Mehmet Akçakaya

Kerstin Hammernik, Thomas Küstner, Burhaneddin Yaman et al.

Physics-driven deep learning methods have emerged as a powerful tool for computational magnetic resonance imaging (MRI) problems, pushing reconstruction performance to new limits. This article provides an overview of the recent developments in incorporating physics information into learning-based MRI reconstruction. We consider inverse problems with both linear and non-linear forward models for computational MRI, and review the classical approaches for solving these. We then focus on physics-driven deep learning approaches, covering physics-driven loss functions, plug-and-play methods, generative models, and unrolled networks. We highlight domain-specific challenges such as real- and complex-valued building blocks of neural networks, and translational applications in MRI with linear and non-linear forward models. Finally, we discuss common issues and open challenges, and draw connections to the importance of physics-driven learning when combined with other downstream tasks in the medical imaging pipeline.

Mehmet Akçakaya, Vahid Tarokh

We consider the problem of sparse phase retrieval, where a $k$-sparse signal ${\bf x} \in {\mathbb R}^n \textrm{ (or } {\mathbb C}^n\textrm{)}$ is measured as ${\bf y} = |{\bf Ax}|,$ where ${\bf A} \in {\mathbb R}^{m \times n} \textrm{ (or } {\mathbb C}^{m \times n}\textrm{ respectively)}$ is a measurement matrix and $|\cdot|$ is the element-wise absolute value. For a real signal and a real measurement matrix ${\bf A}$, we show that $m = 2k$ measurements are necessary and sufficient to recover ${\bf x}$ uniquely. For complex signal ${\bf x} \in {\mathbb C}^n$ and ${\bf A} \in {\mathbb C}^{m \times n}$, we show that $m = 4k-2$ phaseless measurements are sufficient to recover ${\bf x}$. It is known that the multiplying constant $4$ in $m = 4k-2$ cannot be improved.

Yaşar Utku Alçalar, Mehmet Akçakaya

Diffusion models have emerged as powerful generative techniques for solving inverse problems. Despite their success in a variety of inverse problems in imaging, these models require many steps to converge, leading to slow inference time. Recently, there has been a trend in diffusion models for employing sophisticated noise schedules that involve more frequent iterations of timesteps at lower noise levels, thereby improving image generation and convergence speed. However, application of these ideas for solving inverse problems with diffusion models remain challenging, as these noise schedules do not perform well when using empirical tuning for the forward model log-likelihood term weights. To tackle these challenges, we propose zero-shot approximate posterior sampling (ZAPS) that leverages connections to zero-shot physics-driven deep learning. ZAPS fixes the number of sampling steps, and uses zero-shot training with a physics-guided loss function to learn log-likelihood weights at each irregular timestep. We apply ZAPS to the recently proposed diffusion posterior sampling method as baseline, though ZAPS can also be used with other posterior sampling diffusion models. We further approximate the Hessian of the logarithm of the prior using a diagonalization approach with learnable diagonal entries for computational efficiency. These parameters are optimized over a fixed number of epochs with a given computational budget. Our results for various noisy inverse problems, including Gaussian and motion deblurring, inpainting, and super-resolution show that ZAPS reduces inference time, provides robustness to irregular noise schedules and improves reconstruction quality. Code is available at https://github.com/ualcalar17/ZAPS

Hongyi Gu, Burhaneddin Yaman, Steen Moeller et al.

Recent studies show that deep learning (DL) based MRI reconstruction outperforms conventional methods, such as parallel imaging and compressed sensing (CS), in multiple applications. Unlike CS that is typically implemented with pre-determined linear representations for regularization, DL inherently uses a non-linear representation learned from a large database. Another line of work uses transform learning (TL) to bridge the gap between these two approaches by learning linear representations from data. In this work, we combine ideas from CS, TL and DL reconstructions to learn deep linear convolutional transforms as part of an algorithm unrolling approach. Using end-to-end training, our results show that the proposed technique can reconstruct MR images to a level comparable to DL methods, while supporting uniform undersampling patterns unlike conventional CS methods. Our proposed method relies on convex sparse image reconstruction with linear representation at inference time, which may be beneficial for characterizing robustness, stability and generalizability.

