Memory-efficient deep end-to-end posterior network (DEEPEN) for inverse problems

End-to-End (E2E) unrolled optimization frameworks show promise for Magnetic Resonance (MR) image recovery, but suffer from high memory usage during training. In addition, these deterministic approaches do not offer opportunities for sampling from the posterior distribution. In this paper, we introduce a memory-efficient approach for E2E learning of the posterior distribution. We represent this distribution as the combination of a data-consistency-induced likelihood term and an energy model for the prior, parameterized by a Convolutional Neural Network (CNN). The CNN weights are learned from training data in an E2E fashion using maximum likelihood optimization. The learned model enables the recovery of images from undersampled measurements using the Maximum A Posteriori (MAP) optimization. In addition, the posterior model can be sampled to derive uncertainty maps about the reconstruction. Experiments on parallel MR image reconstruction show that our approach performs comparable to the memory-intensive E2E unrolled algorithm, performs better than its memory-efficient counterpart, and can provide uncertainty maps. Our framework paves the way towards MR image reconstruction in 3D and higher dimensions

Surf-CDM: Score-Based Surface Cold-Diffusion Model For Medical Image Segmentation

Diffusion models have shown impressive performance for image generation, often times outperforming other generative models. Since their introduction, researchers have extended the powerful noise-to-image denoising pipeline to discriminative tasks, including image segmentation. In this work we propose a conditional score-based generative modeling framework for medical image segmentation which relies on a parametric surface representation for the segmentation masks. The surface re-parameterization allows the direct application of standard diffusion theory, as opposed to when the mask is represented as a binary mask. Moreover, we adapted an extended variant of the diffusion technique known as the "cold-diffusion" where the diffusion model can be constructed with deterministic perturbations instead of Gaussian noise, which facilitates significantly faster convergence in the reverse diffusion. We evaluated our method on the segmentation of the left ventricle from 65 transthoracic echocardiogram videos (2230 echo image frames) and compared its performance to the most popular and widely used image segmentation models. Our proposed model not only outperformed the compared methods in terms of segmentation accuracy, but also showed potential in estimating segmentation uncertainties for further downstream analyses due to its inherent generative nature.

Local monotone operator learning using non-monotone operators: MnM-MOL

The recovery of magnetic resonance (MR) images from undersampled measurements is a key problem that has seen extensive research in recent years. Unrolled approaches, which rely on end-to-end training of convolutional neural network (CNN) blocks within iterative reconstruction algorithms, offer state-of-the-art performance. These algorithms require a large amount of memory during training, making them difficult to employ in high-dimensional applications. Deep equilibrium (DEQ) models and the recent monotone operator learning (MOL) approach were introduced to eliminate the need for unrolling, thus reducing the memory demand during training. Both approaches require a Lipschitz constraint on the network to ensure that the forward and backpropagation iterations converge. Unfortunately, the constraint often results in reduced performance compared to unrolled methods. The main focus of this work is to relax the constraint on the CNN block in two different ways. Inspired by convex-non-convex regularization strategies, we now impose the monotone constraint on the sum of the gradient of the data term and the CNN block, rather than constrain the CNN itself to be a monotone operator. This approach enables the CNN to learn possibly non-monotone score functions, which can translate to improved performance. In addition, we only restrict the operator to be monotone in a local neighborhood around the image manifold. Our theoretical results show that the proposed algorithm is guaranteed to converge to the fixed point and that the solution is robust to input perturbations, provided that it is initialized close to the true solution. Our empirical results show that the relaxed constraints translate to improved performance and that the approach enjoys robustness to input perturbations similar to MOL.

Motion Compensated Unsupervised Deep Learning for 5D MRI

We propose an unsupervised deep learning algorithm for the motion-compensated reconstruction of 5D cardiac MRI data from 3D radial acquisitions. Ungated free-breathing 5D MRI simplifies the scan planning, improves patient comfort, and offers several clinical benefits over breath-held 2D exams, including isotropic spatial resolution and the ability to reslice the data to arbitrary views. However, the current reconstruction algorithms for 5D MRI take very long computational time, and their outcome is greatly dependent on the uniformity of the binning of the acquired data into different physiological phases. The proposed algorithm is a more data-efficient alternative to current motion-resolved reconstructions. This motion-compensated approach models the data in each cardiac/respiratory bin as Fourier samples of the deformed version of a 3D image template. The deformation maps are modeled by a convolutional neural network driven by the physiological phase information. The deformation maps and the template are then jointly estimated from the measured data. The cardiac and respiratory phases are estimated from 1D navigators using an auto-encoder. The proposed algorithm is validated on 5D bSSFP datasets acquired from two subjects.

