1
|
Karimi D, Jaimes C, Machado-Rivas F, Vasung L, Khan S, Warfield SK, Gholipour A. Deep learning-based parameter estimation in fetal diffusion-weighted MRI. Neuroimage 2021; 243:118482. [PMID: 34455242 PMCID: PMC8573718 DOI: 10.1016/j.neuroimage.2021.118482] [Citation(s) in RCA: 7] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/10/2021] [Revised: 08/03/2021] [Accepted: 08/17/2021] [Indexed: 11/24/2022] Open
Abstract
Diffusion-weighted magnetic resonance imaging (DW-MRI) of fetal brain is challenged by frequent fetal motion and signal to noise ratio that is much lower than non-fetal imaging. As a result, accurate and robust parameter estimation in fetal DW-MRI remains an open problem. Recently, deep learning techniques have been successfully used for DW-MRI parameter estimation in non-fetal subjects. However, none of those prior works has addressed the fetal brain because obtaining reliable fetal training data is challenging. To address this problem, in this work we propose a novel methodology that utilizes fetal scans as well as scans from prematurely-born infants. High-quality newborn scans are used to estimate accurate maps of the parameter of interest. These parameter maps are then used to generate DW-MRI data that match the measurement scheme and noise distribution that are characteristic of fetal data. In order to demonstrate the effectiveness and reliability of the proposed data generation pipeline, we used the generated data to train a convolutional neural network (CNN) to estimate color fractional anisotropy (CFA). We evaluated the trained CNN on independent sets of fetal data in terms of reconstruction accuracy, precision, and expert assessment of reconstruction quality. Results showed significantly lower reconstruction error (n=100,p<0.001) and higher reconstruction precision (n=20,p<0.001) for the proposed machine learning pipeline compared with standard estimation methods. Expert assessments on 20 fetal test scans showed significantly better overall reconstruction quality (p<0.001) and more accurate reconstruction of 11 regions of interest (p<0.001) with the proposed method.
Collapse
Affiliation(s)
- Davood Karimi
- Computational Radiology Laboratory (CRL), Department of Radiology, Boston Children's Hospital, and Harvard Medical School, USA.
| | - Camilo Jaimes
- Computational Radiology Laboratory (CRL), Department of Radiology, Boston Children's Hospital, and Harvard Medical School, USA
| | - Fedel Machado-Rivas
- Computational Radiology Laboratory (CRL), Department of Radiology, Boston Children's Hospital, and Harvard Medical School, USA
| | - Lana Vasung
- Department of Pediatrics at Boston Children's Hospital, and Harvard Medical School, Boston, Massachusetts, USA
| | - Shadab Khan
- Computational Radiology Laboratory (CRL), Department of Radiology, Boston Children's Hospital, and Harvard Medical School, USA
| | - Simon K Warfield
- Computational Radiology Laboratory (CRL), Department of Radiology, Boston Children's Hospital, and Harvard Medical School, USA
| | - Ali Gholipour
- Computational Radiology Laboratory (CRL), Department of Radiology, Boston Children's Hospital, and Harvard Medical School, USA
| |
Collapse
|
2
|
Karimi D, Vasung L, Jaimes C, Machado-Rivas F, Warfield SK, Gholipour A. Learning to estimate the fiber orientation distribution function from diffusion-weighted MRI. Neuroimage 2021; 239:118316. [PMID: 34182101 PMCID: PMC8385546 DOI: 10.1016/j.neuroimage.2021.118316] [Citation(s) in RCA: 6] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/16/2020] [Revised: 05/20/2021] [Accepted: 06/25/2021] [Indexed: 02/06/2023] Open
Abstract
Estimation of white matter fiber orientation distribution function (fODF) is the essential first step for reliable brain tractography and connectivity analysis. Most of the existing fODF estimation methods rely on sub-optimal physical models of the diffusion signal or mathematical simplifications, which can impact the estimation accuracy. In this paper, we propose a data-driven method that avoids some of these pitfalls. Our proposed method is based on a multilayer perceptron that learns to map the diffusion-weighted measurements, interpolated onto a fixed spherical grid in the q space, to the target fODF. Importantly, we also propose methods for synthesizing reliable simulated training data. We show that the model can be effectively trained with simulated or real training data. Our phantom experiments show that the proposed method results in more accurate fODF estimation and tractography than several competing methods including the multi-tensor model, Bayesian estimation, spherical deconvolution, and two other machine learning techniques. On real data, we compare our method with other techniques in terms of accuracy of estimating the ground-truth fODF. The results show that our method is more accurate than other methods, and that it performs better than the competing methods when applied to under-sampled diffusion measurements. We also compare our method with the Sparse Fascicle Model in terms of expert ratings of the accuracy of reconstruction of several commissural, projection, association, and cerebellar tracts. The results show that the tracts reconstructed with the proposed method are rated significantly higher by three independent experts. Our study demonstrates the potential of data-driven methods for improving the accuracy and robustness of fODF estimation.
