Nonnegative Definite EAP and ODF Estimation via a Unified Multi-shell HARDI Reconstruction

Cheng, Jian; Jiang, Tianzi; Deriche, Rachid

doi:10.1007/978-3-642-33418-4_39

Cited by 9 publications

(19 citation statements)

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“…The square root representation has been proposed for the dODF (Cheng et al, 2009) and the EAP , and it has been used for non-negative dODF and EAP estimation (Cheng et al, 2012). In this work, we propose to utilize the square root representation for non-negative fODF estimation by letting…”

Section: Square Root Representation Of the Fodfmentioning

confidence: 99%

“…is a constant resulting from the integration of three real SH functions (Cheng et al, 2012), which can be calculated from the Wigner 3-j symbol and Eq. (3).…”

Section: Square Root Representation Of the Fodfmentioning

confidence: 99%

“…The most widely used dMRI approach, Diffusion Tensor Imaging (DTI), captures one fiber direction per voxel and is incapable of describing complex diffusion processes due to its Gaussian diffusion assumption (Johansen-Berg and Behrens, 2009). In view of this, many High Angular Resolution Diffusion Imaging (HARDI) (Tuch et al, 2002) methods have been developed in recent years to characterize non-Gaussian diffusion and compute quantities such as the Ensemble Average Propagator (EAP) (Wedeen et al, 2005;Descoteaux et al, 2010;Cheng et al, 2010b;Özarslan et al, 2009;Cheng et al, 2012), diffusion Orientation Distribution Function (dODF) (Tuch, 2004;Hess et al, 2006;Descoteaux et al, 2007;Aganj et al, 2010;Cheng et al, 2010a;Cheng et al, 2012), and fiber Orientation Distribution Function (fODF) (Tournier et al, 2004;Tournier et al, 2007;Alexander, 2005;Jian and Vemuri, 2007;Dell'Acqua et al, 2007;Dell'Acqua et al, 2010;Landman et al, 2012;Weldeselassie et al, 2012).…”

Section: Introductionmentioning

confidence: 99%

“…Ad-hoc normalization is also employed in these methods to obtain fODFs with unit integral. Some methods estimate continuously non-negative dODFs (Schwab et al, 2012;Cheng et al, 2012;Krajsek and Scharr, 2012) and EAPs (Cheng et al, 2012) using eigenvalue distribution of spherical functions and square root representation. But to our knowledge, none of these methods has been proposed to estimate continuously non-negative fODF in a SD framework.…”

Section: Introductionmentioning

confidence: 99%

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Non-Negative Spherical Deconvolution (NNSD) for estimation of fiber Orientation Distribution Function in single-/multi-shell diffusion MRI

et al. 2014

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Spherical Deconvolution (SD) is commonly used for estimating fiber Orientation Distribution Functions (fODFs) from diffusion-weighted signals. Existing SD methods can be classified into two categories: 1) Continuous Representation based SD (CR-SD), where typically Spherical Harmonic (SH) representation is used for convenient analytical solutions, and 2) Discrete Representation based SD (DR-SD), where the signal profile is represented by a discrete set of basis functions uniformly oriented on the unit sphere. A feasible fODF should be non-negative and should integrate to unity throughout the unit sphere S(2). However, to our knowledge, most existing SH-based SD methods enforce non-negativity only on discretized points and not the whole continuum of S(2). Maximum Entropy SD (MESD) and Cartesian Tensor Fiber Orientation Distributions (CT-FOD) are the only SD methods that ensure non-negativity throughout the unit sphere. They are however computational intensive and are susceptible to errors caused by numerical spherical integration. Existing SD methods are also known to overestimate the number of fiber directions, especially in regions with low anisotropy. DR-SD introduces additional error in peak detection owing to the angular discretization of the unit sphere. This paper proposes a SD framework, called Non-Negative SD (NNSD), to overcome all the limitations above. NNSD is significantly less susceptible to the false-positive peaks, uses SH representation for efficient analytical spherical deconvolution, and allows accurate peak detection throughout the whole unit sphere. We further show that NNSD and most existing SD methods can be extended to work on multi-shell data by introducing a three-dimensional fiber response function. We evaluated NNSD in comparison with Constrained SD (CSD), a quadratic programming variant of CSD, MESD, and an L1-norm regularized non-negative least-squares DR-SD. Experiments on synthetic and real single-/multi-shell data indicate that NNSD improves estimation performance in terms of mean difference of angles, peak detection consistency, and anisotropy contrast between isotropic and anisotropic regions.

