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 proceedingConference contribution

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 publicationLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Pages639-646
Number of pages8
Volume8149 LNCS
EditionPART 1
DOIs
Publication statusPublished - 2013 Oct 23
Externally publishedYes
Event16th International Conference on Medical Image Computing and Computer Assisted Intervention, MICCAI 2013 - Nagoya, Japan
Duration: 2013 Sep 222013 Sep 26

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
NumberPART 1
Volume8149 LNCS
ISSN (Print)03029743
ISSN (Electronic)16113349

Other

Other16th International Conference on Medical Image Computing and Computer Assisted Intervention, MICCAI 2013
CountryJapan
CityNagoya
Period13/9/2213/9/26

Fingerprint

Glossaries
Magnetic resonance imaging
Compressed sensing
Compressed Sensing
Propagator
Signal Reconstruction
Signal reconstruction
Ensemble
Voxel
Dictionary
Learning
Approach Space
L1-norm
Sparse Representation
Compressibility
Coefficient
Sparsity
Interpolation
Interpolate
Subspace

ASJC Scopus subject areas

  • Computer Science(all)
  • Theoretical Computer Science

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 Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (PART 1 ed., Vol. 8149 LNCS, pp. 639-646). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 8149 LNCS, No. PART 1). https://doi.org/10.1007/978-3-642-40811-3_80

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

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Vol. 8149 LNCS PART 1. ed. 2013. p. 639-646 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 8149 LNCS, No. PART 1).

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Cheng, J, Jiang, T, Deriche, R, Shen, D & Yap, PT 2013, Regularized spherical polar fourier diffusion MRI with optimal dictionary learning. in Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). PART 1 edn, vol. 8149 LNCS, Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), no. PART 1, vol. 8149 LNCS, pp. 639-646, 16th International Conference on Medical Image Computing and Computer Assisted Intervention, MICCAI 2013, Nagoya, Japan, 13/9/22. https://doi.org/10.1007/978-3-642-40811-3_80
Cheng J, Jiang T, Deriche R, Shen D, Yap PT. Regularized spherical polar fourier diffusion MRI with optimal dictionary learning. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). PART 1 ed. Vol. 8149 LNCS. 2013. p. 639-646. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); PART 1). https://doi.org/10.1007/978-3-642-40811-3_80
Cheng, Jian ; Jiang, Tianzi ; Deriche, Rachid ; Shen, Dinggang ; Yap, Pew Thian. / Regularized spherical polar fourier diffusion MRI with optimal dictionary learning. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Vol. 8149 LNCS PART 1. ed. 2013. pp. 639-646 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); PART 1).
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