Medical image reconstruction: a brief overview of past milestones and future directions

This paper briefly reviews past milestones in the field of medical image reconstruction and describes some future directions. It is part of an overview paper on "open problems in signal processing" that will appear in IEEE Signal Processing Magazine, but presented here with citations and equations.Comment: Part of a submission to IEEE Signal Processing Magazin

Fidelity Imposed Network Edit (FINE) for Solving Ill-Posed Image Reconstruction

Deep learning (DL) is increasingly used to solve ill-posed inverse problems in imaging, such as reconstruction from noisy or incomplete data, as DL offers advantages over explicit image feature extractions in defining the needed prior. However, DL typically does not incorporate the precise physics of data generation or data fidelity. Instead, DL networks are trained to output some average response to an input. Consequently, DL image reconstruction contains errors, and may perform poorly when the test data deviates significantly from the training data, such as having new pathological features. To address this lack of data fidelity problem in DL image reconstruction, a novel approach, which we call fidelity-imposed network edit (FINE), is proposed. In FINE, a pre-trained prior network's weights are modified according to the physical model, on a test case. Our experiments demonstrate that FINE can achieve superior performance in two important inverse problems in neuroimaging: quantitative susceptibility mapping (QSM) and under-sampled reconstruction in MRI

Self-Supervised Deep Active Accelerated MRI

We propose to simultaneously learn to sample and reconstruct magnetic resonance images (MRI) to maximize the reconstruction quality given a limited sample budget, in a self-supervised setup. Unlike existing deep methods that focus only on reconstructing given data, thus being passive, we go beyond the current state of the art by considering both the data acquisition and the reconstruction process within a single deep-learning framework. As our network learns to acquire data, the network is active in nature. In order to do so, we simultaneously train two neural networks, one dedicated to reconstruction and the other to progressive sampling, each with an automatically generated supervision signal that links them together. The two supervision signals are created through Monte Carlo tree search (MCTS). MCTS returns a better sampling pattern than what the current sampling network can give and, thus, a better final reconstruction. The sampling network is trained to mimic the MCTS results using the previous sampling network, thus being enhanced. The reconstruction network is trained to give the highest reconstruction quality, given the MCTS sampling pattern. Through this framework, we are able to train the two networks without providing any direct supervision on sampling

RARE: Image Reconstruction using Deep Priors Learned without Ground Truth

Regularization by denoising (RED) is an image reconstruction framework that uses an image denoiser as a prior. Recent work has shown the state-of-the-art performance of RED with learned denoisers corresponding to pre-trained convolutional neural nets (CNNs). In this work, we propose to broaden the current denoiser-centric view of RED by considering priors corresponding to networks trained for more general artifact-removal. The key benefit of the proposed family of algorithms, called regularization by artifact-removal (RARE), is that it can leverage priors learned on datasets containing only undersampled measurements. This makes RARE applicable to problems where it is practically impossible to have fully-sampled groundtruth data for training. We validate RARE on both simulated and experimentally collected data by reconstructing a free-breathing whole-body 3D MRIs into ten respiratory phases from heavily undersampled k-space measurements. Our results corroborate the potential of learning regularizers for iterative inversion directly on undersampled and noisy measurements.Comment: In press for IEEE Journal of Special Topics in Signal Processin

MoDL: Model Based Deep Learning Architecture for Inverse Problems

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.Comment: published in IEEE Transaction on Medical Imagin

Optimal Sampling & Reconstruction: Theory and Applications

The optimization of MRI data sampling and image reconstruction methods has been a priority for the MRI community since the very early days of the field. Designing an "optimal" method requires the definition of an optimality metric (i.e., a quantitative evaluation of the "goodness" of different competing approaches that allows an objective comparison between them). However, a key challenge is that there are many different possible ways of quantitatively evaluating the "goodness" of a data sampling scheme or a reconstruction result, and there are no acquisition or reconstruction methods that are known to be universally optimal with respect to all of these possible metrics simultaneously. Thus, optimization of MRI methods requires a subjective choice about what aspects of quality matter most in the context of a given MRI experiment, and subsequently the subjective choice of an optimality metric that hopefully does a reasonable job of quantifying those aspects of quality. Once these choices are made, the optimization problem becomes well-defined, and it remains to choose an algorithm that can identify data sampling or image reconstruction methods that are optimal with respect to the chosen metric. All of these choices are generally nontrivial. In this presentation, we will discuss optimal sampling and reconstruction designs from multiple different perspectives, including ideas from information and estimation theory and various practical perspectives.Comment: Syllabus material for an invited talk at the 2020 ISMRM Workshop on Data Sampling & Image Reconstructio

