatial and temporal characteristics of neural dynamics can contribute to our understanding of information processing in the human brain. Graph neural networks (GNNs) provide a new possibility to interpret graph structured signals like those observed in complex brain networks. In our study we compare different spatio-temporal GNN architectures and study their ability to model neural activity distributions obtained in functional MRI (fMRI) studies. We evaluate the performance of the GNN models on a variety of scenarios in MRI studies and also compare it to a …
Trustworthy MRI Reconstruction via Bayesian Uncertainty Quantification with Sparsity Prior Models
Department of Computer Science, University of Exeter（埃克塞特大学计算机科学系）；UCL Hawkes Institute, Department of Computer Science, University College London（伦敦大学学院计算机科学系霍克斯研究所）
University of Notre Dame（圣母大学）；IBM Thomas J. Watson Research Center（IBM托马斯·J·沃森研究中心）；Guangdong General Hospital（广东省人民医院）
Cardiac magnetic resonance imaging (MRI) is an essential tool for MRI-guided surgery and real-time intervention. The MRI videos are expected to be segmented on-the-fly in real practice. However, existing segmentation methods would suffer from drastic accuracy loss when modified for speedup. In this work, we propose Multiscale Statistical U-Net (MSU-Net) for real-time 3D MRI video segmentation in cardiac surgical guidance. Our idea is to model the input samples as multiscale canonical form distributions for speedup, while the spatio-temporal correlation is still fully utilized. A parallel stati…
Zhejiang University（浙江大学）；University of Notre Dame（圣母大学）
Automatic segmentation of cardiac magnetic resonance imaging (MRI) facilitates efficient and accurate volume measurement in clinical applications. However, due to anisotropic resolution and ambiguous border (e.g., right ventricular endocardium), existing methods suffer from the degradation of accuracy and robustness in 3D cardiac MRI video segmentation. In this paper, we propose a novel Deformable U-Net (DeU-Net) to fully exploit spatio-temporal information from 3D cardiac MRI video, including a Temporal Deformable Aggregation Module (TDAM) and a Deformable Global Position Attention (DGPA) net…
Model-based Dynamic 3D MRI Reconstructions using Neural Fields and Tensor Product Expansions
Computational Imaging Group for MRI Therapy & Diagnostics, Department of Radiotherapy, University Medical Center Utrecht（MRI治疗与诊断计算成像组，放射治疗系，乌得勒支大学医学中心）
Technische Universität München（慕尼黑工业大学）；University of Edinburgh（爱丁堡大学）；University of Sheffield（谢菲尔德大学）
Dynamic contrast-enhanced (DCE) MRI is an evolving imaging technique that provides a quantitative measure of pharmacokinetic (PK) parameters in body tissues, in which series of T1-weighted images are collected following the administration of a paramagnetic contrast agent. Unfortunately, in many applications, conventional clinical DCE-MRI suffers from low spatiotemporal resolution and insufficient volume coverage. In this paper, we propose a novel deep learning based approach to directly estimate the PK parameters from undersampled DCE-MRI data. Specifically, we design a custom loss function wh…
Dynamic Magnetic Resonance Imaging (MRI) is known to be a powerful and reliable technique for the dynamic imaging of internal organs and tissues, making it a leading diagnostic tool. A major difficulty in using MRI in this setting is the relatively long acquisition time (and, hence, increased cost) required for imaging in high spatio-temporal resolution, leading to the appearance of related motion artifacts and decrease in resolution. Compressed Sensing (CS) techniques have become a common tool to reduce MRI acquisition time by subsampling images in the k-space according to some acquisition tr…
Indian Institute of Technology Indore（印度理工学院印多尔分校）
Alzheimer's Disease (AD) is a neurodegenerative disease that is one of the significant causes of death in the elderly population. Many deep learning techniques have been proposed to diagnose AD using Magnetic Resonance Imaging (MRI) scans. Predicting AD using 2D slices extracted from 3D MRI scans is challenging as the inter-slice information gets lost. To this end, we propose a novel and lightweight framework termed 'Biceph-Net' for AD diagnosis using 2D MRI scans that model both the intra-slice and inter-slice information. Biceph-Net has been experimentally shown to perform similar to other S…