Collapse
Affiliation(s)
- Davood Karimi
- Computational Radiology Laboratory (CRL), Department of Radiology, Boston Children's Hospital, and Harvard Medical School, USA.
| | - Lana Vasung
- Department of Pediatrics, Boston Children's Hospital, and Harvard Medical School, Boston, MA, USA
| | - Camilo Jaimes
- Computational Radiology Laboratory (CRL), Department of Radiology, Boston Children's Hospital, and Harvard Medical School, USA
| | - Fedel Machado-Rivas
- Computational Radiology Laboratory (CRL), Department of Radiology, Boston Children's Hospital, and Harvard Medical School, USA
| | - Simon K Warfield
- Computational Radiology Laboratory (CRL), Department of Radiology, Boston Children's Hospital, and Harvard Medical School, USA
| | - Ali Gholipour
- Computational Radiology Laboratory (CRL), Department of Radiology, Boston Children's Hospital, and Harvard Medical School, USA
| |
Collapse
|
3
|
Karimi D, Vasung L, Jaimes C, Machado-Rivas F, Khan S, Warfield SK, Gholipour A. A machine learning-based method for estimating the number and orientations of major fascicles in diffusion-weighted magnetic resonance imaging. Med Image Anal 2021; 72:102129. [PMID: 34182203 PMCID: PMC8320341 DOI: 10.1016/j.media.2021.102129] [Citation(s) in RCA: 7] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/01/2020] [Revised: 05/26/2021] [Accepted: 05/28/2021] [Indexed: 12/29/2022]
Abstract
Accurate modeling of diffusion-weighted magnetic resonance imaging measurements is necessary for accurate brain connectivity analysis. Existing methods for estimating the number and orientations of fascicles in an imaging voxel either depend on non-convex optimization techniques that are sensitive to initialization and measurement noise, or are prone to predicting spurious fascicles. In this paper, we propose a machine learning-based technique that can accurately estimate the number and orientations of fascicles in a voxel. Our method can be trained with either simulated or real diffusion-weighted imaging data. Our method estimates the angle to the closest fascicle for each direction in a set of discrete directions uniformly spread on the unit sphere. This information is then processed to extract the number and orientations of fascicles in a voxel. On realistic simulated phantom data with known ground truth, our method predicts the number and orientations of crossing fascicles more accurately than several classical and machine learning methods. It also leads to more accurate tractography. On real data, our method is better than or compares favorably with other methods in terms of robustness to measurement down-sampling and also in terms of expert quality assessment of tractography results.
Collapse
Affiliation(s)
- Davood Karimi
- Department of Radiology, Boston Children's Hospital, Harvard Medical School, Boston, MA, USA.
