Hybrid data fidelity term approach for quantitative susceptibility mapping.

PURPOSE: Susceptibility maps are usually derived from local magnetic field estimations by minimizing a functional composed of a data consistency term and a regularization term. The data-consistency term measures the difference between the desired solution and the measured data using typically the L2-norm. It has been proposed to replace this L2-norm with the L1-norm, due to its robustness to outliers and reduction of streaking artifacts arising from highly noisy or strongly perturbed regions. However, in regions with high SNR, the L1-norm yields a suboptimal denoising performance. In this work, we present a hybrid data fidelity approach that uses the L1-norm and subsequently the L2-norm to exploit the strengths of both norms. METHODS: We developed a hybrid data fidelity term approach for QSM (HD-QSM) based on linear susceptibility inversion methods, with total variation regularization. Each functional is solved with ADMM. The HD-QSM approach is a two-stage method that first finds a fast solution of the L1-norm functional and then uses this solution to initialize the L2-norm functional. In both norms we included spatially variable weights that improve the quality of the reconstructions. RESULTS: The HD-QSM approach produced good quantitative reconstructions in terms of structural definition, noise reduction, and avoiding streaking artifacts comparable with nonlinear methods, but with higher computational efficiency. Reconstructions performed with this method achieved first place at the lowest RMS error category in stage 1 of the 2019 QSM Reconstruction Challenge. CONCLUSIONS: The proposed method allows robust and accurate QSM reconstructions, obtaining superior performance to state-of-the-art methods.

Streaking artifact suppression of quantitative susceptibility mapping reconstructions via L1-norm data fidelity optimization (L1-QSM).

PURPOSE: 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. METHODS: 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. RESULTS: 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. CONCLUSION: 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.

The 2016 QSM Challenge: Lessons learned and considerations for a future challenge design.

PURPOSE: The 4th International Workshop on MRI Phase Contrast and QSM (2016, Graz, Austria) hosted the first QSM Challenge. A single-orientation gradient recalled echo acquisition was provided, along with COSMOS and the χ33 STI component as ground truths. The submitted solutions differed more than expected depending on the error metric used for optimization and were generally over-regularized. This raised (unanswered) questions about the ground truths and the metrics utilized. METHODS: We investigated the influence of background field remnants by applying additional filters. We also estimated the anisotropic contributions from the STI tensor to the apparent susceptibility to amend the χ33 ground truth and to investigate the impact on the reconstructions. Lastly, we used forward simulations from the COSMOS reconstruction to investigate the impact noise had on the metric scores. RESULTS: Reconstructions compared against the amended STI ground truth returned lower errors. We show that the background field remnants had a minor impact in the errors. In the absence of inconsistencies, all metrics converged to the same regularization weights, whereas structural similarity index metric was more insensitive to such inconsistencies. CONCLUSION: There was a mismatch between the provided data and the ground truths due to the presence of unaccounted anisotropic susceptibility contributions and noise. Given the lack of reliable ground truths when using in vivo acquisitions, simulations are suggested for future QSM Challenges.

Weak-harmonic regularization for quantitative susceptibility mapping.

PURPOSE: Background-field removal is a crucial preprocessing step for quantitative susceptibility mapping (QSM). Remnants from this step often contaminate the estimated local field, which in turn leads to erroneous tissue-susceptibility reconstructions. The present work aimed to mitigate this undesirable behavior with the development of a new approach that simultaneously decouples background contributions and local susceptibility sources on QSM inversion. METHODS: Input phase data for QSM can be seen as a composite scalar field of local effects and residual background components. We developed a new weak-harmonic regularizer to constrain the latter and to separate the 2 components. The resulting optimization problem was solved with the alternating directions of multipliers method framework to achieve fast convergence. In addition, for convenience, a new alternating directions of multipliers method-based preconditioned nonlinear projection onto dipole fields solver was developed to enable initializations with wrapped-phase distributions. Weak-harmonic QSM, with and without nonlinear projection onto dipole fields preconditioning, was compared with the original (alternating directions of multipliers method-based) total variation QSM algorithm in phantom and in vivo experiments. RESULTS: Weak-harmonic QSM returned improved reconstructions regardless of the method used for background-field removal, although the proposed nonlinear projection onto dipole fields method often obtained better results. Streaking and shadowing artifacts were substantially suppressed, and residual background components were effectively removed. CONCLUSION: Weak-harmonic QSM with field preconditioning is a robust dipole inversion technique and has the potential to be extended as a single-step formulation for initialization with uncombined multi-echo data.