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Quantum dynamics and Gram's matrix
[article]
1999
arXiv
pre-print
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We propose to analyse the statistical properties of a sequence of vectors using the spectrum of the associated Gram matrix. Such sequences arise e.g. by the repeated action of a deterministic kicked quantum dynamics on an initial condition or by a random process. We argue that, when the number of time-steps, suitably scaled with respect to ħ, increases, the limiting eigenvalue distribution of the Gram matrix reflects the possible quantum chaoticity of the original system as it tends to its
arXiv:math-ph/9901009v2
fatcat:jwvoi7d53ra4palguxrqweibxi
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... ical limit. This idea is subsequently applied to study the long-time properties of sequences of random vectors at the time scale of the dimension of the Hilbert space of available states.
Bayesian Learning of Probabilistic Dipole Inversion for Quantitative Susceptibility Mapping
[article]
2020
arXiv
pre-print
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Spincemaille, T. Nguyen & Y. Wang. ...
arXiv:2004.12573v1
fatcat:doixboxtnjafpo7waly5vaq7uy
Geometric Loss for Deep Multiple Sclerosis lesion Segmentation
[article]
2020
arXiv
pre-print
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Multiple sclerosis (MS) lesions occupy a small fraction of the brain volume, and are heterogeneous with regards to shape, size and locations, which poses a great challenge for training deep learning based segmentation models. We proposed a new geometric loss formula to address the data imbalance and exploit the geometric property of MS lesions. We showed that traditional region-based and boundary-aware loss functions can be associated with the formula. We further develop and instantiate two
arXiv:2009.13755v1
fatcat:tjmncz2qsnfxbhe5dkb6ryucxm
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... functions containing first- and second-order geometric information of lesion regions to enforce regularization on optimizing deep segmentation models. Experimental results on two MS lesion datasets with different scales, acquisition protocols and resolutions demonstrated the superiority of our proposed methods compared to other state-of-the-art methods.
Motion Artifact Reduction in Quantitative Susceptibility Mapping using Deep Neural Network
[article]
2021
arXiv
pre-print
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An approach to reduce motion artifacts in Quantitative Susceptibility Mapping using deep learning is proposed. We use an affine motion model with randomly created motion profiles to simulate motion-corrupted QSM images. The simulated QSM image is paired with its motion-free reference to train a neural network using supervised learning. The trained network is tested on unseen simulated motion-corrupted QSM images, in healthy volunteers and in Parkinson's disease patients. The results show that
arXiv:2105.01746v1
fatcat:psfq6tpeorbbfd2qhe6i5gf4ri
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... tion artifacts, such as ringing and ghosting, were successfully suppressed.
Efficient Folded Attention for 3D Medical Image Reconstruction and Segmentation
[article]
2020
arXiv
pre-print
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Recently, 3D medical image reconstruction (MIR) and segmentation (MIS) based on deep neural networks have been developed with promising results, and attention mechanism has been further designed to capture global contextual information for performance enhancement. However, the large size of 3D volume images poses a great computational challenge to traditional attention methods. In this paper, we propose a folded attention (FA) approach to improve the computational efficiency of traditional
arXiv:2009.05576v1
fatcat:x2yictbsobgy5gd67nqlqioqde
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... tion methods on 3D medical images. The main idea is that we apply tensor folding and unfolding operations with four permutations to build four small sub-affinity matrices to approximate the original affinity matrix. Through four consecutive sub-attention modules of FA, each element in the feature tensor can aggregate spatial-channel information from all other elements. Compared to traditional attention methods, with moderate improvement of accuracy, FA can substantially reduce the computational complexity and GPU memory consumption. We demonstrate the superiority of our method on two challenging tasks for 3D MIR and MIS, which are quantitative susceptibility mapping and multiple sclerosis lesion segmentation.
