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Keywords = non-Cartesian sampling

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17 pages, 3398 KB  
Article
VQ-SToRM: Vector-Quantized Smoothness Regularization on Manifolds for Free-Breathing, Ungated Real-Time Cardiac MRI Reconstruction
by Mahrusa Billah, Junpu Hu and Qing Zou
Bioengineering 2026, 13(7), 764; https://doi.org/10.3390/bioengineering13070764 - 30 Jun 2026
Viewed by 307
Abstract
Real-time, free-breathing, ungated cardiac magnetic resonance imaging (CMR) is a clinically valuable alternative to conventional breath-held, ECG-gated cine imaging for patients who cannot sustain breath holds or produce reliable cardiac rhythms, including pediatric, arrhythmic, and respiratory-compromised populations. Achieving diagnostic image quality in this [...] Read more.
Real-time, free-breathing, ungated cardiac magnetic resonance imaging (CMR) is a clinically valuable alternative to conventional breath-held, ECG-gated cine imaging for patients who cannot sustain breath holds or produce reliable cardiac rhythms, including pediatric, arrhythmic, and respiratory-compromised populations. Achieving diagnostic image quality in this setting requires aggressive k-space undersampling and sophisticated reconstruction. Because no fully sampled reference exists for such acquisitions, supervised deep learning is not directly applicable, motivating unsupervised, subject-specific methods. Existing approaches typically rely on low-dimensional continuous latent spaces, which can limit their capacity to represent concurrent cardiac and respiratory motions as distinct states and may suffer from posterior collapse. We introduce VQ-SToRM (Vector-Quantized Smoothness Regularization on Manifolds), an unsupervised framework that adapts the Vector-Quantized Variational Autoencoder to real-time CMR by replacing the continuous latent manifold of prior existing methods with a learned discrete codebook. The encoder, decoder, and codebook are trained jointly on the undersampled non-Cartesian k-t space data of a single subject. On free-breathing, ungated spiral acquisitions from healthy volunteers, VQ-SToRM accurately resolved cardiac and respiratory motion across all phases of the cardiac cycle. A systematic ablation study identified a compact configuration—a codebook of only five embeddings of dimension ten—as optimal, indicating that a small discrete codebook is sufficient to represent the dominant cardiac and respiratory motion content. Compared with V-SToRM and Time-DIP, VQ-SToRM achieved smoother frame-to-frame transitions and comparable or superior signal-to-noise and contrast-to-noise ratios with lower variance across frames and datasets, offering a promising path toward clinically practical real-time CMR. Full article
(This article belongs to the Special Issue Recent Advances in Cardiac MRI)
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19 pages, 12395 KB  
Article
Refined Aircraft Positioning Based on Stochastic Hybrid Estimation with Adaptive Square-Root Unscented Particle Filtering
by Yangyang Zhang, Zhenxing Gao, Kai Qi and Jiawei Li
Aerospace 2024, 11(5), 413; https://doi.org/10.3390/aerospace11050413 - 20 May 2024
Cited by 1 | Viewed by 1776
Abstract
The positioning of civil aviation aircraft relative to a geographic reference point on Earth in a Cartesian frame is significant to detect the deviations from the desired path, especially for high-altitude airports or special airports based on performance-based navigation (PBN). To obtain these [...] Read more.