Burhaneddin Yaman, Seyed Amir Hossein Hosseini, Mehmet Akçakaya

Deep learning (DL) has emerged as a powerful tool for accelerated MRI reconstruction, but often necessitates a database of fully-sampled measurements for training. Recent self-supervised and unsupervised learning approaches enable training without fully-sampled data. However, a database of undersampled measurements may not be available in many scenarios, especially for scans involving contrast or translational acquisitions in development. Moreover, recent studies show that database-trained models may not generalize well when the unseen measurements differ in terms of sampling pattern, acceleration rate, SNR, image contrast, and anatomy. Such challenges necessitate a new methodology to enable subject-specific DL MRI reconstruction without external training datasets, since it is clinically imperative to provide high-quality reconstructions that can be used to identify lesions/disease for \emph{every individual}. In this work, we propose a zero-shot self-supervised learning approach to perform subject-specific accelerated DL MRI reconstruction to tackle these issues. The proposed approach partitions the available measurements from a single scan into three disjoint sets. Two of these sets are used to enforce data consistency and define loss during training for self-supervision, while the last set serves to self-validate, establishing an early stopping criterion. In the presence of models pre-trained on a database with different image characteristics, we show that the proposed approach can be combined with transfer learning for faster convergence time and reduced computational complexity. The code is available at \url{https://github.com/byaman14/ZS-SSL}.

Yaşar Utku Alçalar, Mehmet Akçakaya

Physics-driven deep learning (PD-DL) models have proven to be a powerful approach for improved reconstruction of rapid MRI scans. In order to train these models in scenarios where fully-sampled reference data is unavailable, self-supervised learning has gained prominence. However, its application at high acceleration rates frequently introduces artifacts, compromising image fidelity. To mitigate this shortcoming, we propose a novel way to train PD-DL networks via carefully-designed perturbations. In particular, we enhance the k-space masking idea of conventional self-supervised learning with a novel consistency term that assesses the model's ability to accurately predict the added perturbations in a sparse domain, leading to more reliable and artifact-free reconstructions. The results obtained from the fastMRI knee and brain datasets show that the proposed training strategy effectively reduces aliasing artifacts and mitigates noise amplification at high acceleration rates, outperforming state-of-the-art self-supervised methods both visually and quantitatively.

Hongyi Gu, Chi Zhang, Zidan Yu et al.

Functional MRI (fMRI) is an important tool for non-invasive studies of brain function. Over the past decade, multi-echo fMRI methods that sample multiple echo times has become popular with potential to improve quantification. While these acquisitions are typically performed with Cartesian trajectories, non-Cartesian trajectories, in particular spiral acquisitions, hold promise for denser sampling of echo times. However, such acquisitions require very high acceleration rates for sufficient spatiotemporal resolutions. In this work, we propose to use a physics-driven deep learning (PD-DL) reconstruction to accelerate multi-echo spiral fMRI by 10-fold. We modify a self-supervised learning algorithm for optimized training with non-Cartesian trajectories and use it to train the PD-DL network. Results show that the proposed self-supervised PD-DL reconstruction achieves high spatio-temporal resolution with meaningful BOLD analysis.

