Browsing by Author "Blumenthal, Moritz"

Purpose We introduce a framework that enables efficient sampling from learned probability distributions for MRI reconstruction. Method Samples are drawn from the posterior distribution given the measured k-space using the Markov chain Monte Carlo (MCMC) method, different from conventional deep learning-based MRI reconstruction techniques. In addition to the maximum a posteriori estimate for the image, which can be obtained by maximizing the log-likelihood indirectly or directly, the minimum mean square error estimate and uncertainty maps can also be computed from those drawn samples. The data-driven Markov chains are constructed with the score-based generative model learned from a given image database and are independent of the forward operator that is used to model the k-space measurement. Results We numerically investigate the framework from these perspectives: (1) the interpretation of the uncertainty of the image reconstructed from undersampled k-space; (2) the effect of the number of noise scales used to train the generative models; (3) using a burn-in phase in MCMC sampling to reduce computation; (4) the comparison to conventional -wavelet regularized reconstruction; (5) the transferability of learned information; and (6) the comparison to fastMRI challenge. Conclusion A framework is described that connects the diffusion process and advanced generative models with Markov chains. We demonstrate its flexibility in terms of contrasts and sampling patterns using advanced generative priors and the benefits of also quantifying the uncertainty for every pixel.

We introduce a framework that enables efficient sampling from learned probability distributions for MRI reconstruction. Different from conventional deep learning-based MRI reconstruction techniques, samples are drawn from the posterior distribution given the measured k-space using the Markov chain Monte Carlo (MCMC) method. In addition to the maximum a posteriori (MAP) estimate for the image, which can be obtained with conventional methods, the minimum mean square error (MMSE) estimate and uncertainty maps can also be computed. The data-driven Markov chains are constructed from the generative model learned from a given image database and are independent of the forward operator that is used to model the k-space measurement. This provides flexibility because the method can be applied to k-space acquired with different sampling schemes or receive coils using the same pre-trained models. Furthermore, we use a framework based on a reverse diffusion process to be able to utilize advanced generative models. The performance of the method is evaluated on an open dataset using 10-fold undersampling in k-space.

Purpose: To develop a deep-learning-based image reconstruction framework for reproducible research in MRI. Methods: The BART toolbox offers a rich set of implementations of calibration and reconstruction algorithms for parallel imaging and compressed sensing. In this work, BART was extended by a non-linear operator framework that provides automatic differentiation to allow computation of gradients. Existing MRI-specific operators of BART, such as the non-uniform fast Fourier transform, are directly integrated into this framework and are complemented by common building blocks used in neural networks. To evaluate the use of the framework for advanced deep-learning-based reconstruction, two state-of-the-art unrolled reconstruction networks, namely the Variational Network [1] and MoDL [2], were implemented. Results: State-of-the-art deep image-reconstruction networks can be constructed and trained using BART's gradient based optimization algorithms. The BART implementation achieves a similar performance in terms of training time and reconstruction quality compared to the original implementations based on TensorFlow. Conclusion: By integrating non-linear operators and neural networks into BART, we provide a general framework for deep-learning-based reconstruction in MRI.

Purpose To develop a deep‐learning‐based image reconstruction framework for reproducible research in MRI. Methods The BART toolbox offers a rich set of implementations of calibration and reconstruction algorithms for parallel imaging and compressed sensing. In this work, BART was extended by a nonlinear operator framework that provides automatic differentiation to allow computation of gradients. Existing MRI‐specific operators of BART, such as the nonuniform fast Fourier transform, are directly integrated into this framework and are complemented by common building blocks used in neural networks. To evaluate the use of the framework for advanced deep‐learning‐based reconstruction, two state‐of‐the‐art unrolled reconstruction networks, namely the Variational Network and MoDL, were implemented. Results State‐of‐the‐art deep image‐reconstruction networks can be constructed and trained using BART's gradient‐based optimization algorithms. The BART implementation achieves a similar performance in terms of training time and reconstruction quality compared to the original implementations based on TensorFlow. Conclusion By integrating nonlinear operators and neural networks into BART, we provide a general framework for deep‐learning‐based reconstruction in MRI.