| | - Lana Vasung
- Department of Pediatrics at Boston Children's Hospital, and Harvard Medical School, Boston, Massachusetts, USA
| | - Camilo Jaimes
- Department of Radiology, Boston Children's Hospital, Harvard Medical School, Boston, MA, USA
| | - Fedel Machado-Rivas
- Department of Radiology, Boston Children's Hospital, Harvard Medical School, Boston, MA, USA
| | - Shadab Khan
- Department of Radiology, Boston Children's Hospital, Harvard Medical School, Boston, MA, USA
| | - Simon K Warfield
- Department of Radiology, Boston Children's Hospital, Harvard Medical School, Boston, MA, USA
| | - Ali Gholipour
- Department of Radiology, Boston Children's Hospital, Harvard Medical School, Boston, MA, USA
| |
Collapse
|
4
|
Lin Z, Gong T, Wang K, Li Z, He H, Tong Q, Yu F, Zhong J. Fast learning of fiber orientation distribution function for MR tractography using convolutional neural network. Med Phys 2019; 46:3101-3116. [PMID: 31009085 DOI: 10.1002/mp.13555] [Citation(s) in RCA: 30] [Impact Index Per Article: 6.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/17/2018] [Revised: 04/07/2019] [Accepted: 04/14/2019] [Indexed: 12/13/2022] Open
Abstract
PURPOSE In diffusion-weighted magnetic resonance imaging (DW-MRI), the fiber orientation distribution function (fODF) is of great importance for solving complex fiber configurations to achieve reliable tractography throughout the brain, which ultimately facilitates the understanding of brain connectivity and exploration of neurological dysfunction. Recently, multi-shell multi-tissue constrained spherical deconvolution (MSMT-CSD) method has been explored for reconstructing full fODFs. To achieve a reliable fitting, similar to other model-based approaches, a large number of diffusion measurements is typically required for MSMT-CSD method. The prolonged acquisition is, however, not feasible in practical clinical routine and is prone to motion artifacts. To accelerate the acquisition, we proposed a method to reconstruct the fODF from downsampled diffusion-weighted images (DWIs) by leveraging the strong inference ability of the deep convolutional neural network (CNN). METHODS The method treats spherical harmonics (SH)-represented DWI signals and fODF coefficients as inputs and outputs, respectively. To compensate for the reduced gradient directions with reduced number of DWIs in acquisition in each voxel, its surrounding voxels are incorporated by the network for exploiting their spatial continuity. The resulting fODF coefficients are fitted with applying the CNN in a multi-target regression model. The network is composed of two convolutional layers and three fully connected layers. To obtain an initial evaluation of the method, we quantitatively measured its performance on a simulated dataset. Then, for in vivo tests, we employed data from 24 subjects from the Human Connectome Project (HCP) as training set and six subjects as test set. The performance of the proposed method was primarily compared to the super-resolved MSMT-CSD with the decreasing number of DWIs. The fODFs reconstructed by MSMT-CSD from all available 288 DWIs were used as training labels and the reference standard. The performance was quantitatively measured by the angular correlation coefficient (ACC) and the mean angular error (MAE). RESULTS For the simulated dataset, the proposed method exhibited the potential advantage over the model reconstruction. For the in vivo dataset, it achieved superior results over the MSMT-CSD in all the investigated cases, with its advantage more obvious when a limited number of DWIs were used. As the number of DWIs was reduced from 95 to 25, the median ACC ranged from 0.96 to 0.91 for the CNN, but 0.93 to 0.77 for the MSMT-CSD (with perfect score of 1). The angular error in the typical regions of interest (ROIs) was also much lower, especially in multi-fiber regions. The average MAE for the CNN method in regions containing one, two, three fibers was, respectively, 1.09°, 2.75°, and 8.35° smaller than the MSMT-CSD method. The visual inception of the fODF further confirmed this superiority. Moreover, the tractography results validated the effectiveness of the learned fODF, in preserving known major branching fibers with only 25 DWIs. CONCLUSION Experiments on HCP datasets demonstrated the feasibility of the proposed method in recovering fODFs from up to 11-fold reduced number of DWIs. The proposed method offers a new streamlined reconstruction procedure and exhibits promising potential in acquisition acceleration for the reconstruction of fODFs with good accuracy.
