Undersampled MRI Research Articles

Attention-Enhanced Convolutional Iterative Unrolling Network for Under-Sampled MRI Reconstruction

Attention-Enhanced Convolutional Iterative Unrolling Network for Under-Sampled MRI Reconstruction

Correlated and Multi-Frequency Diffusion Modeling for Highly Under-Sampled MRI Reconstruction.

Given the obstacle in accentuating the reconstruction accuracy for diagnostically significant tissues, most existing MRI reconstruction methods perform targeted reconstruction of the entire MR image without considering fine details, especially when dealing with highly under-sampled images. Therefore, a considerable volume of efforts has been directed towards surmounting this challenge, as evidenced by the emergence of numerous methods dedicated to preserving high-frequency content as well as fine textural details in the reconstructed image. In this case, exploring the merits associated with each method of mining high-frequency information and formulating a reasonable principle to maximize the joint utilization of these approaches will be a more effective solution to achieve accurate reconstruction. Specifically, this work constructs an innovative principle named Correlated and Multi-frequency Diffusion Model (CM-DM) for highly under-sampled MRI reconstruction. In essence, the rationale underlying the establishment of such principle lies not in assembling arbitrary models, but in pursuing the effective combinations and replacement of components. It also means that the novel principle focuses on forming a correlated and multi-frequency prior through different high-frequency operators in the diffusion process. Moreover, multi-frequency prior further constraints the noise term closer to the target distribution in the frequency domain, thereby making the diffusion process converge faster. Experimental results verify that the proposed method achieved superior reconstruction accuracy, with a notable enhancement of approximately 2dB in PSNR compared to state-of-the-art methods.

MA-RECON: Mask-aware deep-neural-network for robust fast MRI k-space interpolation

Background and objectiveHigh-quality reconstruction of MRI images from under-sampled ‘k-space’ data, which is in the Fourier domain, is crucial for shortening MRI acquisition times and ensuring superior temporal resolution. Over recent years, a wealth of deep neural network (DNN) methods have emerged, aiming to tackle the complex, ill-posed inverse problem linked to this process. However, their instability against variations in the acquisition process and anatomical distribution exposes a deficiency in the generalization of relevant physical models within these DNN architectures. The goal of our work is to enhance the generalization capabilities of DNN methods for k-space interpolation by introducing ‘MA-RECON’, an innovative mask-aware DNN architecture and associated training method. MethodsUnlike preceding approaches, our ‘MA-RECON’ architecture encodes not only the observed data but also the under-sampling mask within the model structure. It implements a tailored training approach that leverages data generated with a variety of under-sampling masks to stimulate the model's generalization of the under-sampled MRI reconstruction problem. Therefore, effectively represents the associated inverse problem, akin to the classical compressed sensing approach. ResultsThe benefits of our MA-RECON approach were affirmed through rigorous testing with the widely accessible fastMRI dataset. Compared to standard DNN methods and DNNs trained with under-sampling mask augmentation, our approach demonstrated superior generalization capabilities. This resulted in a considerable improvement in robustness against variations in both the acquisition process and anatomical distribution, especially in regions with pathology. ConclusionIn conclusion, our mask-aware strategy holds promise for enhancing the generalization capacity and robustness of DNN-based methodologies for MRI reconstruction from undersampled k-space data.Code is available in the following link: https://github.com/nitzanavidan/PD_Recon

Adapting model-based deep learning to multiple acquisition conditions: Ada-MoDL.

The aim of this work is to introduce a single model-based deep network that can provide high-quality reconstructions from undersampled parallel MRI data acquired with multiple sequences, acquisition settings, and field strengths. A single unrolled architecture, which offers good reconstructions for multiple acquisition settings, is introduced. The proposed scheme adapts the model to each setting by scaling the convolutional neural network (CNN) features and the regularization parameter with appropriate weights. The scaling weights and regularization parameter are derived using a multilayer perceptron model from conditional vectors, which represents the specific acquisition setting. The perceptron parameters and the CNN weights are jointly trained using data from multiple acquisition settings, including differences in field strengths, acceleration, and contrasts. The conditional network is validated using datasets acquired with different acquisition settings. The comparison of the adaptive framework, which trains a single model using the data from all the settings, shows that it can offer consistently improved performance for each acquisition condition. The comparison of the proposed scheme with networks that are trained independently for each acquisition setting shows that it requires less training data per acquisition setting to offer good performance. The Ada-MoDL framework enables the use of a single model-based unrolled network for multiple acquisition settings. In addition to eliminating the need to train and store multiple networks for different acquisition settings, this approach reduces the training data needed for each acquisition setting.

