A signal transformational framework for breaking the noise floor and its applications in MRI

Koay, Cheng Guan; Özarslan, Evren; Basser, Peter J.

doi:10.1016/j.jmr.2008.11.015

Cited by 135 publications

(154 citation statements)

References 45 publications

(95 reference statements)

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“…From the estimates for ES g 1 the non-centrality parameter of the v-distribution can be estimated using standard methods, see e.g. Koay et al (2009a).…”

Section: Position-orientation Adaptive Smoothing (Poas)mentioning

confidence: 99%

Position-orientation adaptive smoothing of diffusion weighted magnetic resonance data (POAS)

Becker

Tabelow

Voss

et al. 2012

Medical Image Analysis

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We introduce an algorithm for diffusion weighted magnetic resonance imaging data enhancement based on structural adaptive smoothing in both voxel space and diffusion-gradient space. The method, called POAS, does not refer to a specific model for the data, like the diffusion tensor or higher order models. It works by embedding the measurement space into a space with defined metric, in this case the Lie group of three-dimensional Euclidean motion SE(3). Subsequently, pairwise comparisons of the values of the diffusion weighted signal are used for adaptation. POAS preserves the edges of the observed fine and anisotropic structures. It is designed to reduce noise directly in the diffusion weighted images and consequently also to reduce bias and variability of quantities derived from the data for specific models. We evaluate the algorithm on simulated and experimental data and demonstrate that it can be used to reduce the number of applied diffusion gradients and hence acquisition time while achieving a similar quality of data, or to improve the quality of data acquired in a clinically feasible scan time setting.

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“…From the estimates for ES g 1 the non-centrality parameter of the v-distribution can be estimated using standard methods, see e.g. Koay et al (2009a).…”

Section: Position-orientation Adaptive Smoothing (Poas)mentioning

confidence: 99%

Position-orientation adaptive smoothing of diffusion weighted magnetic resonance data (POAS)

Becker

Tabelow

Voss

et al. 2012

Medical Image Analysis

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“…This continuous operator is rotational invariant, and independent on the choice of a specific basis. Besides, the Laplace operator was already applied successfully for several applications ranging from natural image denoising (You and Kaveh, 2000;Chan and Shen, 2005) to diffusion MRI analysis (Descoteaux et al, 2007;Koay et al, 2009;Descoteaux et al, 2010).…”

Section: Laplace Regularization In the Mspf Basismentioning

confidence: 99%

“…This algorithm, as well as the L-curve method (Hansen, 2000), have already been applied successfully for other applications in Q-ball diffusion MRI (Koay et al, 2009;Descoteaux et al, 2010;Descoteaux et al, 2007). The GCV method has the major advantage to be generalizable to the situation where there is more than one k parameter to optimize.…”

Section: Optimal Regularization Parametersmentioning

confidence: 99%

Diffusion MRI signal reconstruction with continuity constraint and optimal regularization

Caruyer

Deriche

2012

Medical Image Analysis

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In diffusion MRI, the reconstruction of the full Ensemble Average Propagator (EAP) provides new insights in the diffusion process and the underlying microstructure. The reconstruction of the signal in the whole Q-space is still extremely challenging however. It requires very long acquisition protocols, and robust reconstruction to cope with the very low SNR at large b-values. Several reconstruction methods were proposed recently, among which the Spherical Polar Fourier (SPF) expansion, a promising basis for signal reconstruction. Yet the reconstruction in SPF is still subject to noise and discontinuity of the reconstruction. In this work, we present a method for the reconstruction of the diffusion attenuation in the whole Q-space, with a special focus on continuity and optimal regularization. We derive a modified Spherical Polar Fourier (mSPF) basis, orthonormal and compatible with SPF, for the reconstruction of a signal with continuity constraint. We also derive the expression of a Laplace regularization operator in the basis, together with a method based on generalized cross validation for the optimal choice of the parameter. Our method results in a noticeable dimension reduction as compared with SPF. Tested on synthetic and real data, the reconstruction with this method is more robust to noise and better preserves fiber directions and crossings.

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“…The integer k is the size of the dictionary. The noise e i ∈ R d + is known to have a Rician distribution and non-central χ-distribution when using parallel imaging [3,4]. However, for the current contribution, it will be assumed Gaussian with mean µ ∈ R d and diagonal covariance Σ = diag((σ…”

Section: Learning a Dictionary Of Dsi Profiles With Sparse Codingmentioning

confidence: 99%

Sparse DSI: Learning DSI Structure for Denoising and Fast Imaging

Gramfort

Poupon²,

Descoteaux

2012

Medical Image Computing and Computer-Assisted Intervention – MICCAI 2012

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Abstract. Diffusion spectrum imaging (DSI) from multiple diffusionweighted images (DWI) allows to image the complex geometry of water diffusion in biological tissue. To capture the structure of DSI data, we propose to use sparse coding constrained by physical properties of the signal, namely symmetry and positivity, to learn a dictionary of diffusion profiles. Given this estimated model of the signal, we can extract better estimates of the signal from noisy measurements and also speed up acquisition by reducing the number of acquired DWI while giving access to high resolution DSI data. The method learns jointly for all the acquired DWI and scales to full brain data. Working with two sets of 515 DWI images acquired on two different subjects we show that using just half of the data (258 DWI) we can better predict the other 257 DWI than the classic symmetry procedure. The observation holds even if the diffusion profiles are estimated on a different subject dataset from an undersampled q-space of 40 measurements.

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A signal transformational framework for breaking the noise floor and its applications in MRI

Cited by 135 publications

References 45 publications

Position-orientation adaptive smoothing of diffusion weighted magnetic resonance data (POAS)

Position-orientation adaptive smoothing of diffusion weighted magnetic resonance data (POAS)

Diffusion MRI signal reconstruction with continuity constraint and optimal regularization

Sparse DSI: Learning DSI Structure for Denoising and Fast Imaging

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