The positioning of civil aviation aircraft relative to a geographic reference point on Earth in a Cartesian frame is significant to detect the deviations from the desired path, especially for high-altitude airports or special airports based on performance-based navigation (PBN). To obtain these critical deviations during aircraft approach and landing, it is fundamental to estimate the continuous flight variables and discrete flight modes simultaneously with enough accuracy. With the coordinate conversion between the North, East, and Down (NED) frame and the geographic coordinate system based on World Geodetic System 1984 (WGS-84) considered, this study proposed a non-linear stochastic hybrid estimation algorithm with adaptive square-root unscented particle filtering (ASR-UPF) to estimate the true path. The probabilities of mode transition, represented by the normal cumulative density function of continuous states, determine whether to proceed with mode transitions. In addition, the adaptive update characterized by tracking variable noise and the importance sampling distributions based on the results of square-root unscented Kalman filtering (SR-UKF), as a comparative study of continuous system filtering, were used. The experiments illustrated the ASR-UPF is able to reduce the state estimation error more effectively, and more promptly track the error caused by incorrect mode estimation with adaptability compared to the SR-UKF. A further test with real flight data indicates that the proposed method gives the refined estimation of position and azimuth in NED frame. Full article
(This article belongs to the Section Aeronautics)
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44 pages, 1448 KB  
Systematic Review
Emerging Trends in Fast MRI Using Deep-Learning Reconstruction on Undersampled k-Space Data: A Systematic Review
by Dilbag Singh, Anmol Monga, Hector L. de Moura, Xiaoxia Zhang, Marcelo V. W. Zibetti and Ravinder R. Regatte
Bioengineering 2023, 10(9), 1012; https://doi.org/10.3390/bioengineering10091012 - 26 Aug 2023
Cited by 47 | Viewed by 12773
Abstract
Magnetic Resonance Imaging (MRI) is an essential medical imaging modality that provides excellent soft-tissue contrast and high-resolution images of the human body, allowing us to understand detailed information on morphology, structural integrity, and physiologic processes. However, MRI exams usually require lengthy acquisition times. [...] Read more.
Magnetic Resonance Imaging (MRI) is an essential medical imaging modality that provides excellent soft-tissue contrast and high-resolution images of the human body, allowing us to understand detailed information on morphology, structural integrity, and physiologic processes. However, MRI exams usually require lengthy acquisition times. Methods such as parallel MRI and Compressive Sensing (CS) have significantly reduced the MRI acquisition time by acquiring less data through undersampling k-space. The state-of-the-art of fast MRI has recently been redefined by integrating Deep Learning (DL) models with these undersampled approaches. This Systematic Literature Review (SLR) comprehensively analyzes deep MRI reconstruction models, emphasizing the key elements of recently proposed methods and highlighting their strengths and weaknesses. This SLR involves searching and selecting relevant studies from various databases, including Web of Science and Scopus, followed by a rigorous screening and data extraction process using the Preferred Reporting Items for Systematic Reviews and Meta-Analyses (PRISMA) guidelines. It focuses on various techniques, such as residual learning, image representation using encoders and decoders, data-consistency layers, unrolled networks, learned activations, attention modules, plug-and-play priors, diffusion models, and Bayesian methods. This SLR also discusses the use of loss functions and training with adversarial networks to enhance deep MRI reconstruction methods. Moreover, we explore various MRI reconstruction applications, including non-Cartesian reconstruction, super-resolution, dynamic MRI, joint learning of reconstruction with coil sensitivity and sampling, quantitative mapping, and MR fingerprinting. This paper also addresses research questions, provides insights for future directions, and emphasizes robust generalization and artifact handling. Therefore, this SLR serves as a valuable resource for advancing fast MRI, guiding research and development efforts of MRI reconstruction for better image quality and faster data acquisition. Full article
(This article belongs to the Special Issue Machine-Learning-Driven Medical Image Analysis)
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17 pages, 3306 KB  
Article
Feasibility of Dynamic Inhaled Gas MRI-Based Measurements Using Acceleration Combined with the Stretched Exponential Model
by Ramanpreet Sembhi, Tuneesh Ranota, Matthew Fox, Marcus Couch, Tao Li, Iain Ball and Alexei Ouriadov
Diagnostics 2023, 13(3), 506; https://doi.org/10.3390/diagnostics13030506 - 30 Jan 2023
Cited by 1 | Viewed by 2355
Abstract
Dynamic inhaled gas (3He/129Xe/19F) MRI permits the acquisition of regional fractional-ventilation which is useful for detecting gas-trapping in lung-diseases such as lung fibrosis and COPD. Deninger’s approach used for analyzing the wash-out data can be substituted with [...] Read more.