An analysis of reconstruction noise from undersampled 4D flow MRI

Novel Magnetic Resonance (MR) imaging modalities can quantify hemodynamics but require long acquisition times, precluding its widespread use for early diagnosis of cardiovascular disease. To reduce acquisition times, flow reconstruction from undersampled data is routinely performed.Reconstructed anatomical and hemodynamic images may present visual artifacts. While some artifacts are reconstruction errors, and a consequence of undersampling, others are due to measurement noise or the random choice of samples. A reconstructed image becomes thus a random variable: its bias leads to systematic reconstruction errors, whereas its fluctuations may induce spatial correlations that may be misconstrued for visual information or that may carry to quantities of interest computed from the image. Although the former has been studied in the literature, the latter has not received as much attention.In this study, we investigate the theoretical properties of the random perturbations arising from the reconstruction process. To our knowledge, this is the first study on this topic. We perform numerical experiments on simulated flow, on aortic phantom flow, and on aortic flow. These show that the correlation length remains limited to two to three pixels when a Gaussian undersampling pattern is combined with ℓ1-norm minimization methods. The correlation length may increase significantly for other undersampling patterns, higher undersampling factors (i.e., higher than 8× compression), and other reconstruction methods. Our findings suggest that the reconstruction method has a large impact on the correlation. As reconstruction methods are routinely used in practice, the impact of these random perturbations in practical applications merits further study.

Undersampled MRI reconstruction based on spectral graph wavelet transform

Compressed sensing magnetic resonance imaging (CS-MRI) has exhibited great potential to accelerate magnetic resonance imaging if an image can be sparsely represented. How to sparsify the image significantly affects the reconstruction quality of images. In this paper, a spectral graph wavelet transform (SGWT) is introduced to sparsely represent magnetic resonance images in iterative image reconstructions. The SGWT is achieved by extending the traditional wavelets transform to the signal defined on the vertices of the weighted graph, i.e. the spectral graph domain. This SGWT uses only the connectivity information encoded in the edge weights, and does not rely on any other attributes of the vertices. Therefore, SGWT can be defined and calculated for any domain where the underlying relations between data locations can be represented by a weighted graph. Furthermore, we present a Chebyshev polynomial approximation algorithm for fast computing this SGWT transform. The l1 norm regularized CS-MRI reconstruction model is introduced and solved by the projected iterative soft-thresholding algorithm to verify its feasibility. Numerical experiment results demonstrate that our proposed method outperforms several state-of-the-art sparsify transforms in terms of suppressing artifacts and achieving lower reconstruction errors on the tested datasets.

Fast Low Rank Column-Wise Compressive Sensing for Accelerated Dynamic MRI

This work develops a novel set of algorithms, alternating Gradient Descent (GD) and minimization for MRI (altGDmin-MRI1 and altGDmin-MRI2), for accelerated dynamic MRI by assuming an approximate low-rank (LR) model on the matrix formed by the vectorized images of the sequence. The LR model itself is well-known in the MRI literature; our contribution is the novel GD-based algorithms which are much faster, memory-efficient, and ‘general’ compared with existing work; and careful use of a 3-level hierarchical LR model. By ‘general,’ we mean that, with a single choice of parameters, our method provides accurate reconstructions for multiple accelerated dynamic MRI applications, multiple sampling rates and sampling schemes. We show that our methods outperform many of the popular existing approaches while also being faster than all of them, on average. This claim is based on comparisons on 8 different retrospectively undersampled multi-coil dynamic MRI applications, sampled using either 1D Cartesian or 2D pseudo-radial undersampling, at multiple sampling rates. Evaluations on some prospectively undersampled datasets are also provided. Our second contribution is a mini-batch subspace tracking extension that can process new measurements and return reconstructions within a short delay after they arrive. The recovery algorithm itself is also faster than its batch counterpart.

Towards Accurate Microstructure Estimation via 3D Hybrid Graph Transformer.