Primitive Representation Learning for Unsupervised Dynamic Contrast Enhanced MRI Reconstruction
Helmholtz Munich（亥姆霍兹慕尼黑）；Technical University of Munich（慕尼黑工业大学）；Boston Children’s Hospital（波士顿儿童医院）；Harvard Medical School（哈佛医学院）；Munich Center for Machine Learning（慕尼黑机器学习中心）；Imperial College London（伦敦帝国理工学院）；King’s College London（伦敦国王学院）
Self-Supervised k-Space Regularization for Motion-Resolved Abdominal MRI Using Neural Implicit k-Space Representation
Helmholtz Center Munich（慕尼黑亥姆霍兹中心）；Technical University of Munich（慕尼黑工业大学）；Imperial College London（伦敦帝国学院）；Millenium Institute for Intelligent Healthcare Engineering（千禧智能医疗工程研究所）；Pontificia Universidad Católica de Chile（智利天主教大学）；King’s College London（伦敦国王学院）
A novel neural network architecture, known as DL-ESPIRiT, is proposed to reconstruct rapidly acquired cardiac MRI data without field-of-view limitations which are present in previously proposed deep learning-based reconstruction frameworks. Additionally, a novel convolutional neural network based on separable 3D convolutions is integrated into DL-ESPIRiT to more efficiently learn spatiotemporal priors for dynamic image reconstruction. The network is trained on fully-sampled 2D cardiac cine datasets collected from eleven healthy volunteers with IRB approval. DL-ESPIRiT is compared against a sta…
Gabor Primitives for Accelerated Cardiac Cine MRI Reconstruction
Chair for AI in Healthcare and Medicine, Technical University of Munich (TUM) and TUM University Hospital, Munich, Germany（人工智能在医疗与医学中的chair，慕尼黑技术大学（TUM）和慕尼黑技术大学医院，德国慕尼黑）；School of Computation and Information Technology, Technical University of Munich, Munich, Germany（计算与信息科技学院，慕尼黑技术大学，德国慕尼黑）；Institute of Machine Learning in Biomedical Imaging, Helmholtz Munich, Neuherberg, Germany（生物医学影像中的机器学习研究所，海德堡慕尼黑，德国纽赫堡）；Department of Radiology, Boston Children's Hospital and Harvard Medical School, Boston, USA（放射科，波士顿儿童医院和哈佛医学院，美国波士顿）；Munich Center for Machine Learning, Technical University of Munich, Munich, Germany（慕尼黑机器学习中心，慕尼黑技术大学，德国慕尼黑）；GE HealthCare, Munich, Germany（通用电气医疗系统，德国慕尼黑）；School of Biomedical Engineering and Imaging Sciences, King's College London, London, United Kingdom（生物医学工程与成像科学学院，伦敦国王学院，英国伦敦）；Department of Computing, Imperial College London, London, United Kingdom（计算学院，伦敦帝国学院，英国伦敦）
本文提出 Gabor 原始要素用于加速心脏 cine MRI 重建，通过调制高斯包络实现灵活频谱支持，提升对光滑结构和锐利边界的表示能力。
Evaluation of Machine Learning Reconstruction Techniques for Accelerated Brain MRI Scans
Humber River Hospital（亨伯河医院）；Toronto Western Hospital, University of Toronto（多伦多大学多伦多西区医院）；Foqus Technologies Inc.（Foqus 技术公司）；Robarts Research Institute, Western University（西安大略大学罗巴茨研究所）
Rutgers University（罗格斯大学）；New York University School of Medicine（纽约大学医学院）；NVIDIA（英伟达）；SenseBrain；Shanghai AI Laboratory（上海人工智能实验室）
Cardiac tagging magnetic resonance imaging (t-MRI) is the gold standard for regional myocardium deformation and cardiac strain estimation. However, this technique has not been widely used in clinical diagnosis, as a result of the difficulty of motion tracking encountered with t-MRI images. In this paper, we propose a novel deep learning-based fully unsupervised method for in vivo motion tracking on t-MRI images. We first estimate the motion field (INF) between any two consecutive t-MRI frames by a bi-directional generative diffeomorphic registration neural network. Using this result, we then e…
University of Minnesota（明尼苏达大学）；Center for Magnetic Resonance Research（磁共振研究中心）
Functional MRI (fMRI) is commonly used for interpreting neural activities across the brain. Numerous accelerated fMRI techniques aim to provide improved spatiotemporal resolutions. Among these, simultaneous multi-slice (SMS) imaging has emerged as a powerful strategy, becoming a part of large-scale studies, such as the Human Connectome Project. However, when SMS imaging is combined with in-plane acceleration for higher acceleration rates, conventional SMS reconstruction methods may suffer from noise amplification and other artifacts. Recently, deep learning (DL) techniques have gained interest…
