arXiv subjects

Mathews Jacob

Publications and source records attributed to Mathews Jacob.

At least 37 records · Page 2Linked to original sources

arXiv2023

Deep Factor Model: A Novel Approach for Motion Compensated Multi-Dimensional MRI

Recent quantitative parameter mapping methods including MR fingerprinting (MRF) collect a time series of images that capture the evolution of magnetization. The focus of this work is to introduce a novel approach termed as Deep Factor Model(DFM), which offers an efficient representation of the multi-contrast image time series. The higher efficiency of the representation enables the acquisition of the images in a highly undersampled fashion, which translates to reduced scan time in 3D high-resolution multi-contrast applications. The approach integrates motion estimation and compensation, making the approach robust to subject motion during the scan.

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arXiv2023

Memory-efficient model-based deep learning with convergence and robustness guarantees

Computational imaging has been revolutionized by compressed sensing algorithms, which offer guaranteed uniqueness, convergence, and stability properties. Model-based deep learning methods that combine imaging physics with learned regularization priors have emerged as more powerful alternatives for image recovery. The main focus of this paper is to introduce a memory efficient model-based algorithm with similar theoretical guarantees as CS methods. The proposed iterative algorithm alternates between a gradient descent involving the score function and a conjugate gradient algorithm to encourage data consistency. The score function is modeled as a monotone convolutional neural network. Our analysis shows that the monotone constraint is necessary and sufficient to enforce the uniqueness of the fixed point in arbitrary inverse problems. In addition, it also guarantees the convergence to a fixed point, which is robust to input perturbations. We introduce two implementations of the proposed MOL framework, which differ in the way the monotone property is imposed. The first approach enforces a strict monotone constraint, while the second one relies on an approximation. The guarantees are not valid for the second approach in the strict sense. However, our empirical studies show that the convergence and robustness of both approaches are comparable, while the less constrained approximate implementation offers better performance. The proposed deep equilibrium formulation is significantly more memory efficient than unrolled methods, which allows us to apply it to 3D or 2D+time problems that current unrolled algorithms cannot handle.

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arXiv2023

Plug-and-Play Deep Energy Model for Inverse problems

We introduce a novel energy formulation for Plug- and-Play (PnP) image recovery. Traditional PnP methods that use a convolutional neural network (CNN) do not have an energy based formulation. The primary focus of this work is to introduce an energy-based PnP formulation, which relies on a CNN that learns the log of the image prior from training data. The score function is evaluated as the gradient of the energy model, which resembles a UNET with shared encoder and decoder weights. The proposed score function is thus constrained to a conservative vector field, which is the key difference with classical PnP models. The energy-based formulation offers algorithms with convergence guarantees, even when the learned score model is not a contraction. The relaxation of the contraction constraint allows the proposed model to learn more complex priors, thus offering improved performance over traditional PnP schemes. Our experiments in magnetic resonance image reconstruction demonstrates the improved performance offered by the proposed energy model over traditional PnP methods.

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arXiv2022

ENSURE: A General Approach for Unsupervised Training of Deep Image Reconstruction Algorithms

Image reconstruction using deep learning algorithms offers improved reconstruction quality and lower reconstruction time than classical compressed sensing and model-based algorithms. Unfortunately, clean and fully sampled ground-truth data to train the deep networks is often unavailable in several applications, restricting the applicability of the above methods. We introduce a novel metric termed the ENsemble Stein's Unbiased Risk Estimate (ENSURE) framework, which can be used to train deep image reconstruction algorithms without fully sampled and noise-free images. The proposed framework is the generalization of the classical SURE and GSURE formulation to the setting where the images are sampled by different measurement operators, chosen randomly from a set. We evaluate the expectation of the GSURE loss functions over the sampling patterns to obtain the ENSURE loss function. We show that this loss is an unbiased estimate for the true mean-square error, which offers a better alternative to GSURE, which only offers an unbiased estimate for the projected error. Our experiments show that the networks trained with this loss function can offer reconstructions comparable to the supervised setting. While we demonstrate this framework in the context of MR image recovery, the ENSURE framework is generally applicable to arbitrary inverse problems.

