3D space-varying coefficient models with application to diffusion tensor imaging

Heim, Susanne; Fahrmeir, Ludwig; Eilers, Paul H.C.; Marx, Brian D.

doi:10.1016/j.csda.2007.01.005

Cited by 15 publications

(11 citation statements)

References 31 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…We observe that there exist approaches which accommodate the spatial information in the stage of DT estimation, such as Heim et al (2007) and Tabelow et al (2008). Intuitively, by incorporating the spatial information, these methods improve the DT estimation, and therefore the accuracy of FA and RA.…”

Section: Introductionmentioning

confidence: 94%

See 1 more Smart Citation

Local tests for identifying anisotropic diffusion areas in human brain with DTI

Zhang

Alexander

et al. 2013

Ann. Appl. Stat.

View full text Add to dashboard Cite

Diffusion tensor imaging (DTI) plays a key role in analyzing the physical structures of biological tissues, particularly in reconstructing fiber tracts of the human brain in vivo. On the one hand, eigenvalues of diffusion tensors (DTs) estimated from diffusion weighted imaging (DWI) data usually contain systematic bias, which subsequently biases the diffusivity measurements popularly adopted in fiber tracking algorithms. On the other hand, correctly accounting for the spatial information is important in the construction of these diffusivity measurements since the fiber tracts are typically spatially structured. This paper aims to establish test-based approaches to identify anisotropic water diffusion areas in the human brain. These areas in turn indicate the areas passed by fiber tracts. Our proposed test statistic not only takes into account the bias components in eigenvalue estimates, but also incorporates the spatial information of neighboring voxels. Under mild regularity conditions, we demonstrate that the proposed test statistic asymptotically follows a χ2 distribution under the null hypothesis. Simulation and real DTI data examples are provided to illustrate the efficacy of our proposed methods.

show abstract

Section: Introductionmentioning

confidence: 94%

“…Examples include Mangin et al (2002), Chang, Jones and Pierpaoli (2005), Salvador et al (2005), Heim et al (2007), Zhu et al (2007), Tabelow et al (2008) and many others.…”

Section: Introductionmentioning

confidence: 99%

Local tests for identifying anisotropic diffusion areas in human brain with DTI

Zhang

Alexander

et al. 2013

Ann. Appl. Stat.

View full text Add to dashboard Cite

show abstract

“…Thus, while we consider the same continuous-domain model in (2) and (18), standard and regularized schemes differ in the way the coefficients are obtained. However, when in (20), the regularized scheme (19) reduces to the standard case (2) since we only minimize which leads to close-fitting of data; at the other extreme, as , (19) results in a maximum-likelihood estimate within the null-space of .…”

Section: B Discretization Of the Problemmentioning

confidence: 99%

“…Then, the original problem (5) can be posed as the discrete-domain optimization problem (19) with (20) where is now given by (18) so that with in the data-fidelity term. Thus, while we consider the same continuous-domain model in (2) and (18), standard and regularized schemes differ in the way the coefficients are obtained.…”

Section: B Discretization Of the Problemmentioning

confidence: 99%

See 1 more Smart Citation

Regularized Interpolation for Noisy Images

Ramani

Thévenaz

Unser

2010

IEEE Trans. Med. Imaging

View full text Add to dashboard Cite

Abstract-Interpolation is the means by which a continuously defined model is fit to discrete data samples. When the data samples are exempt of noise, it seems desirable to build the model by fitting them exactly. In medical imaging, where quality is of paramount importance, this ideal situation unfortunately does not occur. In this paper, we propose a scheme that improves on the quality by specifying a tradeoff between fidelity to the data and robustness to the noise. We resort to variational principles, which allow us to impose smoothness constraints on the model for tackling noisy data. Based on shift-, rotation-, and scale-invariant requirements on the model, we show that the -norm of an appropriate vector derivative is the most suitable choice of regularization for this purpose. In addition to Tikhonov-like quadratic regularization, this includes edge-preserving total-variation-like (TV) regularization. We give algorithms to recover the continuously defined model from noisy samples and also provide a data-driven scheme to determine the optimal amount of regularization. We validate our method with numerical examples where we demonstrate its superiority over an exact fit as well as the benefit of TV-like nonquadratic regularization over Tikhonov-like quadratic regularization.

show abstract

Mathematical Methods for Signal and Image Analysis and Representation

Florack¹,

Duits²,

Jongbloed³

et al. 2011

Computational Imaging and Vision

View full text Add to dashboard Cite

This comprehensive book series embraces state-of-the-art expository works and advanced research monographs on any aspect of this interdisciplinary field.Topics covered by the series fall in the following four main categories:• Imaging Systems and Image Processing • Computer Vision and Image Understanding • Visualization •Applications of Imaging TechnologiesOnly monographs or multi-authored books that have a distinct subject area, that is where each chapter has been invited in order to fulfill this purpose, will be considered for the series. Volume 41 For further volumes: www.springer.com/series/5754 Luc Florack r Remco Duits r Geurt Jongbloed r Marie-Colette van Lieshout r Laurie Davies Editors

show abstract

3D space-varying coefficient models with application to diffusion tensor imaging

Cited by 15 publications

References 31 publications

Local tests for identifying anisotropic diffusion areas in human brain with DTI

Local tests for identifying anisotropic diffusion areas in human brain with DTI

Regularized Interpolation for Noisy Images

Mathematical Methods for Signal and Image Analysis and Representation

Contact Info

Product

Resources

About