Dynamic inhaled gas (3He/129Xe/19F) MRI permits the acquisition of regional fractional-ventilation which is useful for detecting gas-trapping in lung-diseases such as lung fibrosis and COPD. Deninger’s approach used for analyzing the wash-out data can be substituted with the stretched-exponential-model (SEM) because signal-intensity is attenuated as a function of wash-out-breath in 19F lung imaging. Thirteen normal-rats were studied using 3He/129Xe and 19F MRI and the ventilation measurements were performed using two 3T clinical-scanners. Two Cartesian-sampling-schemes (Fast-Gradient-Recalled-Echo/X-Centric) were used to test the proposed method. The fully sampled dynamic wash-out images were retrospectively under-sampled (acceleration-factors (AF) of 10/14) using a varying-sampling-pattern in the wash-out direction. Mean fractional-ventilation maps using Deninger’s and SEM-based approaches were generated. The mean fractional-ventilation-values generated for the fully sampled k-space case using the Deninger method were not significantly different from other fractional-ventilation-values generated for the non-accelerated/accelerated data using both Deninger and SEM methods (p > 0.05 for all cases/gases). We demonstrated the feasibility of the SEM-based approach using retrospective under-sampling, mimicking AF = 10/14 in a small-animal-cohort from the previously reported dynamic-lung studies. A pixel-by-pixel comparison of the Deninger-derived and SEM-derived fractional-ventilation-estimates obtained for AF = 10/14 (≤16% difference) has confirmed that even at AF = 14, the accuracy of the estimates is high enough to consider this method for prospective measurements. Full article
(This article belongs to the Special Issue Advances in Chest Imaging Diagnostics)
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17 pages, 5231 KB  
Article
Jointly Learning Non-Cartesian k-Space Trajectories and Reconstruction Networks for 2D and 3D MR Imaging through Projection
by Chaithya Giliyar Radhakrishna and Philippe Ciuciu
Bioengineering 2023, 10(2), 158; https://doi.org/10.3390/bioengineering10020158 - 24 Jan 2023
Cited by 17 | Viewed by 5789
Abstract
Compressed sensing in magnetic resonance imaging essentially involves the optimization of (1) the sampling pattern in k-space under MR hardware constraints and (2) image reconstruction from undersampled k-space data. Recently, deep learning methods have allowed the community to address both problems [...] Read more.
Compressed sensing in magnetic resonance imaging essentially involves the optimization of (1) the sampling pattern in k-space under MR hardware constraints and (2) image reconstruction from undersampled k-space data. Recently, deep learning methods have allowed the community to address both problems simultaneously, especially in the non-Cartesian acquisition setting. This work aims to contribute to this field by tackling some major concerns in existing approaches. Particularly, current state-of-the-art learning methods seek hardware compliant k-space sampling trajectories by enforcing the hardware constraints through additional penalty terms in the training loss. Through ablation studies, we rather show the benefit of using a projection step to enforce these constraints and demonstrate that the resulting k-space trajectories are more flexible under a projection-based scheme, which results in superior performance in reconstructed image quality. In 2D studies, our novel method trajectories present an improved image reconstruction quality at a 20-fold acceleration factor on the fastMRI data set with SSIM scores of nearly 0.92–0.95 in our retrospective studies as compared to the corresponding Cartesian reference and also see a 3–4 dB gain in PSNR as compared to earlier state-of-the-art methods. Finally, we extend the algorithm to 3D and by comparing optimization as learning-based projection schemes, we show that data-driven joint learning-based method trajectories outperform model-based methods such as SPARKLING through a 2 dB gain in PSNR and 0.02 gain in SSIM. Full article
(This article belongs to the Special Issue AI in MRI: Frontiers and Applications)
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18 pages, 1345 KB  
Article
Embedded Quantitative MRI T Mapping Using Non-Linear Primal-Dual Proximal Splitting
by Matti Hanhela, Antti Paajanen, Mikko J. Nissi and Ville Kolehmainen
J. Imaging 2022, 8(6), 157; https://doi.org/10.3390/jimaging8060157 - 31 May 2022
Cited by 4 | Viewed by 3280
Abstract
Quantitative MRI (qMRI) methods allow reducing the subjectivity of clinical MRI by providing numerical values on which diagnostic assessment or predictions of tissue properties can be based. However, qMRI measurements typically take more time than anatomical imaging due to requiring multiple measurements with [...] Read more.