CRUNet-MR-Univ: A Foundation Model for Diverse Cardiac MRI Reconstruction
Department of Radiology, Leiden University Medical Center, Leiden, The Netherlands（莱顿大学医学中心放射科）；Philips Innovative Technologies, Hamburg, Germany（飞利浦创新技术）
Erasmus MC（伊拉斯姆斯大学医学中心）；Delft University of Technology（代尔夫特理工大学）
This work presents a single-step deep-learning framework for longitudinal image analysis, coined Segis-Net. To optimally exploit information available in longitudinal data, this method concurrently learns a multi-class segmentation and nonlinear registration. Segmentation and registration are modeled using a convolutional neural network and optimized simultaneously for their mutual benefit. An objective function that optimizes spatial correspondence for the segmented structures across time-points is proposed. We applied Segis-Net to the analysis of white matter tracts from N=8045 longitudinal …
University of Bath（巴斯大学）；GE Healthcare（通用电气医疗集团）；Technical University of Munich（慕尼黑工业大学）；Technische Hochschule Ingolstadt（英戈尔施塔特应用技术大学）
Current state-of-the-art reconstruction for quantitative tissue maps from fast, compressive, Magnetic Resonance Fingerprinting (MRF), use supervised deep learning, with the drawback of requiring high-fidelity ground truth tissue map training data which is limited. This paper proposes NonLinear Equivariant Imaging (NLEI), a self-supervised learning approach to eliminate the need for ground truth for deep MRF image reconstruction. NLEI extends the recent Equivariant Imaging framework to nonlinear inverse problems such as MRF. Only fast, compressed-sampled MRF scans are used for training. NLEI le…
University at Buffalo（布法罗大学）；INRIA（法国国家信息与自动化研究所）；Université Côte d’ Azur（蔚蓝海岸大学）；Stanford University（斯坦福大学）；Purdue University（普渡大学）
This paper puts forth a novel bi-linear modeling framework for data recovery via manifold-learning and sparse-approximation arguments and considers its application to dynamic magnetic-resonance imaging (dMRI). Each temporal-domain MR image is viewed as a point that lies onto or close to a smooth manifold, and landmark points are identified to describe the point cloud concisely. To facilitate computations, a dimensionality reduction module generates low-dimensional/compressed renditions of the landmark points. Recovery of the high-fidelity MRI data is realized by solving a non-convex minimizati…
Objective: We present a technique for identification and statistical analysis of quasiperiodic spatiotemporal pressure signals recorded from multiple closely spaced sensors in the human colon. Methods: Identification is achieved by computing the continuous wavelet transform and cross-wavelet transform of these recorded signals. Statistical analysis is achieved by modelling the resulting time-averaged amplitudes or coherences in the frequency and frequency-phase domains as Gaussian processes over a regular grid, under the influence of categorical and numerical predictors that are specified by t…
The most studies on functional connectivity have been done by analyzing the brain's hemodynamic response to a stimulation. On the other hand, the low-frequency spontaneous fluctuations in the blood oxygen level dependent (BOLD) signals of functional MRI have been observed in the resting state. However, the BOLD signals in resting state are significantly corrupted by huge noises arising from cardiac pulsation, respiration, subject motion, scanner, and so forth. Especially, the noise compounds are stronger in the rat brain than in the human brain. To overcome such an artifact, we assumed that fr…
Since its discovery over the last decade, Compressed Sensing (CS) has been successfully applied to Magnetic Reso- nance Imaging (MRI). It has been shown to be a powerful way to reduce scanning time without sacrificing image quality. MR images are actually strongly compressible in a wavelet basis, the latter being largely incoherent with the k-space or spatial Fourier domain where acquisition is performed. Nevertheless, since its first application to MRI [1], the theoretical justification of actual k-space sampling strategies is questionable. Indeed, the vast majority of k-space sampling distri…
