Spinet-QSM: model-based deep learning with schatten p-norm regularization for improved quantitative susceptibility mapping

OBJECTIVE

Quantitative susceptibility mapping (QSM) provides an estimate of the magnetic susceptibility of tissue using magnetic resonance (MR) phase measurements. The tissue magnetic susceptibility (source) from the measured magnetic field distribution/local tissue field (effect) inherent in the MR phase images is estimated by numerically solving the inverse source-effect problem. This study aims to develop an effective model-based deep-learning framework to solve the inverse problem of QSM.

MATERIALS AND METHODS

This work proposes a Schatten p -norm-driven model-based deep learning framework for QSM with a learnable norm parameter p to adapt to the data. In contrast to other model-based architectures that enforce the l2 -norm or l1 -norm for the denoiser, the proposed approach can enforce any p -norm ( 0 < p ≤ 2 ) on a trainable regulariser.

RESULTS

The proposed method was compared with deep learning-based approaches, such as QSMnet, and model-based deep learning approaches, such as learned proximal convolutional neural network (LPCNN). Reconstructions performed using 77 imaging volumes with different acquisition protocols and clinical conditions, such as hemorrhage and multiple sclerosis, showed that the proposed approach outperformed existing state-of-the-art methods by a significant margin in terms of quantitative merits.

CONCLUSION

The proposed SpiNet-QSM showed a consistent improvement of at least 5% in terms of the high-frequency error norm (HFEN) and normalized root mean squared error (NRMSE) over other QSM reconstruction methods with limited training data.

Dynamic low-count PET image reconstruction using spatio-temporal primal dual network

OBJECTIVE

Dynamic positron emission tomography (PET) imaging, which can provide information on dynamic changes in physiological metabolism, is now widely used in clinical diagnosis and cancer treatment. However, the reconstruction from dynamic data is extremely challenging due to the limited counts received in individual frame, especially in ultra short frames. Recently, the unrolled model-based deep learning methods have shown inspiring results for low-count PET image reconstruction with good interpretability. Nevertheless, the existing model-based deep learning methods mainly focus on the spatial correlations while ignore the temporal domain. &#xD;&#xD;Approach. In this paper, inspired by the Learned Primal Dual algorithm, we propose the spatio-temporal primal dual network for dynamic low-count PET image reconstruction. Both spatial and temporal correlations are encoded by 3D convolution operators. The physical projection of PET is embedded in the iterative learning process of the network, which provides the physical constraints and enhances interpretability. &#xD;&#xD;Main results. The experiments of both simulation data and real rat scan data have shown that the proposed method can achieve substantial noise reduction in both temporal and spatial domains and outperform the maximum likelihood expectation maximization (MLEM), spatio-temporal kernel method (KEM-ST), Learned Primal Dual (LPD) and FBPnet.&#xD;&#xD;Significance. Experimental results show STPDnet better reconstruction performance in the low count situation, which makes the proposed method particularly suitable in whole-body dynamic imaging and parametric PET imaging that require extreme short frames and usually suffer from high level of noise.

Memory-efficient model-based deep learning with convergence and robustness guarantees

Computational imaging has been revolutionized by compressed sensing algorithms, which offer guaranteed uniqueness, convergence, and stability properties. Model-based deep learning methods that combine imaging physics with learned regularization priors have emerged as more powerful alternatives for image recovery. The main focus of this paper is to introduce a memory efficient model-based algorithm with similar theoretical guarantees as CS methods. The proposed iterative algorithm alternates between a gradient descent involving the score function and a conjugate gradient algorithm to encourage data consistency. The score function is modeled as a monotone convolutional neural network. Our analysis shows that the monotone constraint is necessary and sufficient to enforce the uniqueness of the fixed point in arbitrary inverse problems. In addition, it also guarantees the convergence to a fixed point, which is robust to input perturbations. We introduce two implementations of the proposed MOL framework, which differ in the way the monotone property is imposed. The first approach enforces a strict monotone constraint, while the second one relies on an approximation. The guarantees are not valid for the second approach in the strict sense. However, our empirical studies show that the convergence and robustness of both approaches are comparable, while the less constrained approximate implementation offers better performance. The proposed deep equilibrium formulation is significantly more memory efficient than unrolled methods, which allows us to apply it to 3D or 2D+time problems that current unrolled algorithms cannot handle.

MoDL-QSM: Model-based deep learning for quantitative susceptibility mapping

Quantitative susceptibility mapping (QSM) has demonstrated great potential in quantifying tissue susceptibility in various brain diseases. However, the intrinsic ill-posed inverse problem relating the tissue phase to the underlying susceptibility distribution affects the accuracy for quantifying tissue susceptibility. Recently, deep learning has shown promising results to improve accuracy by reducing the streaking artifacts. However, there exists a mismatch between the observed phase and the theoretical forward phase estimated by the susceptibility label. In this study, we proposed a model-based deep learning architecture that followed the STI (susceptibility tensor imaging) physical model, referred to as MoDL-QSM. Specifically, MoDL-QSM accounts for the relationship between STI-derived phase contrast induced by the susceptibility tensor terms (χ₁₃, χ₂₃ and χ₃₃) and the acquired single-orientation phase. The convolutional neural networks are embedded into the physical model to learn a regularization term containing prior information. χ₃₃ and phase induced by χ₁₃ and χ₂₃ terms were used as the labels for network training. Quantitative evaluation metrics were compared with recently developed deep learning QSM methods. The results showed that MoDL-QSM achieved superior performance, demonstrating its potential for future applications.