Collapse
Affiliation(s)
- Zhichao Lin
- Department of Instrument Science & Technology, Zhejiang University, Hangzhou, 310027, China
| | - Ting Gong
- Center for Brain Imaging Science and Technology, Key Laboratory for Biomedical Engineering of Ministry of Education, College of Biomedical Engineering and Instrumental Science, Zhejiang University, Hangzhou, Zhejiang, China
| | - Kewen Wang
- College of Natural Science, Computer Science, The University of Texas at Austin, Austin, TX, USA
| | - Zhiwei Li
- Department of Instrument Science & Technology, Zhejiang University, Hangzhou, 310027, China
| | - Hongjian He
- Center for Brain Imaging Science and Technology, Key Laboratory for Biomedical Engineering of Ministry of Education, College of Biomedical Engineering and Instrumental Science, Zhejiang University, Hangzhou, Zhejiang, China
| | - Qiqi Tong
- Center for Brain Imaging Science and Technology, Key Laboratory for Biomedical Engineering of Ministry of Education, College of Biomedical Engineering and Instrumental Science, Zhejiang University, Hangzhou, Zhejiang, China
| | - Feng Yu
- Department of Instrument Science & Technology, Zhejiang University, Hangzhou, 310027, China
| | - Jianhui Zhong
- Center for Brain Imaging Science and Technology, Key Laboratory for Biomedical Engineering of Ministry of Education, College of Biomedical Engineering and Instrumental Science, Zhejiang University, Hangzhou, Zhejiang, China.,University of Rochester, Rochester, NY, USA
| |
Collapse
|
5
|
Tobisch A, Stirnberg R, Harms RL, Schultz T, Roebroeck A, Breteler MMB, Stöcker T. Compressed Sensing Diffusion Spectrum Imaging for Accelerated Diffusion Microstructure MRI in Long-Term Population Imaging. Front Neurosci 2018; 12:650. [PMID: 30319336 PMCID: PMC6165908 DOI: 10.3389/fnins.2018.00650] [Citation(s) in RCA: 15] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/28/2018] [Accepted: 08/30/2018] [Indexed: 11/23/2022] Open
Abstract
Mapping non-invasively the complex microstructural architecture of the living human brain, diffusion magnetic resonance imaging (dMRI) is one of the core imaging modalities in current population studies. For the application in longitudinal population imaging, the dMRI protocol should deliver reliable data with maximum potential for future analysis. With the recent introduction of novel MRI hardware, advanced dMRI acquisition strategies can be applied within reasonable scan time. In this work we conducted a pilot study based on the requirements for high resolution dMRI in a long-term and high throughput population study. The key question was: can diffusion spectrum imaging accelerated by compressed sensing theory (CS-DSI) be used as an advanced imaging protocol for microstructure dMRI in a long-term population imaging study? As a minimum requirement we expected a high level of agreement of several diffusion metrics derived from both CS-DSI and a 3-shell high angular resolution diffusion imaging (HARDI) acquisition, an established imaging strategy used in other population studies. A wide spectrum of state-of-the-art diffusion processing and analysis techniques was applied to the pilot study data including quantitative diffusion and microstructural parameter mapping, fiber orientation estimation and white matter fiber tracking. When considering diffusion weighted images up to the same maximum diffusion weighting for both protocols, group analysis across 20 subjects indicates that CS-DSI performs comparable to 3-shell HARDI in the estimation of diffusion and microstructural parameters. Further, both protocols provide similar results in the estimation of fiber orientations and for local fiber tracking. CS-DSI provides high radial resolution while maintaining high angular resolution and it is well-suited for analysis strategies that require high b-value acquisitions, such as CHARMED modeling and biomarkers from the diffusion propagator.
Collapse
Affiliation(s)
- Alexandra Tobisch
- German Center for Neurodegenerative Diseases, Bonn, Germany.,Department of Computer Science, University of Bonn, Bonn, Germany
| | | | - Robbert L Harms
- Department of Cognitive Neuroscience, Faculty of Psychology and Neuroscience, Maastricht University, Maastricht, Netherlands
| | - Thomas Schultz
- Department of Computer Science, University of Bonn, Bonn, Germany.,Bonn-Aachen International Center for Information Technology, University of Bonn, Bonn, Germany
| | - Alard Roebroeck
- Department of Cognitive Neuroscience, Faculty of Psychology and Neuroscience, Maastricht University, Maastricht, Netherlands
| | - Monique M B Breteler
- German Center for Neurodegenerative Diseases, Bonn, Germany.,Faculty of Medicine, Institute for Medical Biometry, Informatics and Epidemiology, University of Bonn, Bonn, Germany
| | - Tony Stöcker
- German Center for Neurodegenerative Diseases, Bonn, Germany.,Department of Physics and Astronomy, University of Bonn, Bonn, Germany
| |
Collapse
|
6
|
|
7
|
Diffusion MRI Signal Augmentation: From Single Shell to Multi Shell with Deep Learning. COMPUTATIONAL DIFFUSION MRI 2017. [DOI: 10.1007/978-3-319-54130-3_5] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 12/02/2022]
|
8
|
|
9
|
Golkov V, Dosovitskiy A, Sperl JI, Menzel MI, Czisch M, Samann P, Brox T, Cremers D. q-Space Deep Learning: Twelve-Fold Shorter and Model-Free Diffusion MRI Scans. IEEE TRANSACTIONS ON MEDICAL IMAGING 2016; 35:1344-1351. [PMID: 27071165 DOI: 10.1109/tmi.2016.2551324] [Citation(s) in RCA: 145] [Impact Index Per Article: 18.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/07/2023]
Abstract
Numerous scientific fields rely on elaborate but partly suboptimal data processing pipelines. An example is diffusion magnetic resonance imaging (diffusion MRI), a non-invasive microstructure assessment method with a prominent application in neuroimaging. Advanced diffusion models providing accurate microstructural characterization so far have required long acquisition times and thus have been inapplicable for children and adults who are uncooperative, uncomfortable, or unwell. We show that the long scan time requirements are mainly due to disadvantages of classical data processing. We demonstrate how deep learning, a group of algorithms based on recent advances in the field of artificial neural networks, can be applied to reduce diffusion MRI data processing to a single optimized step. This modification allows obtaining scalar measures from advanced models at twelve-fold reduced scan time and detecting abnormalities without using diffusion models. We set a new state of the art by estimating diffusion kurtosis measures from only 12 data points and neurite orientation dispersion and density measures from only 8 data points. This allows unprecedentedly fast and robust protocols facilitating clinical routine and demonstrates how classical data processing can be streamlined by means of deep learning.