Cerebral Microbleeds: Burden Assessment by Using Quantitative Susceptibility Mapping
2012
Radiology
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Purpose: To assess quantitative susceptibility mapping (QSM) for reducing the inconsistency of standard magnetic resonance (MR) imaging sequences in measurements of cerebral microbleed burden. Materials and Methods: This retrospective study was HIPAA compliant and institutional review board approved. Ten patients (5.6%) were selected from among 178 consecutive patients suspected of having experienced a stroke who were imaged with a multiecho gradient-echo sequence at 3.0 T and who had cerebral
doi:10.1148/radiol.11110251
pmid:22056688
pmcid:PMC3244668
fatcat:6nothg5khjeifmrvxcei3z5u2i
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... icrobleeds on T2*-weighted images. QSM was performed for various ranges of echo time by using both the magnitude and phase components in the morphologyenabled dipole inversion method. Cerebral microbleed size was measured by two neuroradiologists on QSM images, T2*-weighted images, susceptibility-weighted (SW) images, and R2* maps calculated by using different echo times. The sum of susceptibility over a region containing a cerebral microbleed was also estimated on QSM images as its total susceptibility. Measurement differences were assessed by using the Student t test and the F test; P , .05 was considered to indicate a statistically signifi cant difference. Results: When echo time was increased from approximately 20 to 40 msec, the measured cerebral microbleed volume increased by mean factors of 1 .49 6 0.86 (standard deviation), 1.64 6 0.84, 2.30 6 1.20, and 2.30 6 1.19 for QSM, R2*, T2*-weighted, and SW images, respectively ( P , .01). However, the measured total susceptibility with QSM did not show signifi cant change over echo time ( P = .31), and the variation was signifi cantly smaller than any of the volume increases ( P , .01 for each). Conclusion: The total susceptibility of a cerebral microbleed measured by using QSM is a physical property that is independent of echo time. q RSNA, 2011
Fidelity Imposed Network Edit (FINE) for Solving Ill-Posed Image Reconstruction
[article]
2019
arXiv
pre-print
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Deep learning (DL) is increasingly used to solve ill-posed inverse problems in imaging, such as reconstruction from noisy or incomplete data, as DL offers advantages over explicit image feature extractions in defining the needed prior. However, DL typically does not incorporate the precise physics of data generation or data fidelity. Instead, DL networks are trained to output some average response to an input. Consequently, DL image reconstruction contains errors, and may perform poorly when
arXiv:1905.07284v1
fatcat:tiahl37cfzadhoqyl34kcrwbla
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... test data deviates significantly from the training data, such as having new pathological features. To address this lack of data fidelity problem in DL image reconstruction, a novel approach, which we call fidelity-imposed network edit (FINE), is proposed. In FINE, a pre-trained prior network's weights are modified according to the physical model, on a test case. Our experiments demonstrate that FINE can achieve superior performance in two important inverse problems in neuroimaging: quantitative susceptibility mapping (QSM) and under-sampled reconstruction in MRI.
Flow compensated quantitative susceptibility mapping for venous oxygenation imaging
2013
Magnetic Resonance in Medicine
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Purpose-Venous blood oxygen saturation is an indicator of brain oxygen consumption and can be measured directly from quantitative susceptibility mapping (QSM) by deconvolving the MR phase signal. However, accurate estimation of the susceptibility of blood may be affected by flow induced phase in the presence of imaging gradient and the inhomogeneous susceptibility field gradient. The purpose of this study is to correct the flow induced error in QSM for improved venous oxygenation
doi:10.1002/mrm.24937
pmid:24006187
pmcid:PMC3979497
fatcat:ypzj55xrwbb2hc6b36bctpi4qa
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... Methods-Flow compensation is proposed for QSM by using a fully flow compensated multiecho gradient echo sequence for data acquisition. A quadratic fit of the phase with respect to echo time is employed for the flow phase in the presence of inhomogeneity field gradients. Phantom and in vivo experiments were carried out to validate the proposed method. Results-Phantom experiments demonstrated reduced error in the estimated field map and susceptibility map. Initial data in in vivo human imaging demonstrated improvements in the quantitative susceptibility map and in the estimated venous oxygen saturation values. Conclusion-Flow compensated multi-echo acquisition and an adaptive-quadratic fit of the phase images improves the quantitative susceptibility map of blood flow. The improved vein susceptibility enables in vivo measurement of venous oxygen saturation throughout the brain.
