MR image reconstruction using deep density priors

Algorithms for Magnetic Resonance (MR) image reconstruction from undersampled measurements exploit prior information to compensate for missing k-space data. Deep learning (DL) provides a powerful framework for extracting such information from existing image datasets, through learning, and then using it for reconstruction. Leveraging this, recent methods employed DL to learn mappings from undersampled to fully sampled images using paired datasets, including undersampled and corresponding fully sampled images, integrating prior knowledge implicitly. In this article, we propose an alternative approach that learns the probability distribution of fully sampled MR images using unsupervised DL, specifically Variational Autoencoders (VAE), and use this as an explicit prior term in reconstruction, completely decoupling the encoding operation from the prior. The resulting reconstruction algorithm enjoys a powerful image prior to compensate for missing k-space data without requiring paired datasets for training nor being prone to associated sensitivities, such as deviations in undersampling patterns used in training and test time or coil settings. We evaluated the proposed method with T1 weighted images from a publicly available dataset, multi-coil complex images acquired from healthy volunteers (N=8) and images with white matter lesions. The proposed algorithm, using the VAE prior, produced visually high quality reconstructions and achieved low RMSE values, outperforming most of the alternative methods on the same dataset. On multi-coil complex data, the algorithm yielded accurate magnitude and phase reconstruction results. In the experiments on images with white matter lesions, the method faithfully reconstructed the lesions. Keywords: Reconstruction, MRI, prior probability, machine learning, deep learning, unsupervised learning, density estimationComment: Published in IEEE TMI. Main text and supplementary material, 19 pages tota

Bayesian intravoxel incoherent motion parameter mapping in the human heart

Background: Intravoxel incoherent motion (IVIM) imaging of diffusion and perfusion in the heart suffers from high parameter estimation error. The purpose of this work is to improve cardiac IVIM parameter mapping using Bayesian inference. Methods: A second-order motion-compensated diffusion weighted spin-echo sequence with navigator-based slice tracking was implemented to collect cardiac IVIM data in early systole in eight healthy subjects on a clinical 1.5 T CMR system. IVIM data were encoded along six gradient optimized directions with b-values of 0–300 s/mm2. Subjects were scanned twice in two scan sessions one week apart to assess intra-subject reproducibility. Bayesian shrinkage prior (BSP) inference was implemented to determine IVIM parameters (diffusion D, perfusion fraction F and pseudo-diffusion D*). Results were compared to least-squares (LSQ) parameter estimation. Signal-to-noise ratio (SNR) requirements for a given fitting error were assessed for the two methods using simulated data. Reproducibility analysis of parameter estimation in-vivo using BSP and LSQ was performed. Results: BSP resulted in reduced SNR requirements when compared to LSQ in simulations. In-vivo, BSP analysis yielded IVIM parameter maps with smaller intra-myocardial variability and higher estimation certainty relative to LSQ. Mean IVIM parameter estimates in eight healthy subjects were (LSQ/BSP): 1.63 ± 0.28/1.51 ± 0.14·10−3 mm2/s for D, 13.13 ± 19.81/13.11 ± 5.95% for F and 201.45 ± 313.23/13.11 ± 14.53·10−3 mm2/s for D ∗. Parameter variation across all volunteers and measurements was lower with BSP compared to LSQ (coefficient of variation BSP vs. LSQ: 9% vs. 17% for D, 45% vs. 151% for F and 111% vs. 155% for D ∗). In addition, reproducibility of the IVIM parameter estimates was higher with BSP compared to LSQ (Bland-Altman coefficients of repeatability BSP vs. LSQ: 0.21 vs. 0.26·10−3 mm2/s for D, 5.55 vs. 6.91% for F and 15.06 vs. 422.80·10−3 mm2/s for D*). Conclusion: Robust free-breathing cardiac IVIM data acquisition in early systole is possible with the proposed method. BSP analysis yields improved IVIM parameter maps relative to conventional LSQ fitting with fewer outliers, improved estimation certainty and higher reproducibility. IVIM parameter mapping holds promise for myocardial perfusion measurements without the need for contrast agents

Unsupervised Lesion Detection via Image Restoration with a Normative Prior

ISSN:2640-349

Sampling Possible Reconstructions of Undersampled Acquisitions in MR Imaging With a Deep Learned Prior