Collapse
|
10
|
Improved fidelity of brain microstructure mapping from single-shell diffusion MRI. Med Image Anal 2015; 26:268-86. [PMID: 26529580 DOI: 10.1016/j.media.2015.10.004] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/14/2015] [Revised: 07/15/2015] [Accepted: 10/02/2015] [Indexed: 01/29/2023]
Abstract
Diffusion weighted imaging (DWI) is sensitive to alterations in the diffusion of water molecules caused by microstructural barriers. Different microstructural compartments are characterized by differences in DWI signal. Diffusion tensor imaging conflates the signal from these compartments into a single tensor, which poorly represents multiple white matter fascicles and extra-axonal space. Diffusion compartment imaging (DCI) models overcome this limitation by providing parametric representations for the signal contribution of each compartment, thereby improving the fidelity of brain microstructure mapping. However, current approaches fail to identify DCI model parameters from conventional single-shell DWI with the desired accuracy. It has been demonstrated that part of this inaccuracy is due to the ill-posedness of the estimation of DCI model parameters from conventional single-shell acquisitions. In this paper, we propose to regularize the estimation problem for single-shell DWI by learning a prior distribution of DCI model parameters from DWI acquired at multiple b-values in an external population of subjects. We demonstrate that this population-informed prior enables, for the first time, accurate estimation of DCI models from single-shell DWI typically acquired in clinical practice. We validated our approach on synthetic and in vivo data of healthy subjects and patients with autism spectrum disorder. We applied the approach to population studies of brain microstructure in autism and found that introducing a population-informed prior leads to reliable detection of group differences. Our algorithm enables novel investigation from large existing DWI datasets in normal development and in disease and injury.
Collapse
|
11
|
Golkov V, Dosovitskiy A, Sämann P, Sperl JI, Sprenger T, Czisch M, Menzel MI, Gómez PA, Haase A, Brox T, Cremers D. q-Space Deep Learning for Twelve-Fold Shorter and Model-Free Diffusion MRI Scans. LECTURE NOTES IN COMPUTER SCIENCE 2015. [DOI: 10.1007/978-3-319-24553-9_5] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 12/23/2022]
|
12
|
Mishra V, Guo X, Delgado MR, Huang H. Toward tract-specific fractional anisotropy (TSFA) at crossing-fiber regions with clinical diffusion MRI. Magn Reson Med 2014; 74:1768-79. [PMID: 25447208 DOI: 10.1002/mrm.25548] [Citation(s) in RCA: 16] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/19/2014] [Revised: 10/25/2014] [Accepted: 10/31/2014] [Indexed: 12/28/2022]
Abstract
PURPOSE White matter fractional anisotropy (FA), a measure suggesting microstructure, is significantly underestimated with single diffusion tensor model at crossing-fiber regions (CFR). We propose a tract-specific FA (TSFA), corrected for the effects of crossing-fiber geometry and free water at CFR, and adapted for tract analysis with diffusion MRI (dMRI) in clinical research. METHODS At CFR voxels, the proposed technique estimates free water fraction (fiso ) as a linear function of mean apparent diffusion coefficient (mADC), fits the dual tensors and estimates TSFA. Digital phantoms were designed for testing the accuracy of fiso and fitted dual-anisotropies at CFR. The technique was applied to clinical dMRI of normal subjects and hereditary spastic paraplegia (HSP) patients to test the effectiveness of TSFA. RESULTS Phantom simulation showed unbiased estimates of dual-tensor anisotropies at CFR and high accuracy of fiso as a linear function of mADC. TSFA at CFR was highly consistent to the single tensor FA at non-CFR within the same tract with normal human dMRI. Additional HSP imaging biomarkers with significant correlation to clinical motor function scores could be identified with TSFA. CONCLUSION Results suggest the potential of the proposed technique in estimating unbiased TSFA at CFR and conducting tract analysis in clinical research.