Extending LOUPE for K-space Under-sampling Pattern Optimization in Multi-coil MRI
[article]
2020
arXiv
pre-print
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The previously established LOUPE (Learning-based Optimization of the Under-sampling Pattern) framework for optimizing the k-space sampling pattern in MRI was extended in three folds: firstly, fully sampled multi-coil k-space data from the scanner, rather than simulated k-space data from magnitude MR images in LOUPE, was retrospectively under-sampled to optimize the under-sampling pattern of in-vivo k-space data; secondly, binary stochastic k-space sampling, rather than approximate stochastic
arXiv:2007.14450v1
fatcat:mkwqlddxg5b77geht6io3fulkm
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... pace sampling of LOUPE during training, was applied together with a straight-through (ST) estimator to estimate the gradient of the threshold operation in a neural network; thirdly, modified unrolled optimization network, rather than modified U-Net in LOUPE, was used as the reconstruction network in order to reconstruct multi-coil data properly and reduce the dependency on training data. Experimental results show that when dealing with the in-vivo k-space data, unrolled optimization network with binary under-sampling block and ST estimator had better reconstruction performance compared to the ones with either U-Net reconstruction network or approximate sampling pattern optimization network, and once trained, the learned optimal sampling pattern worked better than the hand-crafted variable density sampling pattern when deployed with other conventional reconstruction methods.
Spatially Adaptive Regularization in Total Field Inversion (TFIR) for Quantitative Susceptibility Mapping
2020
iScience
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Resource Availability Lead Contact Further information and requests for data and/or code should be directed to and will be fulfilled by the Lead Contact, Pascal Spincemaille (pas2018@med.cornell.edu). ...
doi:10.1016/j.isci.2020.101553
pmid:33083722
pmcid:PMC7522736
fatcat:t5znrpmsnvcxzfg3tfyx4s3j2q
Preconditioned total field inversion (TFI) method for quantitative susceptibility mapping
2016
Magnetic Resonance in Medicine
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Purpose-To investigate systematic errors in traditional quantitative susceptibility mapping (QSM) where background field removal and local field inversion (LFI) are performed sequentially, to develop a total field inversion (TFI) QSM method to reduce these errors, and to improve QSM quality in the presence of large susceptibility differences. Theory and Methods-The proposed TFI is a single optimization problem which simultaneously estimates the background and local fields, preventing error
doi:10.1002/mrm.26331
pmid:27464893
pmcid:PMC5274595
fatcat:ezyiqwkwgbhyfocwdobbytlymq
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... gation from background field removal to QSM. To increase the computational speed, a new preconditioner is introduced and analyzed. TFI is compared with the traditional combination of background field removal and LFI in a numerical simulation and in phantom, 5 healthy subjects and 18 patients with intracerebral hemorrhage. Results-Compared with the traditional method PDF+LFI, preconditioned TFI substantially reduced error in QSM along the air-tissue boundaries in simulation, generated high-quality in vivo QSM within similar processing time, and suppressed streaking artifacts in intracerebral hemorrhage QSM. Moreover, preconditioned TFI was capable of generating QSM for the entire head including the brain, air-filled sinus, skull, and fat. Conclusion-Preconditioned total field inversion improves the accuracy of QSM over the traditional method where background and local fields are separately estimated.