Deep learning has drawn increasing attention in microstructure estimation with undersampled diffusion MRI (dMRI) data. A representative method is the hybrid graph transformer (HGT), which achieves promising performance by integrating -space graph learning and -space transformer learning into a unified framework. However, this method overlooks the 3D spatial information as it relies on training with 2D slices. To address this limitation, we propose 3D hybrid graph transformer (3D-HGT), an advanced microstructure estimation model capable of making full use of 3D spatial information and angular information. To tackle the large computation burden associated with 3D -space learning, we propose an efficient -space learning model based on simplified graph neural networks. Furthermore, we propose a 3D -space learning module based on the transformer. Extensive experiments on data from the human connectome project show that our 3D-HGT outperforms state-of-the-art methods, including HGT, in both quantitative and qualitative evaluations.

Incomplete spectrum QSM using support information.

Reconstructing a bounded object from incomplete k-space data is a well posed problem, and it was recently shown that this incomplete spectrum approach can be used to reconstruct undersampled MRI images with similar quality to compressed sensing approaches. Here, we apply this incomplete spectrum approach to the field-to-source inverse problem encountered in quantitative magnetic susceptibility mapping (QSM). The field-to-source problem is an ill-posed problem because of conical regions in frequency space where the dipole kernel is zero or very small, which leads to the kernel's inverse being ill-defined. These "ill-posed" regions typically lead to streaking artifacts in QSM reconstructions. In contrast to compressed sensing, our approach relies on knowledge of the image-space support, more commonly referred to as the mask, of our object as well as the region in k-space with ill-defined values. In the QSM case, this mask is usually available, as it is required for most QSM background field removal and reconstruction methods. We tuned the incomplete spectrum method (mask and band-limit) for QSM on a simulated dataset from the most recent QSM challenge and validated the QSM reconstruction results on brain images acquired in five healthy volunteers, comparing incomplete spectrum QSM to current state-of-the art-methods: FANSI, nonlinear dipole inversion, and conventional thresholded k-space division. Without additional regularization, incomplete spectrum QSM performs slightly better than direct QSM reconstruction methods such as thresholded k-space division (PSNR of 39.9 vs. 39.4 of TKD on a simulated dataset) and provides susceptibility values in key iron-rich regions similar or slightly lower than state-of-the-art algorithms, but did not improve the PSNR in comparison to FANSI or nonlinear dipole inversion. With added (ℓ1-wavelet based) regularization the new approach produces results similar to compressed sensing based reconstructions (at sufficiently high levels of regularization). Incomplete spectrum QSM provides a new approach to handle the "ill-posed" regions in the frequency-space data input to QSM.

PNCS: Pixel-Level Non-Local Method Based Compressed Sensing Undersampled MRI Image Reconstruction

PNCS: Pixel-Level Non-Local Method Based Compressed Sensing Undersampled MRI Image Reconstruction

Semi-Supervised Learning of MRI Synthesis Without Fully-Sampled Ground Truths.

Learning-based translation between MRI contrasts involves supervised deep models trained using high-quality source- and target-contrast images derived from fully-sampled acquisitions, which might be difficult to collect under limitations on scan costs or time. To facilitate curation of training sets, here we introduce the first semi-supervised model for MRI contrast translation (ssGAN) that can be trained directly using undersampled k-space data. To enable semi-supervised learning on undersampled data, ssGAN introduces novel multi-coil losses in image, k-space, and adversarial domains. The multi-coil losses are selectively enforced on acquired k-space samples unlike traditional losses in single-coil synthesis models. Comprehensive experiments on retrospectively undersampled multi-contrast brain MRI datasets are provided. Our results demonstrate that ssGAN yields on par performance to a supervised model, while outperforming single-coil models trained on coil-combined magnitude images. It also outperforms cascaded reconstruction-synthesis models where a supervised synthesis model is trained following self-supervised reconstruction of undersampled data. Thus, ssGAN holds great promise to improve the feasibility of learning-based multi-contrast MRI synthesis.

Deep Learning Reconstruction for Accelerated Spine MRI: Prospective Analysis of Interchangeability.