Undersampling the k-space during MR acquisitions saves time, however results in an ill-posed inversion problem, leading to an infinite set of images as possible solutions. Traditionally, this is tackled as a reconstruction problem by searching for a single "best" image out of this solution set according to some chosen regularization or prior. This approach, however, misses the possibility of other solutions and hence ignores the uncertainty in the inversion process. In this paper, we propose a method that instead returns multiple images which are possible under the acquisition model and the chosen prior to capture the uncertainty in the inversion process. To this end, we introduce a low dimensional latent space and model the posterior distribution of the latent vectors given the acquisition data in k-space, from which we can sample in the latent space and obtain the corresponding images. We use a variational autoencoder for the latent model and the Metropolis adjusted Langevin algorithm for the sampling. We evaluate our method on two datasets; with images from the Human Connectome Project and in-house measured multi-coil images. We compare to five alternative methods. Results indicate that the proposed method produces images that match the measured k-space data better than the alternatives, while showing realistic structural variability. Furthermore, in contrast to the compared methods, the proposed method yields higher uncertainty in the undersampled phase encoding direction, as expected.ISSN:0278-0062ISSN:1558-254

MR image reconstruction using deep density priors

Algorithms for magnetic resonance (MR) image reconstruction from undersampled measurements exploit prior information to compensate for missing k-space data. Deep learning (DL) provides a powerful framework for extracting such information from existing image datasets, through learning, and then using it for reconstruction. Leveraging this, recent methods employed DL to learn mappings from undersampled to fully sampled images using paired datasets, including undersampled and corresponding fully sampled images, integrating prior knowledge implicitly. In this letter, we propose an alternative approach that learns the probability distribution of fully sampled MR images using unsupervised DL, specifically variational autoencoders (VAE), and use this as an explicit prior term in reconstruction, completely decoupling the encoding operation from the prior. The resulting reconstruction algorithm enjoys a powerful image prior to compensate for missing k-space data without requiring paired datasets for training nor being prone to associated sensitivities, such as deviations in undersampling patterns used in training and test time or coil settings. We evaluated the proposed method with T1 weighted images from a publicly available dataset, multi-coil complex images acquired from healthy volunteers ( N=8 ), and images with white matter lesions. The proposed algorithm, using the VAE prior, produced visually high quality reconstructions and achieved low RMSE values, outperforming most of the alternative methods on the same dataset. On multi-coil complex data, the algorithm yielded accurate magnitude and phase reconstruction results. In the experiments on images with white matter lesions, the method faithfully reconstructed the lesions

Analysis of spatiotemporal fidelity in quantitative 3D first-pass perfusion cardiovascular magnetic resonance

Background Whole-heart first-pass perfusion cardiovascular magnetic resonance (CMR) relies on highly accelerated image acquisition. The influence of undersampling on myocardial blood flow (MBF) quantification has not been systematically investigated yet. In the present work, the effect of spatiotemporal scan acceleration on image reconstruction accuracy and MBF error was studied using a numerical phantom and validated in-vivo. Methods Up to 10-fold scan acceleration using k-t PCA and k-t SPARSE-SENSE was simulated using the MRXCAT CMR numerical phantom framework. Image reconstruction results were compared to ground truth data in the k-f domain by means of modulation transfer function (MTF) analysis. In the x-t domain, errors pertaining to specific features of signal intensity-time curves and MBF values derived using Fermi model deconvolution were analysed. In-vivo first-pass CMR data were acquired in ten healthy volunteers using a dual-sequence approach assessing the arterial input function (AIF) and myocardial enhancement. 10x accelerated 3D k-t PCA and k-t SPARSE-SENSE were compared and related to non-accelerated 2D reference images. Results MTF analysis revealed good recovery of data upon k-t PCA reconstruction at 10x undersampling with some attenuation of higher temporal frequencies. For 10x k-t SPARSE-SENSE the MTF was found to decrease to zero at high spatial frequencies for all temporal frequencies indicating a loss in spatial resolution. Signal intensity-time curve errors were most prominent in AIFs from 10x k-t PCA, thereby emphasizing the need for separate AIF acquisition using a dual-sequence approach. These findings were confirmed by MBF estimation based on AIFs from fully sampled and undersampled simulations. Average in-vivo MBF estimates were in good agreement between both accelerated and the fully sampled methods. Intra-volunteer MBF variation for fully sampled 2D scans was lower compared to 10x k-t PCA and k-t SPARSE-SENSE data. Conclusion Quantification of highly undersampled 3D first-pass perfusion CMR yields accurate MBF estimates provided the AIF is obtained using fully sampled or moderately undersampled scans as part of a dual-sequence approach. However, relative to fully sampled 2D perfusion imaging, intra-volunteer variation is increased using 3D approaches prompting for further developments.ISSN:1097-6647ISSN:1532-429