Denoising and fast diffusion imaging with physically constrained sparse dictionary learning

Abstract

To cite this version:Alexandre Gramfort, Cyril Poupon, Maxime Descoteaux. Denoising and fast diffusion imaging with physically constrained sparse dictionary learning. Medical Image Analysis, Elsevier, 2013, 18 (1) Abstract Diffusion-weighted imaging (DWI) allows imaging the geometry of water diffusion in biological tissues. However, DW images are noisy at high b-values and acquisitions are slow when using a large number of measurements, such as in Diffusion Spectrum Imaging (DSI). This work aims to denoise DWI and reduce the number of required measurements, while maintaining data quality. To capture the structure of DWI data, we use sparse dictionary learning constrained by the physical properties of the signal: symmetry and positivity. The method learns a dictionary of diffusion profiles on all the DW images at the same time and then scales to full brain data. Its performance is investigated with simulations and two real DSI datasets. We obtain better signal estimates from noisy measurements than by applying mirror symmetry through the q-space origin, Gaussian denoising or state-ofthe-art non-local means denoising. Using a high-resolution dictionary learnt on another subject, we show that we can reduce the number of images acquired while still generating high resolution DSI data. Using dictionary learning, one can denoise DW images effectively and perform faster acquisitions. Higher b-value acquisitions and DSI techniques are possible with approximately 40 measurements. This opens important perspectives for the connectomics community using DSI.

Dipy, a library for the analysis of diffusion MRI data

“…In practice, the first methods to calculate the PDF were q-space imaging (QSI) (Callaghan et al, 1988) and the most recent diffusion spectrum imaging (DSI) (Wedeen et al, 2005) (see section 6.2). DSI needs long acquisition time although recent techniques based on Compressed Sensing ideas (Menzel et al, 2011; Bilgic et al, 2012; Gramfort et al, 2013), and multi-slice imaging (Setsompop et al, 2012) have considerably accelerated the DSI acquisition. An alternative is to work on reconstructing only an angular projection of the 3D PDF.…”

Harmonization of diffusion MRI datasets with adaptive dictionary learning

“…As updating α needs an optimization scheme, this can be done independently for each α n using coordinate descent (Friedman et al, 2010). For updating D, we use the parameter-free closed form update from Mairal et al (2010, Algorithm 2), which only requires storing intermediary matrices of the previous iteration using α and X n to update D. Building dictionaries for the task at hand has been used previously in the context of diffusion MRI for denoising (Gramfort et al, 2014;St-Jean et al, 2016) and compressed sensing (Gramfort et al, 2014;Merlet et al, 2013;Schwab et al, 2018) amongst other tasks. Note that it is also possible to design dictionaries based on products of fixed basis or adding additional constraints such as positivity or spatial consistency to Eq.…”

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.…”