Purpose: To develop a free-breathing myocardial T1 mapping technique using free-running inversion-recovery (IR) radial fast low-angle shot (FLASH) and calibrationless motion-resolved model-based reconstruction. Methods: A free-running inversion-recovery radial FLASH sequence is used for data acquisition at 3T. To reduce the waiting time between inversions, an analytical formula is derived that takes the incomplete T1 recovery into account for an accurate T1 calculation. The respiratory motion signal is estimated from the filtered k-space center using an adapted singular spectrum analysis (SSA-FARY) technique. The cardiac motion signal is recorded using electrocardiography. A motion-resolved model-based reconstruction is used to estimate both parameter and coil sensitivity maps directly from the sorted k-space data. Spatial-temporal total variation, in addition to the spatial sparsity constraints, is applied to the parameter maps to improve T1 accuracy and precision. Validations are performed on an experimental phantom and five human subjects. Results: In comparison to an IR spin-echo reference, phantom results confirm good T1 accuracy when reducing the waiting time from five seconds to one second using the new correction. The motion-resolved model-based reconstruction further improves T1 precision. Aside from showing that a reliable respiratory motion signal can be estimated using modified SSA-FARY, in vivo studies with five healthy subjects demonstrate that high-resolution dynamic myocardial T1 maps (1.0x1.0x6 mm$^3$)can be obtained within two minutes with good T1 precision and repeatability. Conclusion: High-resolution motion-resolved T1 mapping during free-breathing with good T1 accuracy, precision, and repeatability can be achieved by combining inversion-recovery radial FLASH, self-gating, and a calibrationless motion-resolved model-based reconstruction.

Purpose: To achieve free-breathing quantitative fat and $R_2^{\star}$ mapping of the liver using a generalized model-based iterative reconstruction, dubbed as MERLOT. Methods: For acquisition, we use a multi-echo radial FLASH sequence that acquires multiple echoes with different complementary radial spoke encodings. We investigate real-time single-slice and volumetric multi-echo radial FLASH acquisition. For the latter, the sampling scheme is extended to a volumetric stack-of-stars acquisition. Model-based reconstruction based on generalized nonlinear inversion is used to jointly estimate water, fat, $R_2^{\star}$, $B_0$ field inhomogeneity, and coil sensitivity maps from the multi-coil multi-echo radial spokes. Spatial smoothness regularization is applied onto the B 0 field and coil sensitivity maps, whereas joint sparsity regularization is employed for the other parameter maps. The method integrates calibration-less parallel imaging and compressed sensing and was implemented in BART. For the volumetric acquisition, the respiratory motion is resolved with self-gating using SSA-FARY. The quantitative accuracy of the proposed method was validated via numerical simulation, the NIST phantom, a water/fat phantom, and in in-vivo liver studies. Results: For real-time acquisition, the proposed model-based reconstruction allowed acquisition of dynamic liver fat fraction and $R_2^{\star}$ maps at a temporal resolution of 0.3 s per frame. For the volumetric acquisition, whole liver coverage could be achieved in under 2 minutes using the self-gated motion-resolved reconstruction. Conclusion: The proposed multi-echo radial sampling sequence achieves fast k -space coverage and is robust to motion. The proposed model-based reconstruction yields spatially and temporally resolved liver fat fraction, $R_2^{\star}$ and $B_0$ field maps at high undersampling factor and with volume coverage.