Plug and play methods for magnetic resonance imaging (long version)

Magnetic Resonance Imaging (MRI) is a non-invasive diagnostic tool that provides excellent soft-tissue contrast without the use of ionizing radiation. Compared to other clinical imaging modalities (e.g., CT or ultrasound), however, the data acquisition process for MRI is inherently slow, which motivates undersampling and thus drives the need for accurate, efficient reconstruction methods from undersampled datasets. In this article, we describe the use of "plug-and-play" (PnP) algorithms for MRI image recovery. We first describe the linearly approximated inverse problem encountered in MRI. Then we review several PnP methods, where the unifying commonality is to iteratively call a denoising subroutine as one step of a larger optimization-inspired algorithm. Next, we describe how the result of the PnP method can be interpreted as a solution to an equilibrium equation, allowing convergence analysis from the equilibrium perspective. Finally, we present illustrative examples of PnP methods applied to MRI image recovery

A Gaussian Mixture MRF for Model-Based Iterative Reconstruction with Applications to Low-Dose X-ray CT

Markov random fields (MRFs) have been widely used as prior models in various inverse problems such as tomographic reconstruction. While MRFs provide a simple and often effective way to model the spatial dependencies in images, they suffer from the fact that parameter estimation is difficult. In practice, this means that MRFs typically have very simple structure that cannot completely capture the subtle characteristics of complex images. In this paper, we present a novel Gaussian mixture Markov random field model (GM-MRF) that can be used as a very expressive prior model for inverse problems such as denoising and reconstruction. The GM-MRF forms a global image model by merging together individual Gaussian-mixture models (GMMs) for image patches. In addition, we present a novel analytical framework for computing MAP estimates using the GM-MRF prior model through the construction of surrogate functions that result in a sequence of quadratic optimizations. We also introduce a simple but effective method to adjust the GM-MRF so as to control the sharpness in low- and high-contrast regions of the reconstruction separately. We demonstrate the value of the model with experiments including image denoising and low-dose CT reconstruction.Comment: accepted by IEEE Transactions on Computed Imagin

Least Squares Optimal Density Compensation for the Gridding Non-uniform Discrete Fourier Transform

The Gridding algorithm has shown great utility for reconstructing images from non-uniformly spaced samples in the Fourier domain in several imaging modalities. Due to the non-uniform spacing, some correction for the variable density of the samples must be made. Existing methods for generating density compensation values are either sub-optimal or only consider a finite set of points (a set of measure 0) in the optimization. This manuscript presents the first density compensation algorithm for a general trajectory that takes into account the point spread function over a set of non-zero measure. We show that the images reconstructed with Gridding using the density compensation values of this method are of superior quality when compared to density compensation weights determined in other ways. Results are shown with a numerical phantom and with magnetic resonance images of the abdomen and the knee

Deep Learning Techniques for Inverse Problems in Imaging

Recent work in machine learning shows that deep neural networks can be used to solve a wide variety of inverse problems arising in computational imaging. We explore the central prevailing themes of this emerging area and present a taxonomy that can be used to categorize different problems and reconstruction methods. Our taxonomy is organized along two central axes: (1) whether or not a forward model is known and to what extent it is used in training and testing, and (2) whether or not the learning is supervised or unsupervised, i.e., whether or not the training relies on access to matched ground truth image and measurement pairs. We also discuss the trade-offs associated with these different reconstruction approaches, caveats and common failure modes, plus open problems and avenues for future work