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arXiv2022

Joint cardiac $T_1$ mapping and cardiac function estimation using a deep manifold framework

In this work, we proposed a continuous-acquisition strategy using a gradient echo (GRE) inversion recovery sequence based on spiral trajectories to simultaneously obtain the $T_1$ mapping and CINE imaging. The acquisition is using a free-breathing and ungated fashion. An approach based on variational auto-encoder(VAE) is used for the motion estimation from the centered k-space data. The motion signal is then used to train a deep manifold reconstruction algorithm for image reconstruction. Once the network is trained, we can excite the latent vectors (the estimated motion signals and the contrast signal) in any way as we wanted to generate the image frames in the time series. We can estimate the $T_1$ mapping using the generated image frames where only contrast is varying. We can also generate the breath-hold CINE in different contrast.

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arXiv2021

Variational manifold learning from incomplete data: application to multislice dynamic MRI

Current deep learning-based manifold learning algorithms such as the variational autoencoder (VAE) require fully sampled data to learn the probability density of real-world datasets. Once learned, the density can be used for a variety of tasks, including data imputation. However, fully sampled data is often unavailable in a variety of problems, including the recovery of dynamic and high-resolution MRI data considered in this work. To overcome this problem, we introduce a novel variational approach to learn a manifold from undersampled data. The VAE uses a decoder fed by latent vectors, drawn from a conditional density estimated from the fully sampled images using an encoder. Since fully sampled images are not available in our setting, we approximate the conditional density of the latent vectors by a parametric model whose parameters are estimated from the undersampled measurements using back-propagation. We use the framework for the joint alignment and recovery of multislice free breathing and ungated cardiac MRI data from highly undersampled measurements. Most of the current self-gating and manifold cardiac MRI approaches consider the independent recovery of images from each slice; these methods are not capable of exploiting the inter-slice redundancies in the datasets and require sophisticated post-processing or manual approaches to align the images from different slices. By contrast, the proposed scheme is able to align the multislice data and exploit the redundancies. Experimental results demonstrate the utility of the proposed scheme in dynamic imaging alignment and reconstructions.

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arXiv2021

Dynamic imaging using Motion-Compensated SmooThness Regularization on Manifolds (MoCo-SToRM)

We introduce an unsupervised motion-compensated reconstruction scheme for high-resolution free-breathing pulmonary MRI. We model the image frames in the time series as the deformed version of the 3D template image volume. We assume the deformation maps to be points on a smooth manifold in high-dimensional space. Specifically, we model the deformation map at each time instant as the output of a CNN-based generator that has the same weight for all time-frames, driven by a low-dimensional latent vector. The time series of latent vectors account for the dynamics in the dataset, including respiratory motion and bulk motion. The template image volume, the parameters of the generator, and the latent vectors are learned directly from the k-t space data in an unsupervised fashion. Our experimental results show improved reconstructions compared to state-of-the-art methods, especially in the context of bulk motion during the scans.

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arXiv2021

Improved Model based Deep Learning using Monotone Operator Learning (MOL)

Model-based deep learning (MoDL) algorithms that rely on unrolling are emerging as powerful tools for image recovery. In this work, we introduce a novel monotone operator learning framework to overcome some of the challenges associated with current unrolled frameworks, including high memory cost, lack of guarantees on robustness to perturbations, and low interpretability. Unlike current unrolled architectures that use finite number of iterations, we use the deep equilibrium (DEQ) framework to iterate the algorithm to convergence and to evaluate the gradient of the convolutional neural network blocks using Jacobian iterations. This approach significantly reduces the memory demand, facilitating the extension of MoDL algorithms to high dimensional problems. We constrain the CNN to be a monotone operator, which allows us to introduce algorithms with guaranteed convergence properties and robustness guarantees. We demonstrate the utility of the proposed scheme in the context of parallel MRI.

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arXiv2021

Dynamic imaging using motion-compensated smoothness regularization on manifolds (MoCo-SToRM)

We introduce an unsupervised deep manifold learning algorithm for motion-compensated dynamic MRI. We assume that the motion fields in a free-breathing lung MRI dataset live on a manifold. The motion field at each time instant is modeled as the output of a deep generative model, driven by low-dimensional time-varying latent vectors that capture the temporal variability. The images at each time instant are modeled as the deformed version of an image template using the above motion fields. The template, the parameters of the deep generator, and the latent vectors are learned from the k-t space data in an unsupervised fashion. The manifold motion model serves as a regularizer, making the joint estimation of the motion fields and images from few radial spokes/frame well-posed. The utility of the algorithm is demonstrated in the context of motion-compensated high-resolution lung MRI.

