Regularized spherical polar fourier diffusion MRI with optimal dictionary learning.

Jian Cheng, Tianzi Jiang, Rachid Deriche, Dinggang Shen, Pew Thian Yap

Research output: Chapter in Book/Report/Conference proceedingChapter

9 Citations (Scopus)

Abstract

Compressed Sensing (CS) takes advantage of signal sparsity or compressibility and allows superb signal reconstruction from relatively few measurements. Based on CS theory, a suitable dictionary for sparse representation of the signal is required. In diffusion MRI (dMRI), CS methods proposed for reconstruction of diffusion-weighted signal and the Ensemble Average Propagator (EAP) utilize two kinds of Dictionary Learning (DL) methods: 1) Discrete Representation DL (DR-DL), and 2) Continuous Representation DL (CR-DL). DR-DL is susceptible to numerical inaccuracy owing to interpolation and regridding errors in a discretized q-space. In this paper, we propose a novel CR-DL approach, called Dictionary Learning - Spherical Polar Fourier Imaging (DL-SPFI) for effective compressed-sensing reconstruction of the q-space diffusion-weighted signal and the EAP. In DL-SPFI, a dictionary that sparsifies the signal is learned from the space of continuous Gaussian diffusion signals. The learned dictionary is then adaptively applied to different voxels using a weighted LASSO framework for robust signal reconstruction. Compared with the start-of-the-art CR-DL and DR-DL methods proposed by Merlet et al. and Bilgic et al., respectively, our work offers the following advantages. First, the learned dictionary is proved to be optimal for Gaussian diffusion signals. Second, to our knowledge, this is the first work to learn a voxel-adaptive dictionary. The importance of the adaptive dictionary in EAP reconstruction will be demonstrated theoretically and empirically. Third, optimization in DL-SPFI is only performed in a small subspace resided by the SPF coefficients, as opposed to the q-space approach utilized by Merlet et al. We experimentally evaluated DL-SPFI with respect to L1-norm regularized SPFI (L1-SPFI), which uses the original SPF basis, and the DR-DL method proposed by Bilgic et al. The experiment results on synthetic and real data indicate that the learned dictionary produces sparser coefficients than the original SPF basis and results in significantly lower reconstruction error than Bilgic et al.'s method.

Original languageEnglish
Title of host publicationMedical image computing and computer-assisted intervention : MICCAI ... International Conference on Medical Image Computing and Computer-Assisted Intervention
Pages639-646
Number of pages8
Volume16
EditionPt 1
Publication statusPublished - 2013 Dec 1
Externally publishedYes

Fingerprint

Diffusion Magnetic Resonance Imaging
Learning
Art

ASJC Scopus subject areas

  • Medicine(all)

Cite this

Cheng, J., Jiang, T., Deriche, R., Shen, D., & Yap, P. T. (2013). Regularized spherical polar fourier diffusion MRI with optimal dictionary learning. In Medical image computing and computer-assisted intervention : MICCAI ... International Conference on Medical Image Computing and Computer-Assisted Intervention (Pt 1 ed., Vol. 16, pp. 639-646)

Regularized spherical polar fourier diffusion MRI with optimal dictionary learning. / Cheng, Jian; Jiang, Tianzi; Deriche, Rachid; Shen, Dinggang; Yap, Pew Thian.

Medical image computing and computer-assisted intervention : MICCAI ... International Conference on Medical Image Computing and Computer-Assisted Intervention. Vol. 16 Pt 1. ed. 2013. p. 639-646.

