Fast Dictionary-Based Reconstruction for Diffusion Spectrum Imaging

Abstract

Diffusion Spectrum Imaging (DSI) reveals detailed local diffusion properties at the expense of substantially long imaging times. It is possible to accelerate acquisition by undersampling in q-space, followed by image reconstruction that exploits prior knowledge on the diffusion probability density functions (pdfs). Previously proposed methods impose this prior in the form of sparsity under wavelet and total variation (TV) transforms, or under adaptive dictionaries that are trained on example datasets to maximize the sparsity of the representation. These compressed sensing (CS) methods require full-brain processing times on the order of hours using Matlab running on a workstation. This work presents two dictionary-based reconstruction techniques that use analytical solutions, and are two orders of magnitude faster than the previously proposed dictionary-based CS approach. The first method generates a dictionary from the training data using Principal Component Analysis (PCA), and performs the reconstruction in the PCA space. The second proposed method applies reconstruction using pseudoinverse with Tikhonov regularization with respect to a dictionary. This dictionary can either be obtained using the K-SVD algorithm, or it can simply be the training dataset of pdfs without any training. All of the proposed methods achieve reconstruction times on the order of seconds per imaging slice, and have reconstruction quality comparable to that of dictionary-based CS algorithm.

A model‐based reconstruction for undersampled radial spin‐echo DTI with variational penalties on the diffusion tensor

“…This concept was first applied for relaxometry (32)(33)(34)(35)(36)(37). Both compressed sensing (38)(39)(40) and model-based reconstruction (41) were recently applied to reduce the measurement time of diffusion acquisitions as well. In addition, we recently demonstrated in related work on denoising that improved DTI maps can be obtained by performing nonlinear regularization directly in the domain of the diffusion tensor, instead of denoising the diffusion-weighted images followed by calculating tensor maps from denoised images (42).…”

Comparison of sampling strategies and sparsifying transforms to improve compressed sensing diffusion spectrum imaging

“…Lastly, dictionary learning has recently become popular in dMRI. In particular, several techniques have been introduced in the context of DSI . For instance, learn dictionaries from DSI‐like acquisitions and use it to either denoise full DSI data or to perform undersampled DSI acquisitions and reconstructions.…”

“…In particular, several techniques have been introduced in the context of DSI . For instance, learn dictionaries from DSI‐like acquisitions and use it to either denoise full DSI data or to perform undersampled DSI acquisitions and reconstructions. In particular, Gramfort et al exploit the symmetry and positivity of the signal to assess free parameters of the dictionary learning problem.…”

Q-Space Modeling in Diffusion-Weighted MRI

“…Menzel et al (2011) and Lee et al (2012) constructed the PDF of diffusion while considering it to be sparse in the wavelet domain and to have small total variation. In addition, adaptive dictionaries (Bilgic et al, 2012(Bilgic et al, , 2013 with symmetry and positivity considerations (Gramfort, Poupon, & Descoteaux, 2014) have also been chosen as the sparse domain, significantly reducing the DSI acquisition time. In addition, adaptive dictionaries (Bilgic et al, 2012(Bilgic et al, , 2013 with symmetry and positivity considerations (Gramfort, Poupon, & Descoteaux, 2014) have also been chosen as the sparse domain, significantly reducing the DSI acquisition time.…”