Junno Yun, Yaşar Utku Alçalar, Mehmet Akçakaya

Algorithm unrolling methods have proven powerful for solving the regularized least squares problem in computational magnetic resonance imaging (MRI). These approaches unfold an iterative algorithm with a fixed number of iterations, typically alternating between a neural network-based proximal operator for regularization, a data fidelity operation and auxiliary updates with learnable parameters. While the connection to optimization methods dictate that the proximal operator network should be shared across unrolls, this can introduce artifacts or blurring. Heuristically, practitioners have shown that using distinct networks may be beneficial, but this significantly increases the number of learnable parameters, making it challenging to prevent overfitting. To address these shortcomings, by taking inspirations from proximal operators with varying thresholds in approximate message passing (AMP) and the success of time-embedding in diffusion models, we propose a time-embedded algorithm unrolling scheme for inverse problems. Specifically, we introduce a novel perspective on the iteration-dependent proximal operation in vector AMP (VAMP) and the subsequent Onsager correction in the context of algorithm unrolling, framing them as a time-embedded neural network. Similarly, the scalar weights in the data fidelity operation and its associated Onsager correction are cast as time-dependent learnable parameters. Our extensive experiments on the fastMRI dataset, spanning various acceleration rates and datasets, demonstrate that our method effectively reduces aliasing artifacts and mitigates noise amplification, achieving state-of-the-art performance. Furthermore, we show that our time-embedding strategy extends to existing algorithm unrolling approaches, enhancing reconstruction quality without increasing the computational complexity significantly.

Mahdi Saberi, Chi Zhang, Mehmet Akçakaya

Deep learning (DL) methods have become the state-of-the-art for reconstructing sub-sampled magnetic resonance imaging (MRI) data. However, studies have shown that these methods are susceptible to small adversarial input perturbations, or attacks, resulting in major distortions in the output images. Various strategies have been proposed to reduce the effects of these attacks, but they require retraining and may lower reconstruction quality for non-perturbed/clean inputs. In this work, we propose a novel approach for mitigating adversarial attacks on MRI reconstruction models without any retraining. Based on the idea of cyclic measurement consistency, we devise a novel mitigation objective that is minimized in a small ball around the attack input. Results show that our method substantially reduces the impact of adversarial perturbations across different datasets, attack types/strengths and PD-DL networks, and qualitatively and quantitatively outperforms conventional mitigation methods that involve retraining. We also introduce a practically relevant scenario for small adversarial perturbations that models impulse noise in raw data, which relates to \emph{herringbone artifacts}, and show the applicability of our approach in this setting. Finally, we show our mitigation approach remains effective in two \emph{realistic} extension scenarios: a blind setup, where the attack strength or algorithm is not known to the user; and an adaptive attack setup, where the attacker has full knowledge of the defense strategy.

Yaşar Utku Alçalar, Merve Gülle, Mehmet Akçakaya

Physics-driven deep learning (PD-DL) approaches have become popular for improved reconstruction of fast magnetic resonance imaging (MRI) scans. Though PD-DL offers higher acceleration rates than existing clinical fast MRI techniques, their use has been limited outside specialized MRI centers. A key challenge is generalization to rare pathologies or different populations, noted in multiple studies, with fine-tuning on target populations suggested for improvement. However, current approaches for PD-DL training require access to raw k-space measurements, which is typically only available at specialized MRI centers that have research agreements for such data access. This is especially an issue for rural and under-resourced areas, where commercial MRI scanners only provide access to a final reconstructed image. To tackle these challenges, we propose Compressibility-inspired Unsupervised Learning via Parallel Imaging Fidelity (CUPID) for high-quality PD-DL training using only routine clinical reconstructed images exported from an MRI scanner. CUPID evaluates output quality with a compressibility-based approach while ensuring that the output stays consistent with the clinical parallel imaging reconstruction through well-designed perturbations. Our results show CUPID achieves similar quality to established PD-DL training that requires k-space data while outperforming compressed sensing (CS) and diffusion-based generative methods. We further demonstrate its effectiveness in a zero-shot training setup for retrospectively and prospectively sub-sampled acquisitions, attesting to its minimal training burden. As an approach that radically deviates from existing strategies, CUPID presents an opportunity to provide broader access to fast MRI for remote and rural populations in an attempt to reduce the obstacles associated with this expensive imaging modality.

