
Subject-specific quantitative susceptibility mapping
using patch based deep image priors
Arvind Balachandrasekaran, Davood Karimi, Camilo Jaimes, Ali Gholipour
Computational Radiology lab
Harvard Medical School
Boston, MA 02115
arvind.balachandrasekaran, davood.karimi@childrens.harvard.edu
camilo.jaimescobos, ali.gholipour@childrens.harvard.edu
Abstract
Quantitative Susceptibility Mapping is a parametric imaging technique to estimate
the magnetic susceptibilities of biological tissues from MRI phase measurements.
This problem of estimating the susceptibility map is ill posed. Regularized recovery
approaches exploiting signal properties such as smoothness and sparsity improve
reconstructions, but suffer from over-smoothing artifacts. Deep learning approaches
have shown great potential and generate maps with reduced artifacts. However,
for reasonable reconstructions and network generalization, they require numerous
training datasets resulting in increased data acquisition time. To overcome this
issue, we proposed a subject-specific, patch-based, unsupervised learning algorithm
to estimate the susceptibility map. We make the problem well-posed by exploiting
the redundancies across the patches of the map using a deep convolutional neural
network. We formulated the recovery of the susceptibility map as a regularized
optimization problem and adopted an alternating minimization strategy to solve it.
We tested the algorithm on a 3D invivo dataset and, qualitatively and quantitatively,
demonstrated improved reconstructions over competing methods.
1 Introduction
Quantitative Susceptibility Mapping (QSM) is a parametric imaging technique to estimate the
magnetic susceptibilities of biological tissues. It enables quantification of iron concentration in gray
matter [
1
], myelin content in white matter [
2
], deoxyhemoglobin in veins [
3
] etc. Changes in the
concentrations reflect an underlying pathology, which include micro bleeds [
4
], hemorrhages [
5
] and
neurodegenerative diseases [6, 7], and can potentially be used as a bio-marker [8].
The susceptibility map is related to phase measurements through a 3D convolution with a dipole
kernel. However, the problem of estimating the map through direct inversion is ill posed and results
in streaking artifacts. To improve the quality of reconstructions, regularized recovery approaches
enforcing signal sparsity and smoothness have been introduced [
9
,
10
]. These approaches reduce the
streaking artifacts but introduce blurring in the recovered maps. Recently, supervised deep learning
methods have shown great potential and have generated maps with reduced artifacts [
11
]. However,
to achieve reasonable reconstruction quality and for the network to generalize well to unseen data,
these approaches require a lot of training data, which result in increased data acquisition time.
We propose a subject-specific, patch-based, unsupervised deep learning algorithm to estimate the
susceptibility map from phase measurements. Patch based priors have been successful in many image
restoration tasks including recovery of MR images from undersampled measurements [
12
]. To make
the problem well-posed, we exploit the redundancies across the different patches in the map using a
deep convolutional neural network (CNN). The recovery of the map is then posed as a regularized
Preprint. Under review.
arXiv:2210.06471v1 [eess.IV] 10 Oct 2022