Background Deep learning (DL)-based MRI reconstructions can reduce examination times for turbo spin-echo (TSE) acquisitions. Studies that prospectively employ DL-based reconstructions of rapidly acquired, undersampled spine MRI are needed. Purpose To investigate the diagnostic interchangeability of an unrolled DL-reconstructed TSE (hereafter, TSEDL) T1- and T2-weighted acquisition method with standard TSE and to test their impact on acquisition time, image quality, and diagnostic confidence. Materials and Methods This prospective single-center study included participants with various spinal abnormalities who gave written consent from November 2020 to July 2021. Each participant underwent two MRI examinations: standard fully sampled T1- and T2-weighted TSE acquisitions (reference standard) and prospectively undersampled TSEDL acquisitions with threefold and fourfold acceleration. Image evaluation was performed by five readers. Interchangeability analysis and an image quality-based analysis were used to compare the TSE and TSEDL images. Acquisition time and diagnostic confidence were also compared. Interchangeability was tested using the individual equivalence index regarding various degenerative and nondegenerative entities, which were analyzed on each vertebra and defined as discordant clinical judgments of less than 5%. Interreader and intrareader agreement and concordance (κ and Kendall τ and W statistics) were computed and Wilcoxon and McNemar tests were used. Results Overall, 50 participants were evaluated (mean age, 46 years ± 18 [SD]; 26 men). The TSEDL method enabled up to a 70% reduction in total acquisition time (100 seconds for TSEDL vs 328 seconds for TSE, P < .001). All individual equivalence indexes were less than 4%. TSEDL acquisition was rated as having superior image noise by all readers (P < .001). No evidence of a difference was found between standard TSE and TSEDL regarding frequency of major findings, overall image quality, or diagnostic confidence. Conclusion The deep learning (DL)-reconstructed turbo spin-echo (TSE) method was found to be interchangeable with standard TSE for detecting various abnormalities of the spine at MRI. DL-reconstructed TSE acquisition provided excellent image quality, with a 70% reduction in examination time. German Clinical Trials Register no. DRKS00023278 © RSNA, 2022 Online supplemental material is available for this article. See also the editorial by Hallinan in this issue.

DSMENet: Detail and Structure Mutually Enhancing Network for under-sampled MRI reconstruction

Reconstructing zero-filled MR images (ZF) from partial k-space by convolutional neural networks (CNN) is an important way to accelerate MRI. However, due to the lack of attention to different components in ZF, it is challenging to learn the mapping from ZF to targets effectively. To ameliorate this issue, we propose a Detail and Structure Mutually Enhancing Network (DSMENet), which benefits from the complementary of the Structure Reconstruction UNet (SRUN) and the Detail Feature Refinement Module (DFRM). The SRUN learns structure-dominated information at multiple scales. And the DRFM enriches detail-dominated information from coarse to fine. The bidirectional alternate connections then exchange information between them. Moreover, the Detail Representation Construction Module (DRCM) extracts valuable initial detail representation for DFRM. And the Detail Guided Fusion Module (DGFM) facilitates the deep fusion of these complementary information. With the help of them, various components in ZF can be applied with discriminative attentions and mutually enhanced. In addition, the performance can be further improved by the Deep Enhanced Restoration (DER), a strategy based on recursion and constrain. Extensive experiments on fastMRI and CC-359 datasets demonstrate that DSMENet has robustness in terms of various body parts, under-sampling rates, and masks. Furthermore, DSMENet can achieve promising performance on qualitative and quantitative results, especially the competitive NMSE of 0.0268, PSNE of 33.7, and SSIM of 0.7808 on fastMRI 4 × single-coil knee leaderboard.

Validation and Generalizability of Self-Supervised Image Reconstruction Methods for Undersampled MRI

Deep learning methods have become the state of the art for undersampled MR reconstruction. Particularly for cases where it is infeasible or impossible for ground truth, fully sampled data to be acquired, self-supervised machine learning methods for reconstruction are becoming increasingly used. However potential issues in the validation of such methods, as well as their generalizability, remain underexplored. In this paper, we investigate important aspects of the validation of self-supervised algorithms for reconstruction of undersampled MR images: quantitative evaluation of prospective reconstructions, potential differences between prospective and retrospective reconstructions, suitability of commonly used quantitative metrics, and generalizability. Two self-supervised algorithms based on self-supervised denoising and the deep image prior were investigated. These methods are compared to a least squares fitting and a compressed sensing reconstruction using in-vivo and phantom data. Their generalizability was tested with prospectively under-sampled data from experimental conditions different to the training. We show that prospective reconstructions can exhibit significant distortion relative to retrospective reconstructions/ground truth. Furthermore, pixel-wise quantitative metrics may not capture differences in perceptual quality accurately, in contrast to a perceptual metric. In addition, all methods showed potential for generalization; however, generalizability is more affected by changes in anatomy/contrast than other changes. We further showed that no-reference image metrics correspond well with human rating of image quality for studying generalizability. Finally, we showed that a well-tuned compressed sensing reconstruction and learned denoising perform similarly on all data. The datasets acquired for this paper will be made available online; see &lt;a href='https://www.melba-journal.org/papers/2022:022.html'&gt;https://www.melba-journal.org/papers/2022:022.html&lt;/a&gt; for details.