Yaşar Utku Alçalar, Yu Cao, Mehmet Akçakaya

Physics-driven artificial intelligence (PD-AI) reconstruction methods have emerged as the state-of-the-art for accelerating MRI scans, enabling higher spatial and temporal resolutions. However, the high resolution of these scans generates massive data volumes, leading to challenges in transmission, storage, and real-time processing. This is particularly pronounced in functional MRI, where hundreds of volumetric acquisitions further exacerbate these demands. Edge computing with FPGAs presents a promising solution for enabling PD-AI reconstruction near the MRI sensors, reducing data transfer and storage bottlenecks. However, this requires optimization of PD-AI models for hardware efficiency through quantization and bypassing traditional FFT-based approaches, which can be a limitation due to their computational demands. In this work, we propose a novel PD-AI computational MRI approach optimized for FPGA-based edge computing devices, leveraging 8-bit complex data quantization and eliminating redundant FFT/IFFT operations. Our results show that this strategy improves computational efficiency while maintaining reconstruction quality comparable to conventional PD-AI methods, and outperforms standard clinical methods. Our approach presents an opportunity for high-resolution MRI reconstruction on resource-constrained devices, highlighting its potential for real-world deployment.

Junno Yun, Mehmet Akçakaya

Infrared (IR) imaging is commonly used in various scenarios, including autonomous driving, fire safety and defense applications. Thus, semantic segmentation of such images is of great interest. However, this task faces several challenges, including data scarcity, differing contrast and input channel number compared to natural images, and emergence of classes not represented in databases in certain scenarios, such as defense applications. Few-shot segmentation (FSS) provides a framework to overcome these issues by segmenting query images using a few labeled support samples. However, existing FSS models for IR images require paired visible RGB images, which is a major limitation since acquiring such paired data is difficult or impossible in some applications. In this work, we develop new strategies for FSS of IR images by using generative modeling and fusion techniques. To this end, we propose to synthesize auxiliary data to provide additional channel information to complement the limited contrast in the IR images, as well as IR data synthesis for data augmentation. Here, the former helps the FSS model to better capture the relationship between the support and query sets, while the latter addresses the issue of data scarcity. Finally, to further improve the former aspect, we propose a novel fusion ensemble module for integrating the two different modalities. Our methods are evaluated on different IR datasets, and improve upon the state-of-the-art (SOTA) FSS models.

Mehmet Akçakaya, Burhaneddin Yaman, Hyungjin Chung et al.

Recently, deep learning approaches have become the main research frontier for biological image reconstruction and enhancement problems thanks to their high performance, along with their ultra-fast inference times. However, due to the difficulty of obtaining matched reference data for supervised learning, there has been increasing interest in unsupervised learning approaches that do not need paired reference data. In particular, self-supervised learning and generative models have been successfully used for various biological imaging applications. In this paper, we overview these approaches from a coherent perspective in the context of classical inverse problems, and discuss their applications to biological imaging, including electron, fluorescence and deconvolution microscopy, optical diffraction tomography and functional neuroimaging.

Omer Burak Demirel, Burhaneddin Yaman, Logan Dowdle et al.

High spatial and temporal resolution across the whole brain is essential to accurately resolve neural activities in fMRI. Therefore, accelerated imaging techniques target improved coverage with high spatio-temporal resolution. Simultaneous multi-slice (SMS) imaging combined with in-plane acceleration are used in large studies that involve ultrahigh field fMRI, such as the Human Connectome Project. However, for even higher acceleration rates, these methods cannot be reliably utilized due to aliasing and noise artifacts. Deep learning (DL) reconstruction techniques have recently gained substantial interest for improving highly-accelerated MRI. Supervised learning of DL reconstructions generally requires fully-sampled training datasets, which is not available for high-resolution fMRI studies. To tackle this challenge, self-supervised learning has been proposed for training of DL reconstruction with only undersampled datasets, showing similar performance to supervised learning. In this study, we utilize a self-supervised physics-guided DL reconstruction on a 5-fold SMS and 4-fold in-plane accelerated 7T fMRI data. Our results show that our self-supervised DL reconstruction produce high-quality images at this 20-fold acceleration, substantially improving on existing methods, while showing similar functional precision and temporal effects in the subsequent analysis compared to a standard 10-fold accelerated acquisition.

Omer Burak Demirel, Burhaneddin Yaman, Logan Dowdle et al.

