Complex diffusion-weighted image estimation via matrix recovery under general noise models

Abstract

We propose a patch-based singular value shrinkage method for diffusion magnetic resonance image estimation targeted at low signal to noise ratio and accelerated acquisitions. It operates on the complex data resulting from a sensitivity encoding reconstruction, where asymptotically optimal signal recovery guarantees can be attained by modeling the noise propagation in the reconstruction and subsequently simulating or calculating the limit singular value spectrum. Simple strategies are presented to deal with phase inconsistencies and optimize patch construction. The pertinence of our contributions is quantitatively validated on synthetic data, an in vivo adult example, and challenging neonatal and fetal cohorts. Our methodology is compared with related approaches, which generally operate on magnitude-only data and use data-based noise level estimation and singular value truncation. Visual examples are provided to illustrate effectiveness in generating denoised and debiased diffusion estimates with well preserved spatial and diffusion detail.

Assessment of radial glia in the frontal lobe of fetuses with Down syndrome

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MIXANDMIX: numerical techniques for the computation of empirical spectral distributions of population mixtures

“…Our code has been architectured so that most demanding routines support both CPU and GPU based parallel computations. This includes the parallel computation of the solutions of the system of equations in (6) for the different grid locations but also the parallel computation of different ESDs, required, for instance, in patch-based image denoising applications (Cordero-Grande et al, 2018).…”

In Utero Diffusion MRI

“…The processing pipeline integrates image denoising based on random matrix theory as described in Section 3.2 15 , dynamic distortion correction based on the phase evolution between spin and field echoes as described in Section 3.4, and retrospective slice-level motion correction for multi-shell data 18 . The motion correction leverages a data-driven q-space representation in spherical harmonics and a radial decomposition (SHARD) for multi-shell data 26 , and also incorporates slice outlier rejection.…”