Accelerating the data acquisition of dynamic magnetic resonance imaging (MRI) leads to a challenging ill-posed inverse problem, which has received great interest from both the signal processing and machine learning community over the last decades. The key ingredient to the problem is how to exploit the temporal correlation of the MR sequence to resolve the aliasing artefact. Traditionally, such observation led to a formulation of a non-convex optimisation problem, which were solved using iterative algorithms. Recently, however, deep learning based-approaches have gained significant popularity due to its ability to solve general inversion problems. In this work, we propose a unique, novel convolutional recurrent neural network (CRNN) architecture which reconstructs high quality cardiac MR images from highly undersampled k-space data by jointly exploiting the dependencies of the temporal sequences as well as the iterative nature of the traditional optimisation algorithms. In particular, the proposed architecture embeds the structure of the traditional iterative algorithms, efficiently modelling the recurrence of the iterative reconstruction stages by using recurrent hidden connections over such iterations. In addition, spatiotemporal dependencies are simultaneously learnt by exploiting bidirectional recurrent hidden connections across time sequences. The proposed algorithm is able to learn both the temporal dependency and the iterative reconstruction process effectively with only a very small number of parameters, while outperforming current MR reconstruction methods in terms of computational complexity, reconstruction accuracy and speed.
More recently, several methods on 2D MR image reconstruction were proposed @cite_12 @cite_30 @cite_18 , which share similar idea with our proposed method that integrates data fidelity term and regularisation term into a single deep network so that to enable the end-to-end training. In contrast to these methods which use shared parameters over iterations, as we will show, our architecture integrates hidden connections over optimisation iterations to propagate learnt representations across both iteration and time, whereas such information is discarded in the other methods. Such proposed architecture enables the information used for the reconstruction at each iteration to be shared across all stages of the reconstruction process, aiming for an iterative algorithm that can fully benefit from information extracted at all processing stages. As to the nature of the proposed RNN units, previous work involving RNNs only updated the hidden state of the recurrent connection with a fixed input @cite_22 @cite_9 @cite_19 , while the proposed architecture progressively updates the input as the optimisation iteration increases. In addition, previous work only modelled the recurrence of iteration time @cite_1 exclusively, whereas the proposed method jointly exploits both dimensions, yielding a unique architecture suitable for the dynamic reconstruction problem.
@cite_30 @cite_18 @cite_22 @cite_9 @cite_1 @cite_19 @cite_12
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Recovering images from undersampled linear measurements typically leads to an ill-posed linear inverse problem, that asks for proper statistical priors. Building effective priors is however challenged by the low train and test overhead dictated by real-time tasks; and the need for retrieving visually "plausible" and physically "feasible" images with minimal hallucination. To cope with these challenges, we design a cascaded network architecture that unrolls the proximal gradient iterations by permeating benefits from generative residual networks (ResNet) to modeling the proximal operator. A mixture of pixel-wise and perceptual costs is then deployed to train proximals. The overall architecture resembles back-and-forth projection onto the intersection of feasible and plausible images. Extensive computational experiments are examined for a global task of reconstructing MR images of pediatric patients, and a more local task of superresolving CelebA faces, that are insightful to design efficient architectures. Our observations indicate that for MRI reconstruction, a recurrent ResNet with a single residual block effectively learns the proximal. This simple architecture appears to significantly outperform the alternative deep ResNet architecture by 2dB SNR, and the conventional compressed-sensing MRI by 4dB SNR with 100x faster inference. For image superresolution, our preliminary results indicate that modeling the denoising proximal demands deep ResNets. We introduce a model-based image reconstruction framework with a convolution neural network (CNN) based regularization prior. The proposed formulation provides a systematic approach for deriving deep architectures for inverse problems with the arbitrary structure. Since the forward model is explicitly accounted for, a smaller network with fewer parameters is sufficient to capture the image information compared to black-box deep learning approaches, thus reducing the demand for training data and training time. Since we rely on end-to-end training, the CNN weights are customized to the forward model, thus offering improved performance over approaches that rely on pre-trained denoisers. The main difference of the framework from existing end-to-end training strategies is the sharing of the network weights across iterations and channels. Our experiments show that the decoupling of the number of iterations from the network complexity offered by this approach provides benefits including lower demand for training data, reduced risk of overfitting, and implementations with significantly reduced memory footprint. We propose to enforce data-consistency by using numerical optimization blocks such as conjugate gradients algorithm within the network; this approach offers faster convergence per iteration, compared to methods that rely on proximal gradients steps to enforce data consistency. Our experiments show that the faster convergence translates to improved performance, especially when the available GPU memory restricts the number of iterations. Inspired by recent advances in deep learning, we propose a framework for reconstructing dynamic sequences of 2-D cardiac magnetic resonance (MR) images from undersampled data using a deep cascade of convolutional neural networks (CNNs) to accelerate the data acquisition process. In particular, we address the case where data are acquired using aggressive Cartesian undersampling. First, we show that when each 2-D image frame is reconstructed independently, the proposed method outperforms state-of-the-art 2-D compressed sensing approaches, such as dictionary learning-based MR image reconstruction, in terms of reconstruction error and reconstruction speed. Second, when reconstructing the frames of the sequences jointly, we demonstrate that CNNs can learn spatio-temporal correlations efficiently by combining convolution and data sharing approaches. We show that the proposed method consistently outperforms state-of-the-art methods and is capable of preserving anatomical structure more faithfully up to 11-fold undersampling. Moreover, reconstruction is very fast: each complete dynamic sequence can be reconstructed in less than 10 s and, for the 2-D case, each image frame can be reconstructed in 23 ms, enabling real-time applications. In this paper, we propose a novel 3D-RecGAN approach, which reconstructs the complete 3D structure of a given object from a single arbitrary depth view using generative adversarial networks. Unlike the existing work which typically requires multiple views of the same object or class labels to recover the full 3D geometry, the proposed 3D-RecGAN only takes the voxel grid representation of a depth view of the object as input, and is able to generate the complete 3D occupancy grid by filling in the occluded missing regions. The key idea is to combine the generative capabilities of autoencoders and the conditional Generative Adversarial Networks (GAN) framework, to infer accurate and fine-grained 3D structures of objects in high-dimensional voxel space. Extensive experiments on large synthetic datasets show that the proposed 3D-RecGAN significantly outperforms the state of the art in single view 3D object reconstruction, and is able to reconstruct unseen types of objects. Our code and data are available at: this https URL