Functional MRI (fMRI) is commonly used for interpreting neural activities across the brain. Numerous accelerated fMRI techniques aim to provide improved spatiotemporal resolutions. Among these, simultaneous multi-slice (SMS) imaging has emerged as a powerful strategy, becoming a part of large-scale studies, such as the Human Connectome Project. However, when SMS imaging is combined with in-plane acceleration for higher acceleration rates, conventional SMS reconstruction methods may suffer from noise amplification and other artifacts. Recently, deep learning (DL) techniques have gained interest for improving MRI reconstruction. However, these methods are typically trained in a supervised manner that necessitates fully-sampled reference data, which is not feasible in highly-accelerated fMRI acquisitions. Self-supervised learning that does not require fully-sampled data has recently been proposed and has shown similar performance to supervised learning. However, it has only been applied for in-plane acceleration. Furthermore the effect of DL reconstruction on subsequent fMRI analysis remains unclear. In this work, we extend self-supervised DL reconstruction to SMS imaging. Our results on prospectively 10-fold accelerated 7T fMRI data show that self-supervised DL reduces reconstruction noise and suppresses residual artifacts. Subsequent fMRI analysis remains unaltered by DL processing, while the improved temporal signal-to-noise ratio produces higher coherence estimates between task runs.

Chi Zhang, Jinghan Jia, Burhaneddin Yaman et al.

Although deep learning (DL) has received much attention in accelerated MRI, recent studies suggest small perturbations may lead to instabilities in DL-based reconstructions, leading to concern for their clinical application. However, these works focus on single-coil acquisitions, which is not practical. We investigate instabilities caused by small adversarial attacks for multi-coil acquisitions. Our results suggest that, parallel imaging and multi-coil CS exhibit considerable instabilities against small adversarial perturbations.

Burhaneddin Yaman, Chetan Shenoy, Zilin Deng et al.

Late gadolinium enhancement (LGE) cardiac MRI (CMR) is the clinical standard for diagnosis of myocardial scar. 3D isotropic LGE CMR provides improved coverage and resolution compared to 2D imaging. However, image acceleration is required due to long scan times and contrast washout. Physics-guided deep learning (PG-DL) approaches have recently emerged as an improved accelerated MRI strategy. Training of PG-DL methods is typically performed in supervised manner requiring fully-sampled data as reference, which is challenging in 3D LGE CMR. Recently, a self-supervised learning approach was proposed to enable training PG-DL techniques without fully-sampled data. In this work, we extend this self-supervised learning approach to 3D imaging, while tackling challenges related to small training database sizes of 3D volumes. Results and a reader study on prospectively accelerated 3D LGE show that the proposed approach at 6-fold acceleration outperforms the clinically utilized compressed sensing approach at 3-fold acceleration.

Burhaneddin Yaman, Seyed Amir Hossein Hosseini, Steen Moeller et al.

Physics-guided deep learning (PG-DL) via algorithm unrolling has received significant interest for improved image reconstruction, including MRI applications. These methods unroll an iterative optimization algorithm into a series of regularizer and data consistency units. The unrolled networks are typically trained end-to-end using a supervised approach. Current supervised PG-DL approaches use all of the available sub-sampled measurements in their data consistency units. Thus, the network learns to fit the rest of the measurements. In this study, we propose to improve the performance and robustness of supervised training by utilizing randomness by retrospectively selecting only a subset of all the available measurements for data consistency units. The process is repeated multiple times using different random masks during training for further enhancement. Results on knee MRI show that the proposed multi-mask supervised PG-DL enhances reconstruction performance compared to conventional supervised PG-DL approaches.

Burhaneddin Yaman, Hongyi Gu, Seyed Amir Hossein Hosseini et al.