Quantitative MRI (qMRI) methods allow reducing the subjectivity of clinical MRI by providing numerical values on which diagnostic assessment or predictions of tissue properties can be based. However, qMRI measurements typically take more time than anatomical imaging due to requiring multiple measurements with varying contrasts for, e.g., relaxation time mapping. To reduce the scanning time, undersampled data may be combined with compressed sensing (CS) reconstruction techniques. Typical CS reconstructions first reconstruct a complex-valued set of images corresponding to the varying contrasts, followed by a non-linear signal model fit to obtain the parameter maps. We propose a direct, embedded reconstruction method for T1ρ mapping. The proposed method capitalizes on a known signal model to directly reconstruct the desired parameter map using a non-linear optimization model. The proposed reconstruction method also allows directly regularizing the parameter map of interest and greatly reduces the number of unknowns in the reconstruction, which are key factors in the performance of the reconstruction method. We test the proposed model using simulated radially sampled data from a 2D phantom and 2D cartesian ex vivo measurements of a mouse kidney specimen. We compare the embedded reconstruction model to two CS reconstruction models and in the cartesian test case also the direct inverse fast Fourier transform. The T1ρ RMSE of the embedded reconstructions was reduced by 37–76% compared to the CS reconstructions when using undersampled simulated data with the reduction growing with larger acceleration factors. The proposed, embedded model outperformed the reference methods on the experimental test case as well, especially providing robustness with higher acceleration factors. Full article
(This article belongs to the Special Issue The Present and the Future of Imaging)
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21 pages, 4680 KB  
Article
Tripleurin XIIc: Peptide Folding Dynamics in Aqueous and Hydrophobic Environment Mimic Using Accelerated Molecular Dynamics
by Chetna Tyagi, Tamás Marik, András Szekeres, Csaba Vágvölgyi, László Kredics and Ferenc Ötvös
Molecules 2019, 24(2), 358; https://doi.org/10.3390/molecules24020358 - 19 Jan 2019
Cited by 11 | Viewed by 5535
Abstract
Peptaibols are a special class of fungal peptides with an acetylated N-terminus and a C-terminal 1,2-amino alcohol along with non-standard amino acid residues. New peptaibols named tripleurins were recently identified from a strain of the filamentous fungal species Trichoderma pleuroti, which [...] Read more.
Peptaibols are a special class of fungal peptides with an acetylated N-terminus and a C-terminal 1,2-amino alcohol along with non-standard amino acid residues. New peptaibols named tripleurins were recently identified from a strain of the filamentous fungal species Trichoderma pleuroti, which is known to cause green mould disease on cultivated oyster mushrooms. To understand the mode of action of these peptaibols, the three-dimensional structure of tripleurin (TPN) XIIc, an 18-mer peptide, was elucidated using an enhanced sampling method, accelerated MD, in water and chloroform solvents. Non-standard residues were parameterized by the Restrained Electrostatic Potential (RESP) charge fitting method. The dihedral distribution indicated towards a right-handed helical formation for TPN XIIc in both solvents. Dihedral angle based principal component analysis revealed a propensity for a slightly bent, helical folded conformation in water solvent, while two distinct conformations were revealed in chloroform: One that folds into highly bent helical structure that resembles a beta-hairpin and another with an almost straight peptide backbone appearing as a rare energy barrier crossing event. The hinge-like movement of the terminals was also observed and is speculated to be functionally relevant. The convergence and efficient sampling is addressed using Cartesian PCA and Kullback-Leibler divergence methods. Full article
(This article belongs to the Special Issue Molecular Simulation of Protein Structure, Dynamics and Interactions)
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14 pages, 21753 KB  
Article
The Influence of Radial Undersampling Schemes on Compressed Sensing in Cardiac DTI
by Jianping Huang, Wenlong Song, Lihui Wang and Yuemin Zhu
Sensors 2018, 18(7), 2388; https://doi.org/10.3390/s18072388 - 23 Jul 2018
Cited by 3 | Viewed by 5107
Abstract
Diffusion tensor imaging (DTI) is known to suffer from long acquisition time, which greatly limits its practical and clinical use. Undersampling of k-space data provides an effective way to reduce the amount of data to acquire while maintaining image quality. Radial undersampling is [...] Read more.