Undersampled Multi-Contrast MRI Reconstruction Based on Double-Domain Generative Adversarial Network.

Multi-contrast magnetic resonance imaging can provide comprehensive information for clinical diagnosis. However, multi-contrast imaging suffers from long acquisition time, which makes it inhibitive for daily clinical practice. Subsampling k-space is one of the main methods to speed up scan time. Missing k-space samples will lead to inevitable serious artifacts and noise. Considering the assumption that different contrast modalities share some mutual information, it may be possible to exploit this redundancy to accelerate multi-contrast imaging acquisition. Recently, generative adversarial network shows superior performance in image reconstruction and synthesis. Some studies based on k-space reconstruction also exhibit superior performance over conventional state-of-art method. In this study, we propose a cross-domain two-stage generative adversarial network for multi-contrast images reconstruction based on prior full-sampled contrast and undersampled information. The new approach integrates reconstruction and synthesis, which estimates and completes the missing k-space and then refines in image space. It takes one fully-sampled contrast modality data and highly undersampled data from several other modalities as input, and outputs high quality images for each contrast simultaneously. The network is trained and tested on a public brain dataset from healthy subjects. Quantitative comparisons against baseline clearly indicate that the proposed method can effectively reconstruct undersampled images. Even under high acceleration, the network still can recover texture details and reduce artifacts.

Deep learning for fast low-field MRI acquisitions

Low-field (LF) MRI research currently gains momentum from its potential to offer reduced costs and reduced footprints translating into wider accessibility. However, the impeded signal-to-noise ratio inherent to lower magnetic fields can have a significant impact on acquisition times that challenges LF clinical relevance. Undersampling is an effective way to speed up acquisitions in MRI, and recent work has shown encouraging results when combined with deep learning (DL). Yet, training DL models generally requires large databases that are not yet available at LF regimes. Here, we demonstrate the capability of Residual U-net combined with data augmentation to reconstruct magnitude and phase information of undersampled LF MRI scans at 0.1 T with a limited training dataset (n = 10). The model performance was first evaluated in a retrospective study for different acceleration rates and sampling patterns. Ultimately, the DL approach was validated on prospectively acquired, fivefold undersampled LF data. With varying performances associated to the adopted sampling scheme, our results show that the approach investigated can preserve the global structure and the details sharpness in the reconstructed magnitude and phase images. Overall, promising results could be obtained on acquired LF MR images that may bring this research closer to clinical implementation.

Time efficiency analysis for undersampled quantitative MRI acquisitions.

To realize Quantitative MRI (QMRI) with clinically acceptable scan time, acceleration factors achieved by conventional parallel imaging techniques are often inadequate. Further acceleration is possible using model-based reconstruction. We propose a theoretical metric called TEUSQA: Time Efficiency for UnderSampled QMRI Acquisitions to inform sequence design and sample pattern optimisation. TEUSQA is designed for a particular class of reconstruction techniques that directly estimate tissue parameters, possibly using prior information to regularize the estimation. TEUSQA can be used to evaluate undersampling patterns for multi-contrast QMRI sequences targeting any tissue parameter. To verify the time efficiency predicted by TEUSQA, we performed Monte Carlo simulations and an accelerated parameter mapping with two sequences (Inversion prepared fast spin echo for T1 and T2 mapping and 3D GRASE for T2 and B0 inhomogeneity mapping). Using TEUSQA, we assessed several ways to generate undersampling patterns in silico, providing insight into the relation between sample distribution and time efficiency for different acceleration factors. The time efficiency predicted by TEUSQA was within 15% of that observed in the Monte Carlo simulations and the prospective acquisition experiment. The assessment of undersampling patterns showed that a class of good patterns could be obtained by low-discrepancy sampling. We believe that TEUSQA offers a valuable instrument for developers of novel QMRI sequences pushing the boundaries of acceleration to achieve clinically feasible protocols. Finally, we applied a time-efficient undersampling pattern selected using TEUSQA for a 32-fold accelerated scan to map T1 & T2 mapping of a healthy volunteer.