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Section: Square Root Representation Of the Fodfmentioning

confidence: 99%

“…is a constant resulting from the integration of three real SH functions (Cheng et al, 2012), which can be calculated from the Wigner 3-j symbol and Eq. (3).…”

Section: Square Root Representation Of the Fodfmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Non-Negative Spherical Deconvolution (NNSD) for estimation of fiber Orientation Distribution Function in single-/multi-shell diffusion MRI

et al. 2014

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“…The work of [6] attempts to iteratively enforce nonnegativity of the fiber orientation distribution (FOD) function, but their model does not guarantee nonnegativity everywhere. The work of [7] estimates the SH coefficients of the square root of the ODF and then simply squares the resulting function to obtain a nonnegative ODF. However, this result need not coincide with the optimal nonnegative ODF.…”

Section: Introductionmentioning

confidence: 99%

Nonnegative ODF estimation via optimal constraint selection

Wolfers

Schwab

Vidal

2014

2014 IEEE 11th International Symposium on Biomedical Imaging (ISBI)

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We consider the problem of estimating a nonnegative orientation distribution function (ODF) from high angular resolution diffusion images. Since enforcing nonnegativity of the ODF for all directions on the sphere leads to an optimization problem with infinitely many constraints, prior work cannot guarantee the nonnegativity of the estimated ODF. The first contribution of this paper is to show that, under certain conditions, a single constraint is sufficient to guarantee the nonnegativity of the estimated ODF in all directions. Otherwise, when these conditions are violated, we propose an iterative algorithm that enforces one constraint at a time and is guaranteed to converge to the optimal nonnegative ODF. Experiments on synthetic and real data show that our methods produce more accurate solutions than prior work at a reduced runtime.Index Terms-Diffusion MRI, HARDI, estimation of nonnegative ODFs, semi-infinite optimization.

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Estimation of the CSA‐ODF using Bayesian compressed sensing of multi‐shell HARDI

Duarte-Carvajalino

Lenglet

et al. 2013

Magnetic Resonance in Med

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Purpose Diffusion MRI provides important information about the brain white matter structures and has opened new avenues for neuroscience and translational research. However, acquisition time needed for advanced applications can still be a challenge in clinical settings. There is consequently a need to accelerate diffusion MRI acquisitions. Methods A multi-task Bayesian compressive sensing (MT-BCS) framework is proposed to directly estimate the constant solid angle orientation distribution function (CSA-ODF) from under-sampled (i.e., accelerated image acquisition) multi-shell high angular resolution diffusion imaging (HARDI) datasets, and accurately recover HARDI data at higher resolution in q-space. The proposed MT-BCS approach exploits the spatial redundancy of the data by modeling the statistical relationships within groups (clusters) of diffusion signal. This framework also provides uncertainty estimates of the computed CSA-ODF and diffusion signal, directly computed from the compressive measurements. Experiments validating the proposed framework are performed using realistic multi-shell synthetic images and in-vivo multi-shell high angular resolution HARDI datasets. Results Results indicate a practical reduction in the number of required diffusion volumes (q-space samples) by at least a factor of four to estimate the CSA-ODF from multi-shell data. Conclusion This work presents, for the first time, a multi-task Bayesian compressive sensing approach to simultaneously estimate the full posterior of the CSA-ODF and diffusion-weighted volumes from multi-shell HARDI acquisitions. It demonstrates improvement of the quality of acquired datasets via CS de-noising, and accurate estimation of the CSA-ODF, as well as enables a reduction in the acquisition time by a factor of two to four, especially when “staggered” q-space sampling schemes are used. The proposed MT-BCS framework can naturally be combined with parallel MR imaging to further accelerate HARDI acquisitions.

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Nonnegative Definite EAP and ODF Estimation via a Unified Multi-shell HARDI Reconstruction

Cited by 9 publications

References 11 publications

Non-Negative Spherical Deconvolution (NNSD) for estimation of fiber Orientation Distribution Function in single-/multi-shell diffusion MRI

Non-Negative Spherical Deconvolution (NNSD) for estimation of fiber Orientation Distribution Function in single-/multi-shell diffusion MRI

Nonnegative ODF estimation via optimal constraint selection

Estimation of the CSA‐ODF using Bayesian compressed sensing of multi‐shell HARDI

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