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arXiv2021

Joint alignment and reconstruction of multislice dynamic MRI using variational manifold learning

Free-breathing cardiac MRI schemes are emerging as competitive alternatives to breath-held cine MRI protocols, enabling applicability to pediatric and other population groups that cannot hold their breath. Because the data from the slices are acquired sequentially, the cardiac/respiratory motion patterns may be different for each slice; current free-breathing approaches perform independent recovery of each slice. In addition to not being able to exploit the inter-slice redundancies, manual intervention or sophisticated post-processing methods are needed to align the images post-recovery for quantification. To overcome these challenges, we propose an unsupervised variational deep manifold learning scheme for the joint alignment and reconstruction of multislice dynamic MRI. The proposed scheme jointly learns the parameters of the deep network as well as the latent vectors for each slice, which capture the motion-induced dynamic variations, from the k-t space data of the specific subject. The variational framework minimizes the non-uniqueness in the representation, thus offering improved alignment and reconstructions.

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arXiv2021

Deep Image Prior using Stein's Unbiased Risk Estimator: SURE-DIP

Deep learning algorithms that rely on extensive training data are revolutionizing image recovery from ill-posed measurements. Training data is scarce in many imaging applications, including ultra-high-resolution imaging. The deep image prior (DIP) algorithm was introduced for single-shot image recovery, completely eliminating the need for training data. A challenge with this scheme is the need for early stopping to minimize the overfitting of the CNN parameters to the noise in the measurements. We introduce a generalized Stein's unbiased risk estimate (GSURE) loss metric to minimize the overfitting. Our experiments show that the SURE-DIP approach minimizes the overfitting issues, thus offering significantly improved performance over classical DIP schemes. We also use the SURE-DIP approach with model-based unrolling architectures, which offers improved performance over direct inversion schemes.

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arXiv2021

Dynamic Imaging using Deep Bi-linear Unsupervised Regularization (DEBLUR)

Bilinear models that decompose dynamic data to spatial and temporal factors are powerful and memory-efficient tools for the recovery of dynamic MRI data. These methods rely on sparsity and energy compaction priors on the factors to regularize the recovery. The quality of the recovered images depend on the specific priors. Motivated by deep image prior, we introduce a novel bilinear model whose factors are represented using convolutional neural networks (CNNs). The CNN parameters are learned from the undersampled data off the same subject. To reduce the run time and to improve performance, we initialize the CNN parameters. 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 low-rank and SToRM reconstructions.

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arXiv2021

Joint Calibrationless Reconstruction and Segmentation of Parallel MRI

The volume estimation of brain regions from MRI data is a key problem in many clinical applications, where the acquisition of data at high spatial resolution is desirable. While parallel MRI and constrained image reconstruction algorithms can accelerate the scans, image reconstruction artifacts are inevitable, especially at high acceleration factors. We introduce a novel image domain deep-learning framework for calibrationless parallel MRI reconstruction, coupled with a segmentation network to improve image quality and to reduce the vulnerability of current segmentation algorithms to image artifacts resulting from acceleration. The combination of the proposed image domain deep calibrationless approach with the segmentation algorithm offers improved image quality, while increasing the accuracy of the segmentations. The novel architecture with an encoder shared between the reconstruction and segmentation tasks is seen to reduce the need for segmented training datasets. In particular, the proposed few-shot training strategy requires only 10% of segmented datasets to offer good performance.