DBGAN: A dual-branch generative adversarial network for undersampled MRI reconstruction

Compressed sensing magnetic resonance imaging (CS-MRI) greatly accelerates the acquisition process and yield considerable reconstructed images. Deep learning was introduced into CS-MRI to further speed up the reconstruction process and improve the image quality. Recently, generative adversarial network (GAN) using two-stage cascaded U-Net structure as generator has been proven to be effective in MRI reconstruction. However, previous cascaded structure was limited to few feature information propagation channels thus may lead to information missing. In this paper, we proposed a GAN-based model, DBGAN, for MRI reconstruction from undersampled k-space data. The model uses cross-stage skip connection (CSSC) between two end-to-end cascaded U-Net in our generator to widen the channels of feature propagation. To avoid discrepancy between training and inference, we replaced classical batch normalization (BN) with instance normalization (IN) . A stage loss is involved in the loss function to boost the training performance. In addition, a bilinear interpolation decoder branch is introduced in the generator to supplement the missing information of the deconvolution decoder. Tested under five variant patterns with four undersampling rates on different modality of MRI data, the quantitative results show that DBGAN model achieves mean improvements of 3.65 dB in peak signal-to-noise ratio (PSNR) and 0.016 in normalized mean square error (NMSE) compared with state-of-the-art GAN-based methods on T1-Weighted brain dataset from MICCAI 2013 grand challenge. The qualitative visual results show that our method can reconstruct considerable images on brain and knee MRI data from different modality. Furthermore, DBGAN is light and fast – the model parameters are fewer than half of state-of-the-art GAN-based methods and each 256 × 256 image is reconstructed in 60 milliseconds, which is suitable for real-time processing.

Hybrid deep-learning-based denoising method for compressed sensing in pituitary MRI: comparison with the conventional wavelet-based denoising method.

This study aimed to evaluate the efficacy of a combined wavelet and deep-learning reconstruction (DLR) method for under-sampled pituitary MRI. This retrospective study included 28 consecutive patients who underwent under-sampled pituitary T2-weighted images (T2WI). Images were reconstructed using either the conventional wavelet denoising method (wavelet method) or the wavelet and DLR methods combined (hybrid DLR method) at five denoising levels. The signal-to-noise ratio (SNR) of the CSF, hypothalamic, and pituitary images and the contrast between structures were compared between the two image types. Noise quality, contrast, sharpness, artifacts, and overall image quality were evaluated by two board-certified radiologists. The quantitative and the qualitative analyses were performed with robust two-way repeated analyses of variance. Using the hybrid DLR method, the SNR of the CSF progressively increased as denoising levels increased. By contrast, with the wavelet method, the SNR of the CSF, hypothalamus, and pituitary did not increase at higher denoising levels. There was a significant main effect of denoising methods (p < 0.001) and denoising levels (p < 0.001), and an interaction between denoising methods and denoising levels (p < 0.001). For all five qualitative scores, there was a significant main effect of denoising methods (p < 0.001) and an interaction between denoising methods and denoising levels (p < 0.001). The hybrid DLR method can provide higher image quality for T2WI of the pituitary with compressed sensing (CS) than the wavelet method alone, especially at higher denoising levels. • The signal-to-noise ratios of cerebrospinal fluid progressively increased with the hybrid DLR method, with an increase in the denoising level for cerebrospinal fluid in pituitary T2WI with CS. • The signal-to-noise ratios of cerebrospinal fluid using the conventional wavelet method did not increase at higher denoising levels. • All qualitative scores of hybrid deep-learning reconstructions at all denoising levels were higher than those for the wavelet denoising method.

Bayesian Uncertainty Estimation of Learned Variational MRI Reconstruction.

Recent deep learning approaches focus on improving quantitative scores of dedicated benchmarks, and therefore only reduce the observation-related (aleatoric) uncertainty. However, the model-immanent (epistemic) uncertainty is less frequently systematically analyzed. In this work, we introduce a Bayesian variational framework to quantify the epistemic uncertainty. To this end, we solve the linear inverse problem of undersampled MRI reconstruction in a variational setting. The associated energy functional is composed of a data fidelity term and the total deep variation (TDV) as a learned parametric regularizer. To estimate the epistemic uncertainty we draw the parameters of the TDV regularizer from a multivariate Gaussian distribution, whose mean and covariance matrix are learned in a stochastic optimal control problem. In several numerical experiments, we demonstrate that our approach yields competitive results for undersampled MRI reconstruction. Moreover, we can accurately quantify the pixelwise epistemic uncertainty, which can serve radiologists as an additional resource to visualize reconstruction reliability.