Learning-Assisted Fast Determination of Regularization Parameter in Constrained Image Reconstruction.

OBJECTIVE: To leverage machine learning (ML) for fast selection of optimal regularization parameter in constrained image reconstruction. METHODS: Constrained image reconstruction is often formulated as a regularization problem and selecting a good regularization parameter value is an essential step. We solved this problem using an ML-based approach by leveraging the finding that for a specific constrained reconstruction problem defined for a fixed class of image functions, the optimal regularization parameter value is weakly subject-dependent and the dependence can be captured using few experimental data. The proposed method has four key steps: a) solution of a given constrained reconstruction problem for a few (say, 3) pre-selected regularization parameter values, b) extraction of multiple approximated quality metrics from the initial reconstructions, c) predicting the true quality metrics values from the approximated values using pre-trained neural networks, and d) determination of the optimal regularization parameter by fusing the predicted quality metrics. RESULTS: The effectiveness of the proposed method was demonstrated in two constrained reconstruction problems. Compared with L-curve-based method, the proposed method determined the regularization parameters much faster and produced substantially improved reconstructions. Our method also outperformed state-of-the-art learning-based methods when trained with limited experimental data. CONCLUSION: This paper demonstrates the feasibility and improved reconstruction quality by using machine learning to determine the regularization parameter in constrained reconstruction. SIGNIFICANCE: The proposed method substantially reduces the computational burden of the traditional methods (e.g., L-curve) or relaxes the requirement of large training data by modern learning-based methods, thus enhancing the practical utility of constrained reconstruction.

Universal generative modeling in dual domains for dynamic MRI.

Dynamic magnetic resonance image reconstruction from incomplete k-space data has generated great research interest due to its ability to reduce scan time. Nevertheless, the reconstruction problem remains a thorny issue due to its ill posed nature. Recently, diffusion models, especially score-based generative models, have demonstrated great potential in terms of algorithmic robustness and flexibility of utilization. Moreover, a unified framework through the variance exploding stochastic differential equation is proposed to enable new sampling methods and further extend the capabilities of score-based generative models. Therefore, by taking advantage of the unified framework, we propose a k-space and image dual-domain collaborative universal generative model (DD-UGM), which combines the score-based prior with a low-rank regularization penalty to reconstruct highly under-sampled measurements. More precisely, we extract prior components from both image and k-space domains via a universal generative model and adaptively handle these prior components for faster processing while maintaining good generation quality. Experimental comparisons demonstrate the noise reduction and detail preservation abilities of the proposed method. Moreover, DD-UGM can reconstruct data of different frames by only training a single frame image, which reflects the flexibility of the proposed model.

Equilibrated Zeroth-Order Unrolled Deep Network for Parallel MR Imaging.

In recent times, model-driven deep learning has evolved an iterative algorithm into a cascade network by replacing the regularizer's first-order information, such as the (sub)gradient or proximal operator, with a network module. This approach offers greater explainability and predictability compared to typical data-driven networks. However, in theory, there is no assurance that a functional regularizer exists whose first-order information matches the substituted network module. This implies that the unrolled network output may not align with the regularization models. Furthermore, there are few established theories that guarantee global convergence and robustness (regularity) of unrolled networks under practical assumptions. To address this gap, we propose a safeguarded methodology for network unrolling. Specifically, for parallel MR imaging, we unroll a zeroth-order algorithm, where the network module serves as a regularizer itself, allowing the network output to be covered by a regularization model. Additionally, inspired by deep equilibrium models, we conduct the unrolled network before backpropagation to converge to a fixed point and then demonstrate that it can tightly approximate the actual MR image. We also prove that the proposed network is robust against noisy interferences if the measurement data contain noise. Finally, numerical experiments indicate that the proposed network consistently outperforms state-of-the-art MRI reconstruction methods, including traditional regularization and unrolled deep learning techniques.

B1 mapping using pre-learned subspaces for quantitative brain imaging.

PURPOSE: To develop a machine learning-based method for estimation of both transmitter and receiver B1 fields desired for correction of the B1 inhomogeneity effects in quantitative brain imaging. THEORY AND METHODS: A subspace model-based machine learning method was proposed for estimation of B1t and B1r fields. Probabilistic subspace models were used to capture scan-dependent variations in the B1 fields; the subspace basis and coefficient distributions were learned from pre-scanned training data. Estimation of the B1 fields for new experimental data was achieved by solving a linear optimization problem with prior distribution constraints. We evaluated the performance of the proposed method for B1 inhomogeneity correction in quantitative brain imaging scenarios, including T1 and proton density (PD) mapping from variable-flip-angle spoiled gradient-echo (SPGR) data as well as neurometabolic mapping from MRSI data, using phantom, healthy subject and brain tumor patient data. RESULTS: In both phantom and healthy subject data, the proposed method produced high-quality B1 maps. B1 correction on SPGR data using the estimated B1 maps produced significantly improved T1 and PD maps. In brain tumor patients, the proposed method produced more accurate and robust B1 estimation and correction results than conventional methods. The B1 maps were also applied to MRSI data from tumor patients and produced improved neurometabolite maps, with better separation between pathological and normal tissues. CONCLUSION: This work presents a novel method to estimate B1 variations using probabilistic subspace models and machine learning. The proposed method may make correction of B1 inhomogeneity effects more robust in practical applications.

