Fiber orientation distribution from non-negative sparse recovery

Ghosh, Aurobrata; Megherbi, Thinhinane; Boumghar, Fatima Oulebsir; Deriche, Rachid

doi:10.1109/isbi.2013.6556460

Cited by 7 publications

(4 citation statements)

References 5 publications

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“…In (Ghosh et al, 2013), the fODF corresponding to a single fiber bundle is modeled by a positive-semidefinite rank-1 high-order tensor C = c ⊗2 n and is given by the polynomial C ( u ) ≔ ∑ i+j+k =2 n ( c · u ) 2 n where the vector c ∈ ℝ 3 is aligned with the direction of the underlying fiber bundle. For r fiber bundles, the fODF is given by a linear mixture:

F false(bold-italicu false) = \sum_{i = 1}^{r} w_{i} C_{i} false(bold-italicu false)

with w i ≥ 0.…”

Section: Methodsmentioning

confidence: 99%

“…The response function is assumed to be a bipolar Watson function R ( q, u ) = exp(− bd ‖ ( q · u ) 2 ) which is estimated from voxels with high FA (FA > 0.8) to ensure “single-fiber” configuration. The fODF is estimated by first discretizing the convolution integral with a selected set of points

{false{c_{i} false}}_{i = 1}^{321}

on the unit sphere and computing a least squares fit with non-negative constraints on the fODF coefficients, see (Ghosh et al, 2014). For this challenge, the order of the high order tensor used to represent the fODF was set to 24, i.e.…”

Section: Methodsmentioning

confidence: 99%

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Sparse Reconstruction Challenge for diffusion MRI: Validation on a physical phantom to determine which acquisition scheme and analysis method to use?

Ning

Laun

Gur

et al. 2015

Medical Image Analysis

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Diffusion magnetic resonance imaging (dMRI) is the modality of choice for investigating in-vivo white matter connectivity and neural tissue architecture of the brain. The diffusion-weighted signal in dMRI reflects the diffusivity of water molecules in brain tissue and can be utilized to produce image-based biomarkers for clinical research. Due to the constraints on scanning time, a limited number of measurements can be acquired within a clinically feasible scan time. In order to reconstruct the dMRI signal from a discrete set of measurements, a large number of algorithms have been proposed in recent years in conjunction with varying sampling schemes, i.e., with varying b-values and gradient directions. Thus, it is imperative to compare the performance of these reconstruction methods on a single data set to provide appropriate guidelines to neuroscientists on making an informed decision while designing their acquisition protocols. For this purpose, the SParse Reconstruction Challenge (SPARC) was held along with the workshop on Computational Diffusion MRI (at MICCAI 2014) to validate the performance of multiple reconstruction methods using data acquired from a physical phantom. A total of 16 reconstruction algorithms (9 teams) participated in this community challenge. The goal was to reconstruct single b-value and/or multiple b-value data from a sparse set of measurements. In particular, the aim was to determine an appropriate acquisition protocol (in terms of the number of measurements, b-values) and the analysis method to use for a neuroimaging study. The challenge did not delve on the accuracy of these methods in estimating model specific measures such as fractional anisotropy (FA) or mean diffusivity, but on the accuracy of these methods to fit the data. This paper presents several quantitative results pertaining to each reconstruction algorithm. The conclusions in this paper provide a valuable guideline for choosing a suitable algorithm and the corresponding data-sampling scheme for clinical neuroscience applications.

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F false(bold-italicu false) = \sum_{i = 1}^{r} w_{i} C_{i} false(bold-italicu false)

with w i ≥ 0.…”

Section: Methodsmentioning

confidence: 99%

{false{c_{i} false}}_{i = 1}^{321}

Section: Methodsmentioning

confidence: 99%

Sparse Reconstruction Challenge for diffusion MRI: Validation on a physical phantom to determine which acquisition scheme and analysis method to use?