Research output: Chapter in Book/Report/Conference proceedingChapter

Cheng, J, Jiang, T, Deriche, R, Shen, D & Yap, PT 2013, Regularized spherical polar fourier diffusion MRI with optimal dictionary learning. in Medical image computing and computer-assisted intervention : MICCAI ... International Conference on Medical Image Computing and Computer-Assisted Intervention. Pt 1 edn, vol. 16, pp. 639-646.
Cheng J, Jiang T, Deriche R, Shen D, Yap PT. Regularized spherical polar fourier diffusion MRI with optimal dictionary learning. In Medical image computing and computer-assisted intervention : MICCAI ... International Conference on Medical Image Computing and Computer-Assisted Intervention. Pt 1 ed. Vol. 16. 2013. p. 639-646
Cheng, Jian ; Jiang, Tianzi ; Deriche, Rachid ; Shen, Dinggang ; Yap, Pew Thian. / Regularized spherical polar fourier diffusion MRI with optimal dictionary learning. Medical image computing and computer-assisted intervention : MICCAI ... International Conference on Medical Image Computing and Computer-Assisted Intervention. Vol. 16 Pt 1. ed. 2013. pp. 639-646
@inbook{4e0e3a9796eb461c9bd4b262ba8c8a0a,
title = "Regularized spherical polar fourier diffusion MRI with optimal dictionary learning.",
abstract = "Compressed Sensing (CS) takes advantage of signal sparsity or compressibility and allows superb signal reconstruction from relatively few measurements. Based on CS theory, a suitable dictionary for sparse representation of the signal is required. In diffusion MRI (dMRI), CS methods proposed for reconstruction of diffusion-weighted signal and the Ensemble Average Propagator (EAP) utilize two kinds of Dictionary Learning (DL) methods: 1) Discrete Representation DL (DR-DL), and 2) Continuous Representation DL (CR-DL). DR-DL is susceptible to numerical inaccuracy owing to interpolation and regridding errors in a discretized q-space. In this paper, we propose a novel CR-DL approach, called Dictionary Learning - Spherical Polar Fourier Imaging (DL-SPFI) for effective compressed-sensing reconstruction of the q-space diffusion-weighted signal and the EAP. In DL-SPFI, a dictionary that sparsifies the signal is learned from the space of continuous Gaussian diffusion signals. The learned dictionary is then adaptively applied to different voxels using a weighted LASSO framework for robust signal reconstruction. Compared with the start-of-the-art CR-DL and DR-DL methods proposed by Merlet et al. and Bilgic et al., respectively, our work offers the following advantages. First, the learned dictionary is proved to be optimal for Gaussian diffusion signals. Second, to our knowledge, this is the first work to learn a voxel-adaptive dictionary. The importance of the adaptive dictionary in EAP reconstruction will be demonstrated theoretically and empirically. Third, optimization in DL-SPFI is only performed in a small subspace resided by the SPF coefficients, as opposed to the q-space approach utilized by Merlet et al. We experimentally evaluated DL-SPFI with respect to L1-norm regularized SPFI (L1-SPFI), which uses the original SPF basis, and the DR-DL method proposed by Bilgic et al. The experiment results on synthetic and real data indicate that the learned dictionary produces sparser coefficients than the original SPF basis and results in significantly lower reconstruction error than Bilgic et al.'s method.",
author = "Jian Cheng and Tianzi Jiang and Rachid Deriche and Dinggang Shen and Yap, {Pew Thian}",
year = "2013",
month = "12",
day = "1",
language = "English",
volume = "16",
pages = "639--646",
booktitle = "Medical image computing and computer-assisted intervention : MICCAI ... International Conference on Medical Image Computing and Computer-Assisted Intervention",
edition = "Pt 1",

}

TY - CHAP

T1 - Regularized spherical polar fourier diffusion MRI with optimal dictionary learning.