DIMENSION: Dynamic MR imaging with both k-space and spatial prior knowledge obtained via multi-supervised network training.

Dynamic MR image reconstruction from incomplete k-space data has generated great research interest due to its capability in reducing scan time. Nevertheless, the reconstruction problem is still challenging due to its ill-posed nature. Most existing methods either suffer from long iterative reconstruction time or explore limited prior knowledge. This paper proposes a dynamic MR imaging method with both k-space and spatial prior knowledge integrated via multi-supervised network training, dubbed as DIMENSION. Specifically, the DIMENSION architecture consists of a frequential prior network for updating the k-space with its network prediction and a spatial prior network for capturing image structures and details. Furthermore, a multi-supervised network training technique is developed to constrain the frequency domain information and the spatial domain information. The comparisons with classical k-t FOCUSS, k-t SLR, L+S and the state-of-the-art CNN-based method on in vivo datasets show our method can achieve improved reconstruction results in shorter time.

Deep low-Rank plus sparse network for dynamic MR imaging.

In dynamic magnetic resonance (MR) imaging, low-rank plus sparse (L+S) decomposition, or robust principal component analysis (PCA), has achieved stunning performance. However, the selection of the parameters of L+S is empirical, and the acceleration rate is limited, which are common failings of iterative compressed sensing MR imaging (CS-MRI) reconstruction methods. Many deep learning approaches have been proposed to address these issues, but few of them use a low-rank prior. In this paper, a model-based low-rank plus sparse network, dubbed L+S-Net, is proposed for dynamic MR reconstruction. In particular, we use an alternating linearized minimization method to solve the optimization problem with low-rank and sparse regularization. Learned soft singular value thresholding is introduced to ensure the clear separation of the L component and S component. Then, the iterative steps are unrolled into a network in which the regularization parameters are learnable. We prove that the proposed L+S-Net achieves global convergence under two standard assumptions. Experiments on retrospective and prospective cardiac cine datasets show that the proposed model outperforms state-of-the-art CS and existing deep learning methods and has great potential for extremely high acceleration factors (up to 24×).

Learned Low-Rank Priors in Dynamic MR Imaging.

Deep learning methods have achieved attractive performance in dynamic MR cine imaging. However, most of these methods are driven only by the sparse prior of MR images, while the important low-rank (LR) prior of dynamic MR cine images is not explored, which may limit further improvements in dynamic MR reconstruction. In this paper, a learned singular value thresholding (Learned-SVT) operator is proposed to explore low-rank priors in dynamic MR imaging to obtain improved reconstruction results. In particular, we put forward a model-based unrolling sparse and low-rank network for dynamic MR imaging, dubbed as SLR-Net. SLR-Net is defined over a deep network flow graph, which is unrolled from the iterative procedures in the iterative shrinkage-thresholding algorithm (ISTA) for optimizing a sparse and LR-based dynamic MRI model. Experimental results on a single-coil scenario show that the proposed SLR-Net can further improve the state-of-the-art compressed sensing (CS) methods and sparsity-driven deep learning-based methods with strong robustness to different undersampling patterns, both qualitatively and quantitatively. Besides, SLR-Net has been extended to a multi-coil scenario, and achieved excellent reconstruction results compared with a sparsity-driven multi-coil deep learning-based method under a high acceleration. Prospective reconstruction results on an open real-time dataset further demonstrate the capability and flexibility of the proposed method on real-time scenarios.

Learning Data Consistency and its Application to Dynamic MR Imaging.

Magnetic resonance (MR) image reconstruction from undersampled k-space data can be formulated as a minimization problem involving data consistency and image prior. Existing deep learning (DL)-based methods for MR reconstruction employ deep networks to exploit the prior information and integrate the prior knowledge into the reconstruction under the explicit constraint of data consistency, without considering the real distribution of the noise. In this work, we propose a new DL-based approach termed Learned DC that implicitly learns the data consistency with deep networks, corresponding to the actual probability distribution of system noise. The data consistency term and the prior knowledge are both embedded in the weights of the networks, which provides an utterly implicit manner of learning reconstruction model. We evaluated the proposed approach with highly undersampled dynamic data, including the dynamic cardiac cine data with up to 24-fold acceleration and dynamic rectum data with the acceleration factor equal to the number of phases. Experimental results demonstrate the superior performance of the Learned DC both quantitatively and qualitatively than the state-of-the-art.