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arXiv2021

Dynamic imaging using a deep generative SToRM (Gen-SToRM) model

We introduce a generative smoothness regularization on manifolds (SToRM) model for the recovery of dynamic image data from highly undersampled measurements. The model assumes that the images in the dataset are non-linear mappings of low-dimensional latent vectors. We use the deep convolutional neural network (CNN) to represent the non-linear transformation. The parameters of the generator as well as the low-dimensional latent vectors are jointly estimated only from the undersampled measurements. This approach is different from traditional CNN approaches that require extensive fully sampled training data. We penalize the norm of the gradients of the non-linear mapping to constrain the manifold to be smooth, while temporal gradients of the latent vectors are penalized to obtain a smoothly varying time-series. The proposed scheme brings in the spatial regularization provided by the convolutional network. The main benefit of the proposed scheme is the improvement in image quality and the orders-of-magnitude reduction in memory demand compared to traditional manifold models. To minimize the computational complexity of the algorithm, we introduce an efficient progressive training-in-time approach and an approximate cost function. These approaches speed up the image reconstructions and offers better reconstruction performance.

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arXiv2021

Recovery of surfaces and functions in high dimensions: sampling theory and links to neural networks

Several imaging algorithms including patch-based image denoising, image time series recovery, and convolutional neural networks can be thought of as methods that exploit the manifold structure of signals. While the empirical performance of these algorithms is impressive, the understanding of recovery of the signals and functions that live on manifold is less understood. In this paper, we focus on the recovery of signals that live on a union of surfaces. In particular, we consider signals living on a union of smooth band-limited surfaces in high dimensions. We show that an exponential mapping transforms the data to a union of low-dimensional subspaces. Using this relation, we introduce a sampling theoretical framework for the recovery of smooth surfaces from few samples and the learning of functions living on smooth surfaces. The low-rank property of the features is used to determine the number of measurements needed to recover the surface. Moreover, the low-rank property of the features also provides an efficient approach, which resembles a neural network, for the local representation of multidimensional functions on the surface.

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arXiv2021

Reconstruction and Segmentation of Parallel MR Data using Image Domain DEEP-SLR

The main focus of this work is a novel framework for the joint reconstruction and segmentation of parallel MRI (PMRI) brain data. We introduce an image domain deep network for calibrationless recovery of undersampled PMRI data. The proposed approach is the deep-learning (DL) based generalization of local low-rank based approaches for uncalibrated PMRI recovery including CLEAR [6]. Since the image domain approach exploits additional annihilation relations compared to k-space based approaches, we expect it to offer improved performance. To minimize segmentation errors resulting from undersampling artifacts, we combined the proposed scheme with a segmentation network and trained it in an end-to-end fashion. In addition to reducing segmentation errors, this approach also offers improved reconstruction performance by reducing overfitting; the reconstructed images exhibit reduced blurring and sharper edges than independently trained reconstruction network.

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arXiv2021

Deep Generative SToRM model for dynamic imaging

We introduce a novel generative smoothness regularization on manifolds (SToRM) model for the recovery of dynamic image data from highly undersampled measurements. The proposed generative framework represents the image time series as a smooth non-linear function of low-dimensional latent vectors that capture the cardiac and respiratory phases. The non-linear function is represented using a deep convolutional neural network (CNN). Unlike the popular CNN approaches that require extensive fully-sampled training data that is not available in this setting, the parameters of the CNN generator as well as the latent vectors are jointly estimated from the undersampled measurements using stochastic gradient descent. We penalize the norm of the gradient of the generator to encourage the learning of a smooth surface/manifold, while temporal gradients of the latent vectors are penalized to encourage the time series to be smooth. The main benefits of the proposed scheme are (a) the quite significant reduction in memory demand compared to the analysis based SToRM model, and (b) the spatial regularization brought in by the CNN model. We also introduce efficient progressive approaches to minimize the computational complexity of the algorithm.

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arXiv2021

Model Adaptation for Image Reconstruction using Generalized Stein's Unbiased Risk Estimator

Deep learning image reconstruction algorithms often suffer from model mismatches when the acquisition scheme differs significantly from the forward model used during training. We introduce a Generalized Stein's Unbiased Risk Estimate (GSURE) loss metric to adapt the network to the measured k-space data and minimize model misfit impact. Unlike current methods that rely on the mean square error in kspace, the proposed metric accounts for noise in the measurements. This makes the approach less vulnerable to overfitting, thus offering improved reconstruction quality compared to schemes that rely on mean-square error. This approach may be useful to rapidly adapt pre-trained models to new acquisition settings (e.g., multi-site) and different contrasts than training data

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