Self-supervised learning has shown great promise due to its capability to train deep learning MRI reconstruction methods without fully-sampled data. Current self-supervised learning methods for physics-guided reconstruction networks split acquired undersampled data into two disjoint sets, where one is used for data consistency (DC) in the unrolled network and the other to define the training loss. In this study, we propose an improved self-supervised learning strategy that more efficiently uses the acquired data to train a physics-guided reconstruction network without a database of fully-sampled data. The proposed multi-mask self-supervised learning via data undersampling (SSDU) applies a hold-out masking operation on acquired measurements to split it into multiple pairs of disjoint sets for each training sample, while using one of these pairs for DC units and the other for defining loss, thereby more efficiently using the undersampled data. Multi-mask SSDU is applied on fully-sampled 3D knee and prospectively undersampled 3D brain MRI datasets, for various acceleration rates and patterns, and compared to CG-SENSE and single-mask SSDU DL-MRI, as well as supervised DL-MRI when fully-sampled data is available. Results on knee MRI show that the proposed multi-mask SSDU outperforms SSDU and performs closely with supervised DL-MRI. A clinical reader study further ranks the multi-mask SSDU higher than supervised DL-MRI in terms of SNR and aliasing artifacts. Results on brain MRI show that multi-mask SSDU achieves better reconstruction quality compared to SSDU. Reader study demonstrates that multi-mask SSDU at R=8 significantly improves reconstruction compared to single-mask SSDU at R=8, as well as CG-SENSE at R=2.

Burhaneddin Yaman, Seyed Amir Hossein Hosseini, Mehmet Akçakaya

Deep learning based image denoising methods have been recently popular due to their improved performance. Traditionally, these methods are trained in a supervised manner, requiring a set of noisy input and clean target image pairs. More recently, self-supervised approaches have been proposed to learn denoising from only noisy images. These methods assume that noise across pixels is statistically independent, and the underlying image pixels show spatial correlations across neighborhoods. These methods rely on a masking approach that divides the image pixels into two disjoint sets, where one is used as input to the network while the other is used to define the loss. However, these previous self-supervised approaches rely on a purely data-driven regularization neural network without explicitly taking the masking model into account. In this work, building on these self-supervised approaches, we introduce Noise2Inpaint (N2I), a training approach that recasts the denoising problem into a regularized image inpainting framework. This allows us to use an objective function, which can incorporate different statistical properties of the noise as needed. We use algorithm unrolling to unroll an iterative optimization for solving this objective function and train the unrolled network end-to-end. The training paradigm follows the masking approach from previous works, splitting the pixels into two disjoint sets. Importantly, one of these is now used to impose data fidelity in the unrolled network, while the other still defines the loss. We demonstrate that N2I performs successful denoising on real-world datasets, while better preserving details compared to its purely data-driven counterpart Noise2Self.

Arjun D. Desai, Francesco Caliva, Claudia Iriondo et al.

Purpose: To organize a knee MRI segmentation challenge for characterizing the semantic and clinical efficacy of automatic segmentation methods relevant for monitoring osteoarthritis progression. Methods: A dataset partition consisting of 3D knee MRI from 88 subjects at two timepoints with ground-truth articular (femoral, tibial, patellar) cartilage and meniscus segmentations was standardized. Challenge submissions and a majority-vote ensemble were evaluated using Dice score, average symmetric surface distance, volumetric overlap error, and coefficient of variation on a hold-out test set. Similarities in network segmentations were evaluated using pairwise Dice correlations. Articular cartilage thickness was computed per-scan and longitudinally. Correlation between thickness error and segmentation metrics was measured using Pearson's coefficient. Two empirical upper bounds for ensemble performance were computed using combinations of model outputs that consolidated true positives and true negatives. Results: Six teams (T1-T6) submitted entries for the challenge. No significant differences were observed across all segmentation metrics for all tissues (p=1.0) among the four top-performing networks (T2, T3, T4, T6). Dice correlations between network pairs were high (>0.85). Per-scan thickness errors were negligible among T1-T4 (p=0.99) and longitudinal changes showed minimal bias (<0.03mm). Low correlations (<0.41) were observed between segmentation metrics and thickness error. The majority-vote ensemble was comparable to top performing networks (p=1.0). Empirical upper bound performances were similar for both combinations (p=1.0). Conclusion: Diverse networks learned to segment the knee similarly where high segmentation accuracy did not correlate to cartilage thickness accuracy. Voting ensembles did not outperform individual networks but may help regularize individual models.

