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Bilinear models such as low-rank and dictionary methods, which decompose dynamic data to spatial and temporal factor matrices are powerful and memory-efficient tools for the recovery of dynamic MRI data. Current bilinear methods rely on sparsity and energy compaction priors on the factor matrices to regularize the recovery. Motivated by deep image prior, we introduce a novel bilinear model, whose factor matrices are generated using convolutional neural networks (CNNs). The CNN parameters, and equivalently the factors, are learned from the undersampled data of the specific subject. Unlike current unrolled deep learning methods that require the storage of all the time frames in the dataset, the proposed approach only requires the storage of the factors or compressed representation; this approach allows the direct use of this scheme to large-scale dynamic applications, including free breathing cardiac MRI considered in this work. To reduce the run time and to improve performance, we initialize the CNN parameters using existing factor methods. We use sparsity regularization of the network parameters to minimize the overfitting of the network to measurement noise. Our experiments on free-breathing and ungated cardiac cine data acquired using a navigated golden-angle gradient-echo radial sequence show the ability of our method to provide reduced spatial blurring as compared to classical bilinear methods as well as a recent unsupervised deep-learning approach. [ABSTRACT FROM AUTHOR]

Recent theory of mapping an image into a structured low-rank Toeplitz or Hankel matrix has become an effective method to restore images. In this paper, we introduce a generalized structured low-rank algorithm to recover images from their undersampled Fourier coefficients using infimal convolution regularizations. The image is modeled as the superposition of a piecewise constant component and a piecewise linear component. The Fourier coefficients of each component satisfy an annihilation relation, which results in a structured Toeplitz matrix. We exploit the low-rank property of the matrices to formulate a combined regularized optimization problem. In order to solve the problem efficiently and to avoid the high-memory demand resulting from the large-scale Toeplitz matrices, we introduce a fast and a memory-efficient algorithm based on the half-circulant approximation of the Toeplitz matrix. We demonstrate our algorithm in the context of single and multi-channel MR images recovery. Numerical experiments indicate that the proposed algorithm provides improved recovery performance over the state-of-the-art approaches. [ABSTRACT FROM AUTHOR]

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 direct inversion approaches. Thus, reducing the demand for training data and training time. Since we rely on end-to-end training with weight sharing across iterations, the CNN weights are customized to the forward model, thus offering improved performance over approaches that rely on pre-trained denoisers. 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, primarily when the available GPU memory restricts the number of iterations. [ABSTRACT FROM AUTHOR]

We propose a novel deformation corrected compressed sensing (DC-CS) framework to recover contrast enhanced dynamic magnetic resonance images from undersampled measurements. We introduce a formulation that is capable of handling a wide class of sparsity/compactness priors on the deformation corrected dynamic signal. In this work, we consider example compactness priors such as sparsity in temporal Fourier domain, sparsity in temporal finite difference domain, and nuclear norm penalty to exploit low rank structure. Using variable splitting, we decouple the complex optimization problem to simpler and well understood sub problems; the resulting algorithm alternates between simple steps of shrinkage-based denoising, deformable registration, and a quadratic optimization step. Additionally, we employ efficient continuation strategies to reduce the risk of convergence to local minima. The decoupling enabled by the proposed scheme enables us to apply this scheme to contrast enhanced MRI applications. Through experiments on numerical phantom and in vivo myocardial perfusion MRI datasets, we observe superior image quality of the proposed DC-CS scheme in comparison to the classical k-t FOCUSS with motion estimation/correction scheme, and demonstrate reduced motion artifacts over classical compressed sensing schemes that utilize the compact priors on the original deformation uncorrected signal. [ABSTRACT FROM AUTHOR]

We introduce a novel algorithm to reconstruct dynamic magnetic resonance imaging (MRI) data from under-sampled k-t space data. In contrast to classical model based cine MRI schemes that rely on the sparsity or banded structure in Fourier space, we use the compact representation of the data in the Karhunen Louve transform (KLT) domain to exploit the correlations in the dataset. The use of the data-dependent KL transform makes our approach ideally suited to a range of dynamic imaging problems, even when the motion is not periodic. In comparison to current KLT-based methods that rely on a two-step approach to first estimate the basis functions and then use it for reconstruction, we pose the problem as a spectrally regularized matrix recovery problem. By simultaneously determining the temporal basis functions and its spatial weights from the entire measured data, the proposed scheme is capable of providing high quality reconstructions at a range of accelerations. In addition to using the compact representation in the KLT domain, we also exploit the sparsity of the data to further improve the recovery rate. Validations using numerical phantoms and in vivo cardiac perfusion MRI data demonstrate the significant improvement in performance offered by the proposed scheme over existing methods. [ABSTRACT FROM AUTHOR]