Ning

Laun

Gur

et al. 2015

Medical Image Analysis

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show abstract

“…Finally, to take into account the effect of the noise due to the diffusion model, we have introduced a heuristic cleaning that consists in removing all the fiber orientations weighted by λ i ≤ 0.1 λ max⁡ and merging fibers separated by angle α ≤ 15° [20]. …”

Section: Methodsmentioning

confidence: 99%

Crossing Fibers Detection with an Analytical High Order Tensor Decomposition

Megherbi

Kachouane

Oulebsir-Boumghar

et al. 2014

Computational and Mathematical Methods in Medicine

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Diffusion magnetic resonance imaging (dMRI) is the only technique to probe in vivo and noninvasively the fiber structure of human brain white matter. Detecting the crossing of neuronal fibers remains an exciting challenge with an important impact in tractography. In this work, we tackle this challenging problem and propose an original and efficient technique to extract all crossing fibers from diffusion signals. To this end, we start by estimating, from the dMRI signal, the so-called Cartesian tensor fiber orientation distribution (CT-FOD) function, whose maxima correspond exactly to the orientations of the fibers. The fourth order symmetric positive definite tensor that represents the CT-FOD is then analytically decomposed via the application of a new theoretical approach and this decomposition is used to accurately extract all the fibers orientations. Our proposed high order tensor decomposition based approach is minimal and allows recovering the whole crossing fibers without any a priori information on the total number of fibers. Various experiments performed on noisy synthetic data, on phantom diffusion, data and on human brain data validate our approach and clearly demonstrate that it is efficient, robust to noise and performs favorably in terms of angular resolution and accuracy when compared to some classical and state-of-the-art approaches.

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“…The S-NNLS problem is becoming increasingly popular in certain applications where the non-negative solution needs to be recovered from a limited number of measurements. For example, in [16] an S-NNLS method was applied to magnetic resonance imaging (MRI) data to reconstruct narrow fibercrossings from a limited number of acquisitions. In [17], another method was used to uncover regulatory networks from micro-array mRNA expression profiles from breast cancer data.…”

Section: Introductionmentioning

confidence: 99%

Rectified Gaussian Scale Mixtures and the Sparse Non-Negative Least Squares Problem

Nalci

Fedorov

Al-Shoukairi

et al. 2018

IEEE Trans. Signal Process.

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In this paper, we develop a Bayesian evidence maximization framework to solve the sparse non-negative least squares (S-NNLS) problem. We introduce a family of probability densities referred to as the Rectified Gaussian Scale Mixture (R-GSM) to model the sparsity enforcing prior distribution for the solution. The R-GSM prior encompasses a variety of heavy-tailed densities such as the rectified Laplacian and rectified Studentt distributions with a proper choice of the mixing density. We utilize the hierarchical representation induced by the R-GSM prior and develop an evidence maximization framework based on the Expectation-Maximization (EM) algorithm. Using the EM based method, we estimate the hyper-parameters and obtain a point estimate for the solution. We refer to the proposed method as rectified sparse Bayesian learning (R-SBL). We provide four R-SBL variants that offer a range of options for computational complexity and the quality of the E-step computation. These methods include the Markov chain Monte Carlo EM, linear minimum mean-square-error estimation, approximate message passing and a diagonal approximation. Using numerical experiments, we show that the proposed R-SBL method outperforms existing S-NNLS solvers in terms of both signal and support recovery performance, and is also very robust against the structure of the design matrix.

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Fiber orientation distribution from non-negative sparse recovery

Cited by 7 publications

References 5 publications

Sparse Reconstruction Challenge for diffusion MRI: Validation on a physical phantom to determine which acquisition scheme and analysis method to use?

Sparse Reconstruction Challenge for diffusion MRI: Validation on a physical phantom to determine which acquisition scheme and analysis method to use?

Crossing Fibers Detection with an Analytical High Order Tensor Decomposition

Rectified Gaussian Scale Mixtures and the Sparse Non-Negative Least Squares Problem

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