Multi-Scale Energy (MuSE) plug and play framework for inverse problems

We introduce a multi-scale energy formulation for plug and play (PnP) image recovery. The main highlight of the proposed framework is energy formulation, where the log prior of the distribution is learned by a convolutional neural network (CNN) module. The energy formulation enables us to introduce optimization algorithms with guaranteed convergence, even when the CNN module is not constrained as a contraction. Current PnP methods, which do not often have well-defined energy formulations, require a contraction constraint that restricts their performance in challenging applications. The energy and the corresponding score function are learned from reference data using denoising score matching, where the noise variance serves as a smoothness parameter that controls the shape of the learned energy function. We introduce a multi-scale optimization strategy, where a sequence of smooth approximations of the true prior is used in the optimization process. This approach improves the convergence of the algorithm to the global minimum, which translates to improved performance. The preliminary results in the context of MRI show that the multi-scale energy PnP framework offers comparable performance to unrolled algorithms. Unlike unrolled methods, the proposed PnP approach can work with arbitrary forward models, making it an easier option for clinical deployment. In addition, the training of the proposed model is more efficient from a memory and computational perspective, making it attractive in large-scale (e.g., 4D) settings.

Adapting model-based deep learning to multiple acquisition conditions: Ada-MoDL

Purpose: The aim of this work is to introduce a single model-based deep network that can provide high-quality reconstructions from undersampled parallel MRI data acquired with multiple sequences, acquisition settings and field strengths. Methods: A single unrolled architecture, which offers good reconstructions for multiple acquisition settings, is introduced. The proposed scheme adapts the model to each setting by scaling the CNN features and the regularization parameter with appropriate weights. The scaling weights and regularization parameter are derived using a multi-layer perceptron model from conditional vectors, which represents the specific acquisition setting. The perceptron parameters and the CNN weights are jointly trained using data from multiple acquisition settings, including differences in field strengths, acceleration, and contrasts. The conditional network is validated using datasets acquired with different acquisition settings. Results: The comparison of the adaptive framework, which trains a single model using the data from all the settings, shows that it can offer consistently improved performance for each acquisition condition. The comparison of the proposed scheme with networks that are trained independently for each acquisition setting shows that it requires less training data per acquisition setting to offer good performance. Conclusion: The Ada-MoDL framework enables the use of a single model-based unrolled network for multiple acquisition settings. In addition to eliminating the need to train and store multiple networks for different acquisition settings, this approach reduces the training data needed for each acquisition setting.

Accelerated parallel MRI using memory efficient and robust monotone operator learning (MOL)

Model-based deep learning methods that combine imaging physics with learned regularization priors have been emerging as powerful tools for parallel MRI acceleration. The main focus of this paper is to determine the utility of the monotone operator learning (MOL) framework in the parallel MRI setting. The MOL algorithm alternates between a gradient descent step using a monotone convolutional neural network (CNN) and a conjugate gradient algorithm to encourage data consistency. The benefits of this approach include similar guarantees as compressive sensing algorithms including uniqueness, convergence, and stability, while being significantly more memory efficient than unrolled methods. We validate the proposed scheme by comparing it with different unrolled algorithms in the context of accelerated parallel MRI for static and dynamic settings.

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.

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.

Rapid dynamic speech imaging at 3 Tesla using combination of a custom vocal tract coil, variable density spirals and manifold regularization

Purpose: To improve dynamic speech imaging at 3 Tesla. Methods: A novel scheme combining a 16-channel vocal tract coil, variable density spirals (VDS), and manifold regularization was developed. Short readout duration spirals (1.3 ms long) were used to minimize sensitivity to off-resonance. The manifold model leveraged similarities between frames sharing similar vocal tract postures without explicit motion binning. Reconstruction was posed as a SENSE-based non-local soft weighted temporal regularization scheme. The self-navigating capability of VDS was leveraged to learn the structure of the manifold. Our approach was compared against low-rank and finite difference reconstruction constraints on two volunteers performing repetitive and arbitrary speaking tasks. Blinded image quality evaluation in the categories of alias artifacts, spatial blurring, and temporal blurring were performed by three experts in voice research. Results: We achieved a spatial resolution of 2.4mm2/pixel and a temporal resolution of 17.4 ms/frame for single slice imaging, and 52.2 ms/frame for concurrent 3-slice imaging. Implicit motion binning of the manifold scheme for both repetitive and fluent speaking tasks was demonstrated. The manifold scheme provided superior fidelity in modeling articulatory motion compared to low rank and temporal finite difference schemes. This was reflected by higher image quality scores in spatial and temporal blurring categories. Our technique exhibited faint alias artifacts, but offered a reduced interquartile range of scores compared to other methods in alias artifact category. Conclusion: Synergistic combination of a custom vocal-tract coil, variable density spirals and manifold regularization enables robust dynamic speech imaging at 3 Tesla.