Diffusion tensor imaging (DTI) is known to suffer from long acquisition time, which greatly limits its practical and clinical use. Undersampling of k-space data provides an effective way to reduce the amount of data to acquire while maintaining image quality. Radial undersampling is one of the most popular non-Cartesian k-space sampling schemes, since it has relatively lower sensitivity to motion than Cartesian trajectories, and artifacts from linear reconstruction are more noise-like. Therefore, radial imaging is a promising strategy of undersampling to accelerate acquisitions. The purpose of this study is to investigate various radial sampling schemes as well as reconstructions using compressed sensing (CS). In particular, we propose two randomly perturbed radial undersampling schemes: golden-angle and random angle. The proposed methods are compared with existing radial undersampling methods, including uniformity-angle, randomly perturbed uniformity-angle, golden-angle, and random angle. The results on both simulated and real human cardiac diffusion weighted (DW) images show that, for the same amount of k-space data, randomly sampling around a random radial line results in better reconstruction quality for DTI indices, such as fractional anisotropy (FA), mean diffusivities (MD), and that the randomly perturbed golden-angle undersampling yields the best results for cardiac CS-DTI image reconstruction. Full article
(This article belongs to the Section Physical Sensors)
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22 pages, 805 KB  
Article
Calibrationless Parallel Magnetic Resonance Imaging: A Joint Sparsity Model
by Angshul Majumdar, Kunal Narayan Chaudhury and Rabab Ward
Sensors 2013, 13(12), 16714-16735; https://doi.org/10.3390/s131216714 - 5 Dec 2013
Cited by 11 | Viewed by 7088
Abstract
State-of-the-art parallel MRI techniques either explicitly or implicitly require certain parameters to be estimated, e.g., the sensitivity map for SENSE, SMASH and interpolation weights for GRAPPA, SPIRiT. Thus all these techniques are sensitive to the calibration (parameter estimation) stage. In this work, we [...] Read more.
State-of-the-art parallel MRI techniques either explicitly or implicitly require certain parameters to be estimated, e.g., the sensitivity map for SENSE, SMASH and interpolation weights for GRAPPA, SPIRiT. Thus all these techniques are sensitive to the calibration (parameter estimation) stage. In this work, we have proposed a parallel MRI technique that does not require any calibration but yields reconstruction results that are at par with (or even better than) state-of-the-art methods in parallel MRI. Our proposed method required solving non-convex analysis and synthesis prior joint-sparsity problems. This work also derives the algorithms for solving them. Experimental validation was carried out on two datasets—eight channel brain and eight channel Shepp-Logan phantom. Two sampling methods were used—Variable Density Random sampling and non-Cartesian Radial sampling. For the brain data, acceleration factor of 4 was used and for the other an acceleration factor of 6 was used. The reconstruction results were quantitatively evaluated based on the Normalised Mean Squared Error between the reconstructed image and the originals. The qualitative evaluation was based on the actual reconstructed images. We compared our work with four state-of-the-art parallel imaging techniques; two calibrated methods—CS SENSE and l1SPIRiT and two calibration free techniques—Distributed CS and SAKE. Our method yields better reconstruction results than all of them. Full article
(This article belongs to the Special Issue Magnetic Resonance Sensors)
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