Comparison of basis functions and q‐space sampling schemes for robust compressed sensing reconstruction accelerating diffusion spectrum imaging

Abstract

Time constraints placed on magnetic resonance imaging often restrict the application of advanced diffusion MRI (dMRI) protocols in clinical practice and in high throughput research studies. Therefore, acquisition strategies for accelerated dMRI have been investigated to allow for the collection of versatile and high quality imaging data, even if stringent scan time limits are imposed. Diffusion spectrum imaging (DSI), an advanced acquisition strategy that allows for a high resolution of intra‐voxel microstructure, can be sufficiently accelerated by means of compressed sensing (CS) theory. CS theory describes a framework for the efficient collection of fewer samples of a data set than conventionally required followed by robust reconstruction to recover the full data set from sparse measurements. For an accurate recovery of DSI data, a suitable acquisition scheme for sparse q‐space sampling and the sensing and sparsifying bases for CS reconstruction need to be selected. In this work we explore three different types of q‐space undersampling schemes and two frameworks for CS reconstruction based on either Fourier or SHORE basis functions. After CS recovery, diffusion and microstructural parameters and orientational information are estimated from the reconstructed data by means of state‐of‐the‐art processing techniques for dMRI analysis. By means of simulation, diffusion phantom and in vivo DSI data, an isotropic distribution of q‐space samples was found to be optimal for sparse DSI. The CS reconstruction results indicate superior performance of Fourier‐based CS‐DSI compared to the SHORE‐based approach. Based on these findings we outline an experimental design for accelerated DSI and robust CS reconstruction of the sparse measurements that is suitable for the application within time‐limited studies.

Comparison of q-Space Reconstruction Methods for Undersampled Diffusion Spectrum Imaging Data

“…This is confirmed since our results were similar to the results obtained in Bilgic et al 19 where they used wavelets and total variation as sparsifying transforms. Furthermore, in Paquette et al 20 and Tobisch et al 36 it is shown that it produces satisfactory reconstruction performance in comparison to other sparsifying transforms or methods based on other continuous basis functions.…”

“…Future work could include further propagator-based quality measures, such as the non-Gaussianity 36 and the angular error in crossing angle 36 to complement NMSE, PC, MSD, and p0; to increase the characterization of the propagator reconstruction quantitatively. Finally, this comparison could be improved using recent advances of the corresponding methods, like the Laplacian regularized MAP, 24 joint k-q reconstruction, 37 or the implementation of deep learning for CSD like in Rasmussen et al 38…”

MAPL1:q‐space reconstruction using ‐regularized mean apparent propagator

“…We use 600 simulations from high‐contrast q ‐space data from 2 crossing fibers as in 18 . These simulations have the same microstructure but different orientations in 3D space.…”

“…Mean Apparent Propagator (MAP) 16‐22 is a physical model whose basis functions are Gauss‐Hermite functions. The first basis‐function corresponds to Gaussian diffusion as in DTI, and the following basis functions correspond to non‐Gaussian diffusion; hence, it can represent well the complete diffusion propagator.…”

“…One such model is the Simple Harmonic Oscillator‐based Reconstruction and Estimation (SHORE) model 16 . Recently, we compared SHORE‐CS 17 with DSI‐CS; and found that the DSI‐CS reconstruction using the identity as sparsifying basis outperformed SHORE‐CS 18 . However, in this work we explore another model that can benefit from its ability to sparsely characterize the diffusion signal: Mean Apparent Propagator (MAP) 16 …”