Deep Learning Enables Superior Photoacoustic Imaging at Ultralow Laser Dosages.

Optical-resolution photoacoustic microscopy (OR-PAM) is an excellent modality for in vivo biomedical imaging as it noninvasively provides high-resolution morphologic and functional information without the need for exogenous contrast agents. However, the high excitation laser dosage, limited imaging speed, and imperfect image quality still hinder the use of OR-PAM in clinical applications. The laser dosage, imaging speed, and image quality are mutually restrained by each other, and thus far, no methods have been proposed to resolve this challenge. Here, a deep learning method called the multitask residual dense network is proposed to overcome this challenge. This method utilizes an innovative strategy of integrating multisupervised learning, dual-channel sample collection, and a reasonable weight distribution. The proposed deep learning method is combined with an application-targeted modified OR-PAM system. Superior images under ultralow laser dosage (32-fold reduced dosage) are obtained for the first time in this study. Using this new technique, a high-quality, high-speed OR-PAM system that meets clinical requirements is now conceivable.

An unsupervised deep learning method for multi-coil cine MRI.

Deep learning has achieved good success in cardiac magnetic resonance imaging (MRI) reconstruction, in which convolutional neural networks (CNNs) learn a mapping from the undersampled k-space to the fully sampled images. Although these deep learning methods can improve the reconstruction quality compared with iterative methods without requiring complex parameter selection or lengthy reconstruction time, the following issues still need to be addressed: 1) all these methods are based on big data and require a large amount of fully sampled MRI data, which is always difficult to obtain for cardiac MRI; 2) the effect of coil correlation on reconstruction in deep learning methods for dynamic MR imaging has never been studied. In this paper, we propose an unsupervised deep learning method for multi-coil cine MRI via a time-interleaved sampling strategy. Specifically, a time-interleaved acquisition scheme is utilized to build a set of fully encoded reference data by directly merging the k-space data of adjacent time frames. Then these fully encoded data can be used to train a parallel network for reconstructing images of each coil separately. Finally, the images from each coil are combined via a CNN to implicitly explore the correlations between coils. The comparisons with classic k-t FOCUSS, k-t SLR, L+S and KLR methods on in vivo datasets show that our method can achieve improved reconstruction results in an extremely short amount of time.

DeepcomplexMRI: Exploiting deep residual network for fast parallel MR imaging with complex convolution.

This paper proposes a multi-channel image reconstruction method, named DeepcomplexMRI, to accelerate parallel MR imaging with residual complex convolutional neural network. Different from most existing works which rely on the utilization of the coil sensitivities or prior information of predefined transforms, DeepcomplexMRI takes advantage of the availability of a large number of existing multi-channel groudtruth images and uses them as target data to train the deep residual convolutional neural network offline. In particular, a complex convolutional network is proposed to take into account the correlation between the real and imaginary parts of MR images. In addition, the k-space data consistency is further enforced repeatedly in between layers of the network. The evaluations on in vivo datasets show that the proposed method has the capability to recover the desired multi-channel images. Its comparison with state-of-the-art methods also demonstrates that the proposed method can reconstruct the desired MR images more accurately.

Deep Magnetic Resonance Image Reconstruction: Inverse Problems Meet Neural Networks.

Image reconstruction from undersampled k-space data has been playing an important role in fast MRI. Recently, deep learning has demonstrated tremendous success in various fields and has also shown potential in significantly accelerating MRI reconstruction with fewer measurements. This article provides an overview of the deep learning-based image reconstruction methods for MRI. Two types of deep learning-based approaches are reviewed: those based on unrolled algorithms and those which are not. The main structure of both approaches are explained, respectively. Several signal processing issues for maximizing the potential of deep reconstruction in fast MRI are discussed. The discussion may facilitate further development of the networks and the analysis of performance from a theoretical point of view.

A new deep learning method for image deblurring in optical microscopic systems.

Deconvolution is the most commonly used image processing method in optical imaging systems to remove the blur caused by the point-spread function (PSF). While this method has been successful in deblurring, it suffers from several disadvantages, such as slow processing time due to multiple iterations required to deblur and suboptimal in cases where the experimental operator chosen to represent PSF is not optimal. In this paper, we present a deep-learning-based deblurring method that is fast and applicable to optical microscopic imaging systems. We tested the robustness of proposed deblurring method on the publicly available data, simulated data and experimental data (including 2D optical microscopic data and 3D photoacoustic microscopic data), which all showed much improved deblurred results compared to deconvolution. We compared our results against several existing deconvolution methods. Our results are better than conventional techniques and do not require multiple iterations or pre-determined experimental operator. Our method has several advantages including simple operation, short time to compute, good deblur results and wide application in all types of optical microscopic imaging systems. The deep learning approach opens up a new path for deblurring and can be applied in various biomedical imaging fields.