Fidelity imposed network edit (FINE) for solving ill-posed image reconstruction
2020
NeuroImage
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Deep learning (DL) is increasingly used to solve ill-posed inverse problems in medical imaging, such as reconstruction from noisy and/or incomplete data, as DL offers advantages over conventional methods that rely on explicit image features and hand engineered priors. However, supervised DL-based methods may achieve poor performance when the test data deviates from the training data, for example, when it has pathologies not encountered in the training data. Furthermore, DL-based image
doi:10.1016/j.neuroimage.2020.116579
pmid:31981779
pmcid:PMC7093048
fatcat:4a2nltzdpvaizbq6imlwrkt7lq
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... tions do not always incorporate the underlying forward physical model, which may improve performance. Therefore, in this work we introduce a novel approach, called fidelity imposed network edit (FINE), which modifies the weights of a pre-trained reconstruction network for each case in the testing dataset. This is achieved by minimizing an unsupervised fidelity loss function that is based on the forward physical model. FINE is applied to two important inverse problems in neuroimaging: quantitative susceptibility mapping (QSM) and under-sampled image reconstruction in MRI. Our experiments demonstrate that FINE can improve reconstruction accuracy.
RSANet: Recurrent Slice-wise Attention Network for Multiple Sclerosis Lesion Segmentation
[article]
2020
arXiv
pre-print
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Brain lesion volume measured on T2 weighted MRI images is a clinically important disease marker in multiple sclerosis (MS). Manual delineation of MS lesions is a time-consuming and highly operator-dependent task, which is influenced by lesion size, shape and conspicuity. Recently, automated lesion segmentation algorithms based on deep neural networks have been developed with promising results. In this paper, we propose a novel recurrent slice-wise attention network (RSANet), which models 3D MRI
arXiv:2002.12470v1
fatcat:3wdv43v6s5gb3jwe5vj5u4ngoy
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... images as sequences of slices and captures long-range dependencies through a recurrent manner to utilize contextual information of MS lesions. Experiments on a dataset with 43 patients show that the proposed method outperforms the state-of-the-art approaches. Our implementation is available online at https://github.com/tinymilky/RSANet.
Temporal Feature Fusion with Sampling Pattern Optimization for Multi-echo Gradient Echo Acquisition and Image Reconstruction
[article]
2021
arXiv
pre-print
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Quantitative imaging in MRI usually involves acquisition and reconstruction of a series of images at multi-echo time points, which possibly requires more scan time and specific reconstruction technique compared to conventional qualitative imaging. In this work, we focus on optimizing the acquisition and reconstruction process of multi-echo gradient echo pulse sequence for quantitative susceptibility mapping as one important quantitative imaging method in MRI. A multi-echo sampling pattern
arXiv:2103.05878v1
fatcat:paisyy3tzvhwrpibrocpfl34fq
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... zation block extended from LOUPE-ST is proposed to optimize the k-space sampling patterns along echoes. Besides, a recurrent temporal feature fusion block is proposed and inserted into a backbone deep ADMM network to capture the signal evolution along echo time during reconstruction. Experiments show that both blocks help improve multi-echo image reconstruction performance.
An iterative spherical mean value method for background field removal in MRI
2013
Magnetic Resonance in Medicine
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Purpose-The Sophisticated Harmonic Artifact Reduction for Phase data (SHARP) method has been proposed for the removal of background field in MRI phase data. It relies on the spherical mean value (SMV) property of harmonic functions, and its accuracy depends on the radius of the sphere used for computing the SMV and truncation threshold needed for deconvolution. The goal of this work is to develop an alternative SMV based background field removal method with reduced dependences on these
doi:10.1002/mrm.24998
pmid:24254415
pmcid:PMC4026360
fatcat:mlxvxmxopjeahgiz5gxsfzyxua
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... s. Methods- The proposed background field removal method (termed iterative SMV or iSMV) consists of applying the SMV operation repeatedly on the field map and it was validated in a phantom and in vivo brain data of five healthy volunteers. Results-The iSMV method demonstrates accurate background field removal in the phantom. Compared to SHARP, the iSMV method shows a significantly reduced dependence on the SMV radius both in phantom and in human data. Because a smaller radius can be chosen, the iSMV method allows retaining a larger part of the region of interest, compared to SHARP. Conclusion- The iSMV method is an effective background field removal method with a reduced dependence on method parameters.
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