AU - Cheng, Jian

AU - Jiang, Tianzi

AU - Deriche, Rachid

AU - Shen, Dinggang

AU - Yap, Pew Thian

PY - 2013/12/1

Y1 - 2013/12/1

N2 - Compressed Sensing (CS) takes advantage of signal sparsity or compressibility and allows superb signal reconstruction from relatively few measurements. Based on CS theory, a suitable dictionary for sparse representation of the signal is required. In diffusion MRI (dMRI), CS methods proposed for reconstruction of diffusion-weighted signal and the Ensemble Average Propagator (EAP) utilize two kinds of Dictionary Learning (DL) methods: 1) Discrete Representation DL (DR-DL), and 2) Continuous Representation DL (CR-DL). DR-DL is susceptible to numerical inaccuracy owing to interpolation and regridding errors in a discretized q-space. In this paper, we propose a novel CR-DL approach, called Dictionary Learning - Spherical Polar Fourier Imaging (DL-SPFI) for effective compressed-sensing reconstruction of the q-space diffusion-weighted signal and the EAP. In DL-SPFI, a dictionary that sparsifies the signal is learned from the space of continuous Gaussian diffusion signals. The learned dictionary is then adaptively applied to different voxels using a weighted LASSO framework for robust signal reconstruction. Compared with the start-of-the-art CR-DL and DR-DL methods proposed by Merlet et al. and Bilgic et al., respectively, our work offers the following advantages. First, the learned dictionary is proved to be optimal for Gaussian diffusion signals. Second, to our knowledge, this is the first work to learn a voxel-adaptive dictionary. The importance of the adaptive dictionary in EAP reconstruction will be demonstrated theoretically and empirically. Third, optimization in DL-SPFI is only performed in a small subspace resided by the SPF coefficients, as opposed to the q-space approach utilized by Merlet et al. We experimentally evaluated DL-SPFI with respect to L1-norm regularized SPFI (L1-SPFI), which uses the original SPF basis, and the DR-DL method proposed by Bilgic et al. The experiment results on synthetic and real data indicate that the learned dictionary produces sparser coefficients than the original SPF basis and results in significantly lower reconstruction error than Bilgic et al.'s method.

AB - Compressed Sensing (CS) takes advantage of signal sparsity or compressibility and allows superb signal reconstruction from relatively few measurements. Based on CS theory, a suitable dictionary for sparse representation of the signal is required. In diffusion MRI (dMRI), CS methods proposed for reconstruction of diffusion-weighted signal and the Ensemble Average Propagator (EAP) utilize two kinds of Dictionary Learning (DL) methods: 1) Discrete Representation DL (DR-DL), and 2) Continuous Representation DL (CR-DL). DR-DL is susceptible to numerical inaccuracy owing to interpolation and regridding errors in a discretized q-space. In this paper, we propose a novel CR-DL approach, called Dictionary Learning - Spherical Polar Fourier Imaging (DL-SPFI) for effective compressed-sensing reconstruction of the q-space diffusion-weighted signal and the EAP. In DL-SPFI, a dictionary that sparsifies the signal is learned from the space of continuous Gaussian diffusion signals. The learned dictionary is then adaptively applied to different voxels using a weighted LASSO framework for robust signal reconstruction. Compared with the start-of-the-art CR-DL and DR-DL methods proposed by Merlet et al. and Bilgic et al., respectively, our work offers the following advantages. First, the learned dictionary is proved to be optimal for Gaussian diffusion signals. Second, to our knowledge, this is the first work to learn a voxel-adaptive dictionary. The importance of the adaptive dictionary in EAP reconstruction will be demonstrated theoretically and empirically. Third, optimization in DL-SPFI is only performed in a small subspace resided by the SPF coefficients, as opposed to the q-space approach utilized by Merlet et al. We experimentally evaluated DL-SPFI with respect to L1-norm regularized SPFI (L1-SPFI), which uses the original SPF basis, and the DR-DL method proposed by Bilgic et al. The experiment results on synthetic and real data indicate that the learned dictionary produces sparser coefficients than the original SPF basis and results in significantly lower reconstruction error than Bilgic et al.'s method.

UR - http://www.scopus.com/inward/record.url?scp=84894612287&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84894612287&partnerID=8YFLogxK

M3 - Chapter

C2 - 24505721

AN - SCOPUS:84894612287

VL - 16

SP - 639

EP - 646

BT - Medical image computing and computer-assisted intervention : MICCAI ... International Conference on Medical Image Computing and Computer-Assisted Intervention

ER -