Burhaneddin Yaman, Seyed Amir Hossein Hosseini, Steen Moeller et al.

Purpose: To develop a strategy for training a physics-guided MRI reconstruction neural network without a database of fully-sampled datasets. Theory and Methods: Self-supervised learning via data under-sampling (SSDU) for physics-guided deep learning (DL) reconstruction partitions available measurements into two disjoint sets, one of which is used in the data consistency units in the unrolled network and the other is used to define the loss for training. The proposed training without fully-sampled data is compared to fully-supervised training with ground-truth data, as well as conventional compressed sensing and parallel imaging methods using the publicly available fastMRI knee database. The same physics-guided neural network is used for both proposed SSDU and supervised training. The SSDU training is also applied to prospectively 2-fold accelerated high-resolution brain datasets at different acceleration rates, and compared to parallel imaging. Results: Results on five different knee sequences at acceleration rate of 4 shows that proposed self-supervised approach performs closely with supervised learning, while significantly outperforming conventional compressed sensing and parallel imaging, as characterized by quantitative metrics and a clinical reader study. The results on prospectively sub-sampled brain datasets, where supervised learning cannot be employed due to lack of ground-truth reference, show that the proposed self-supervised approach successfully perform reconstruction at high acceleration rates (4, 6 and 8). Image readings indicate improved visual reconstruction quality with the proposed approach compared to parallel imaging at acquisition acceleration. Conclusion: The proposed SSDU approach allows training of physics-guided DL-MRI reconstruction without fully-sampled data, while achieving comparable results with supervised DL-MRI trained on fully-sampled data.

Seyed Amir Hossein Hosseini, Burhaneddin Yaman, Steen Moeller et al.

Inverse problems for accelerated MRI typically incorporate domain-specific knowledge about the forward encoding operator in a regularized reconstruction framework. Recently physics-driven deep learning (DL) methods have been proposed to use neural networks for data-driven regularization. These methods unroll iterative optimization algorithms to solve the inverse problem objective function, by alternating between domain-specific data consistency and data-driven regularization via neural networks. The whole unrolled network is then trained end-to-end to learn the parameters of the network. Due to simplicity of data consistency updates with gradient descent steps, proximal gradient descent (PGD) is a common approach to unroll physics-driven DL reconstruction methods. However, PGD methods have slow convergence rates, necessitating a higher number of unrolled iterations, leading to memory issues in training and slower reconstruction times in testing. Inspired by efficient variants of PGD methods that use a history of the previous iterates, we propose a history-cognizant unrolling of the optimization algorithm with dense connections across iterations for improved performance. In our approach, the gradient descent steps are calculated at a trainable combination of the outputs of all the previous regularization units. We also apply this idea to unrolling variable splitting methods with quadratic relaxation. Our results in reconstruction of the fastMRI knee dataset show that the proposed history-cognizant approach reduces residual aliasing artifacts compared to its conventional unrolled counterpart without requiring extra computational power or increasing reconstruction time.

Florian Knoll, Kerstin Hammernik, Chi Zhang et al.

Following the success of deep learning in a wide range of applications, neural network-based machine learning techniques have received interest as a means of accelerating magnetic resonance imaging (MRI). A number of ideas inspired by deep learning techniques from computer vision and image processing have been successfully applied to non-linear image reconstruction in the spirit of compressed sensing for both low dose computed tomography and accelerated MRI. The additional integration of multi-coil information to recover missing k-space lines in the MRI reconstruction process, is still studied less frequently, even though it is the de-facto standard for currently used accelerated MR acquisitions. This manuscript provides an overview of the recent machine learning approaches that have been proposed specifically for improving parallel imaging. A general background introduction to parallel MRI is given that is structured around the classical view of image space and k-space based methods. Both linear and non-linear methods are covered, followed by a discussion of recent efforts to further improve parallel imaging using machine learning, and specifically using artificial neural networks. Image-domain based techniques that introduce improved regularizers are covered as well as k-space based methods, where the focus is on better interpolation strategies using neural networks. Issues and open problems are discussed as well as recent efforts for producing open datasets and benchmarks for the community.