Purpose: To develop a model-based nonlinear reconstruction for simultaneous water-specific $T_{1}$, $R_{2}^{*}$, $B_{0}$ field and/or fat fraction (FF) mapping using single-shot inversion-recovery (IR) multi-echo radial FLASH. Methods: The proposed model-based reconstruction jointly estimates water-specific $T_{1}$, $R_{2}^{*}$, $B_{0}$ field and/or FF maps, as well as a set of coil sensitivities directly from $k$-space obtained with a single-shot IR multi-echo radial FLASH sequence using blip gradients across echoes. Joint sparsity constraints are exploited on multiple quantitative maps to improve precision. Validations are performed on numerical and NIST phantoms and with in vivo studies of the human brain and liver at 3 T. Results: Numerical phantom studies demonstrate the effects of fat signals in $T_{1}$ estimation and confirm good quantitative accuracy of the proposed method for all parameter maps. NIST phantom results confirm good quantitative $T_{1}$ and $R_{2}^{*}$ accuracy in comparison to Cartesian references. Apart from good quantitative accuracy and precision for multiple parameter maps, in vivo studies show improved image details utilizing the proposed joint estimation. The proposed method can achieve simultaneous water-specific $T_{1}$, $R_{2}^{*}$, $B_{0}$ field and/or FF mapping for brain (0.81 $\times$ 0.81 $\times$ 5 mm$^{3}$) and liver (1.6 $\times$ 1.6 $\times$ 6 mm$^{3}$) imaging within four seconds. Conclusion: The proposed model-based nonlinear reconstruction, in combination with a single-shot IR multi-echo radial FLASH acquisition, enables joint estimation of accurate water-specific $T_{1}$, $R_{2}^{*}$, $B_{0}$ field and/or FF maps within four seconds. The present work is of potential value for specific clinical applications.

Abstract Purpose To develop a generic radial sampling scheme that combines the advantages of golden ratio sampling with simplicity of equidistant angular patterns. The irrational angle between consecutive spokes in golden ratio‐based sampling schemes enables a flexible retrospective choice of temporal resolution, while preserving good coverage of k‐space for each individual bin. Nevertheless, irrational increments prohibit precomputation of the point‐spread function (PSF), can lead to numerical problems, and require more complex processing steps. To avoid these problems, a new sampling scheme based on a rational approximation of golden angles (RAGA) is developed. Methods The theoretical properties of RAGA sampling are mathematically derived. Sidelobe‐to‐peak ratios (SPR) are numerically computed and compared to the corresponding golden ratio sampling schemes. The sampling scheme is implemented in the BART toolbox and in a radial gradient‐echo sequence. Feasibility is shown for quantitative imaging in a phantom and a cardiac scan of a healthy volunteer. Results RAGA sampling can accurately approximate golden ratio sampling and has almost identical PSF and SPR. In contrast to golden ratio sampling, each frame can be reconstructed with the same equidistant trajectory using different sampling masks, and the angle of each acquired spoke can be encoded as a small index, which simplifies processing of the acquired data. Conclusion RAGA sampling provides the advantages of golden ratio sampling while simplifying data processing, rendering it a valuable tool for dynamic and quantitative MRI.

Abstract Purpose To develop a neural network architecture for improved calibrationless reconstruction of radial data when no ground truth is available for training. Methods NLINV‐Net is a model‐based neural network architecture that directly estimates images and coil sensitivities from (radial) k‐space data via nonlinear inversion (NLINV). Combined with a training strategy using self‐supervision via data undersampling (SSDU), it can be used for imaging problems where no ground truth reconstructions are available. We validated the method for (1) real‐time cardiac imaging and (2) single‐shot subspace‐based quantitative T1 mapping. Furthermore, region‐optimized virtual (ROVir) coils were used to suppress artifacts stemming from outside the field of view and to focus the k‐space‐based SSDU loss on the region of interest. NLINV‐Net‐based reconstructions were compared with conventional NLINV and PI‐CS (parallel imaging + compressed sensing) reconstruction and the effect of the region‐optimized virtual coils and the type of training loss was evaluated qualitatively. Results NLINV‐Net‐based reconstructions contain significantly less noise than the NLINV‐based counterpart. ROVir coils effectively suppress streakings which are not suppressed by the neural networks while the ROVir‐based focused loss leads to visually sharper time series for the movement of the myocardial wall in cardiac real‐time imaging. For quantitative imaging, T1‐maps reconstructed using NLINV‐Net show similar quality as PI‐CS reconstructions, but NLINV‐Net does not require slice‐specific tuning of the regularization parameter. Conclusion NLINV‐Net is a versatile tool for calibrationless imaging which can be used in challenging imaging scenarios where a ground truth is not available.