Collapse
Affiliation(s)
- Virendra Mishra
- Advanced Imaging Research Center, University of Texas Southwestern Medical Center, Dallas, Texas, USA
| | - Xiaohu Guo
- Department of Computer Science, University of Texas at Dallas, Richardson, Texas, USA
| | - Mauricio R Delgado
- Department of Neurology, University of Texas Southwestern Medical Center, Dallas, Texas, USA
| | - Hao Huang
- Advanced Imaging Research Center, University of Texas Southwestern Medical Center, Dallas, Texas, USA.,Department of Radiology, University of Texas Southwestern Medical Center, Dallas, Texas, USA
| |
Collapse
|
13
|
Daducci A, Van De Ville D, Thiran JP, Wiaux Y. Sparse regularization for fiber ODF reconstruction: from the suboptimality of ℓ2 and ℓ1 priors to ℓ0. Med Image Anal 2014; 18:820-33. [PMID: 24593935 DOI: 10.1016/j.media.2014.01.011] [Citation(s) in RCA: 47] [Impact Index Per Article: 4.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/02/2013] [Revised: 01/29/2014] [Accepted: 01/31/2014] [Indexed: 11/27/2022]
Abstract
Diffusion MRI is a well established imaging modality providing a powerful way to probe the structure of the white matter non-invasively. Despite its potential, the intrinsic long scan times of these sequences have hampered their use in clinical practice. For this reason, a large variety of methods have been recently proposed to shorten the acquisition times. Among them, spherical deconvolution approaches have gained a lot of interest for their ability to reliably recover the intra-voxel fiber configuration with a relatively small number of data samples. To overcome the intrinsic instabilities of deconvolution, these methods use regularization schemes generally based on the assumption that the fiber orientation distribution (FOD) to be recovered in each voxel is sparse. The well known Constrained Spherical Deconvolution (CSD) approach resorts to Tikhonov regularization, based on an ℓ(2)-norm prior, which promotes a weak version of sparsity. Also, in the last few years compressed sensing has been advocated to further accelerate the acquisitions and ℓ(1)-norm minimization is generally employed as a means to promote sparsity in the recovered FODs. In this paper, we provide evidence that the use of an ℓ(1)-norm prior to regularize this class of problems is somewhat inconsistent with the fact that the fiber compartments all sum up to unity. To overcome this ℓ(1) inconsistency while simultaneously exploiting sparsity more optimally than through an ℓ(2) prior, we reformulate the reconstruction problem as a constrained formulation between a data term and a sparsity prior consisting in an explicit bound on the ℓ(0)norm of the FOD, i.e. on the number of fibers. The method has been tested both on synthetic and real data. Experimental results show that the proposed ℓ(0) formulation significantly reduces modeling errors compared to the state-of-the-art ℓ(2) and ℓ(1) regularization approaches.
Collapse
Affiliation(s)
- Alessandro Daducci
- Signal Processing Lab (LTS5), École Polytechnique Fédérale de Lausanne, Switzerland; University Hospital Center (CHUV) and University of Lausanne (UNIL), Switzerland.
| | - Dimitri Van De Ville
- Medical Image Processing Lab, École Polytechnique Fédérale de Lausanne, Switzerland; Department of Radiology and Medical Informatics, University of Geneva, Switzerland
| | - Jean-Philippe Thiran
- Signal Processing Lab (LTS5), École Polytechnique Fédérale de Lausanne, Switzerland; University Hospital Center (CHUV) and University of Lausanne (UNIL), Switzerland
| | - Yves Wiaux
- Signal Processing Lab (LTS5), École Polytechnique Fédérale de Lausanne, Switzerland; Medical Image Processing Lab, École Polytechnique Fédérale de Lausanne, Switzerland; Department of Radiology and Medical Informatics, University of Geneva, Switzerland; Institute of Sensors, Signals & Systems, Heriot-Watt University, Edinburgh, UK
| |
Collapse
|