A Convex Semi-definite Positive Framework for DTI Estimation and Regularization

Neji, Radhouène; Azzabou, Noura; Paragios, Nikos; Fleury, Gilles

doi:10.1007/978-3-540-76858-6_22

Cited by 8 publications

(5 citation statements)

References 15 publications

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“…From these n images, the tensor is estimated to be the one which minimizes a notion of error to the set of acquired data (Johansen-Berg and Behrens, 2009). There are several methods for the estimation and regularization of second order tensor fields, including: weighted least squares (Basser et al, 1994), variational methods for the estimation of the image volume with positivity and regularity constraints (Chefd'hotel et al, 2002(Chefd'hotel et al, , 2004Neji et al, 2007;Tschumperlé and Deriche, 2003a,b), estimation in a Riemannian space (Arsigny, 2006;Fillard et al, 2007;Lenglet, 2006) and the use of sparse representations (Bao et al, 2009;Luo et al, 2009). …”

Section: Low Angular Resolution Diffusion Imaging (Dti)mentioning

confidence: 99%

Recent advances in diffusion MRI modeling: Angular and radial reconstruction

Assemlal

Tschumperlé

Brun

et al. 2011

Medical Image Analysis

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Recent advances in diffusion magnetic resonance image (dMRI) modeling have led to the development of several state of the art methods for reconstructing the diffusion signal. These methods allow for distinct features to be computed, which in turn reflect properties of fibrous tissue in the brain and in other organs. A practical consideration is that to choose among these approaches requires very specialized knowledge. In order to bridge the gap between theory and practice in dMRI reconstruction and analysis we present a detailed review of the dMRI modeling literature. We place an emphasis on the mathematical and algorithmic underpinnings of the subject, categorizing existing methods according to how they treat the angular and radial sampling of the diffusion signal. We describe the features that can be computed with each method and discuss its advantages and limitations. We also provide a detailed bibliography to guide the reader.

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Section: Low Angular Resolution Diffusion Imaging (Dti)mentioning

confidence: 99%

Recent advances in diffusion MRI modeling: Angular and radial reconstruction

Assemlal

Tschumperlé

Brun

et al. 2011

Medical Image Analysis

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“…This results in noisy estimates of the ODF field. While regularization methods have been developed [15,16], we are not aware of any work addressing all three issues for HARDI.…”

Section: Introductionmentioning

confidence: 99%

Estimating Orientation Distribution Functions with Probability Density Constraints and Spatial Regularity

Goh

Lenglet

Thompson

et al. 2009

Medical Image Computing and Computer-Assisted Intervention – MICCAI 2009

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Abstract. High angular resolution diffusion imaging (HARDI) has become an important magnetic resonance technique for in vivo imaging. Current techniques for estimating the diffusion orientation distribution function (ODF), i.e., the probability density function of water diffusion along any direction, do not enforce the estimated ODF to be nonnegative or to sum up to one. Very often this leads to an estimated ODF which is not a proper probability density function. In addition, current methods do not enforce any spatial regularity of the data. In this paper, we propose an estimation method that naturally constrains the estimated ODF to be a proper probability density function and regularizes this estimate using spatial information. By making use of the spherical harmonic representation, we pose the ODF estimation problem as a convex optimization problem and propose a coordinate descent method that converges to the minimizer of the proposed cost function. We illustrate our approach with experiments on synthetic and real data.

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“…For example, the constraint preserving (gradient) flows of Tschumperlé et al [16] and Chefd'hotel et al [24] served as a basis for the combined approach presented by Tschumperlé and Deriche in [28]. A similar approach employing a different regularizer and a projected gradient descent has also been proposed by Neji et al [25]. Furthermore, the log-Euclidean framework, see [26] for instance, has been used as basis for a combined approach proposed by Fillard et al [10].…”

Section: B Approaches For Combined Tensor Fitting and Regularizationmentioning

confidence: 93%

“…As a consequence, there is a large body of literature on DTI reconstruction. In principle, one may distinguish four different types of approaches: i) fitting the tensors individually, i.e., independently per voxel, while additionally imposing (soft or hard) constraints to enforce the positive definiteness of the reconstructed tensors [11,12], ii) denoising the input data, i.e., the DWIs, and then fitting the tensors individually [13][14][15], iii) regularizing the tensors after reconstruction [16][17][18][19][20][21][22], and iv) reconstructing and regularizing the tensors simultaneously [10,[23][24][25][26][27]. Methods related to the latter approach are more intricate, but they show the best performance with respect to reconstruction quality [10,28].…”

Section: Introductionmentioning

confidence: 99%

Combined Tensor Fitting and TV Regularization in Diffusion Tensor Imaging Based on a Riemannian Manifold Approach

Baust

Weinmann

Wieczorek

et al. 2016

IEEE Trans. Med. Imaging

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In this paper, we consider combined TV denoising and diffusion tensor fitting in DTI using the affine-invariant Riemannian metric on the space of diffusion tensors. Instead of first fitting the diffusion tensors, and then denoising them, we define a suitable TV type energy functional which incorporates the measured DWIs (using an inverse problem setup) and which measures the nearness of neighboring tensors in the manifold. To approach this functional, we propose generalized forward- backward splitting algorithms which combine an explicit and several implicit steps performed on a decomposition of the functional. We validate the performance of the derived algorithms on synthetic and real DTI data. In particular, we work on real 3D data. To our knowledge, the present paper describes the first approach to TV regularization in a combined manifold and inverse problem setup.

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A Convex Semi-definite Positive Framework for DTI Estimation and Regularization

Cited by 8 publications

References 15 publications

Recent advances in diffusion MRI modeling: Angular and radial reconstruction

Recent advances in diffusion MRI modeling: Angular and radial reconstruction

Estimating Orientation Distribution Functions with Probability Density Constraints and Spatial Regularity

Combined Tensor Fitting and TV Regularization in Diffusion Tensor Imaging Based on a Riemannian Manifold Approach

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