Abstract
The presence of dipole-inconsistent data due to substantial noise or artifacts causes streaking artifacts in quantitative susceptibility mapping (QSM) reconstructions. Often used Bayesian approaches rely on regularizers, which in turn yield reduced sharpness. To overcome this problem, we present a novel L1-norm data fidelity approach that is robust with respect to outliers, and therefore prevents streaking artifacts. QSM functionals are solved with linear and nonlinear L1-norm data fidelity terms using functional augmentation, and are compared with equivalent L2-norm methods. Algorithms were tested on synthetic data, with phase inconsistencies added to mimic lesions, QSM Challenge 2.0 data, and in vivo brain images with hemorrhages. The nonlinear L1-norm-based approach achieved the best overall error metric scores and better streaking artifact suppression. Notably, L1-norm methods could reconstruct QSM images without using a brain mask, with similar regularization weights for different data fidelity weighting or masking setups. The proposed L1-approach provides a robust method to prevent streaking artifacts generated by dipole-inconsistent data, renders brain mask calculation unessential, and opens novel challenging clinical applications such asassessing brain hemorrhages and cortical layers.
Highlights
Gradient recalled echo (GRE) sequences encode voxel-w ise information about the magnetic fields in the phase of the complex acquisition.[1]
The regularizers act as constraints to the solutions, such as imposing continuity or smoothness[9], piece-wise constant or piece-wise smooth solutions, sparsity in a specific domain, etc The likelihood of the solution, expressed in the data fidelity term, is typically associated with the L2-norm difference between the acquired phase and the susceptibility distribution convolved with the dipole kernel
Both L1-norm approaches showed better gray/white contrast in cortical areas compared to L2-norm methods
Summary
Gradient recalled echo (GRE) sequences encode voxel-w ise information about the magnetic fields in the phase of the complex acquisition.[1]. From a Bayesian perspective, this is equivalent to assuming that the noise distribution in the phase data is Gaussian This assumption is only valid for high signal-to-noise ration (SNR) areas, ie, with high magnitude signal.[19] A noise-w hitening weight matrix may be used in the data fidelity term to improve the solutions at low-s ignal regions.[10] Another approach is to change the domain of the data fidelity term and calculate the error in the complex image domain.[20,21] This nonlinear approach is commonly implemented jointly with variational penalties,[20] with proposed fast solvers[22] based on the alternating directions of multipliers method23-25 (ADMM). In the image (susceptibility) domain, this creates a “smearing effect.” The phase inconsistencies are propagated following the magic angle and its neighboring voxels to reduce the energy of the errors they create
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