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Register a new userRegularising Inverse Problems with Generative Machine Learning Models
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Deep neural network approaches to inverse imaging problems have produced impressive results in the last few years. In this paper, we consider the use of generative models in a variational regularisation approach to inverse problems. The considered regularisers penalise images that are far from the range of a generative model that has learned to produce images similar to a training dataset. We name this family textit{generative regularisers}. The success of generative regularisers depends on the quality of the generative model and so we propose a set of desired criteria to assess models and guide future research. In our numerical experiments, we evaluate three common generative models, autoencoders, variational autoencoders and generative adversarial networks, against our desired criteria. We also test three different generative regularisers on the inverse problems of deblurring, deconvolution, and tomography. We show that the success of solutions restricted to lie exactly in the range of the generator is highly dependent on the ability of the generative model but that allowing small deviations from the range of the generator produces more consistent results.
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There are various inverse problems -- including reconstruction problems arising in medical imaging -- where one is often aware of the forward operator that maps variables of interest to the observations. It is therefore natural to ask whether such knowledge of the forward operator can be exploited in deep learning approaches increasingly used to solve inverse problems. In this paper, we provide one such way via an analysis of the generalisation error of deep learning methods applicable to inverse problems. In particular, by building on the algorithmic robustness framework, we offer a generalisation error bound that encapsulates key ingredients associated with the learning problem such as the complexity of the data space, the size of the training set, the Jacobian of the deep neural network and the Jacobian of the composition of the forward operator with the neural network. We then propose a plug-and-play regulariser that leverages the knowledge of the forward map to improve the generalization of the network. We likewise also propose a new method allowing us to tightly upper bound the Lipschitz constants of the relevant functions that is much more computational efficient than existing ones. We demonstrate the efficacy of our model-aware regularised deep learning algorithms against other state-of-the-art approaches on inverse problems involving various sub-sampling operators such as those used in classical compressed sensing setup and accelerated Magnetic Resonance Imaging (MRI).
Advances in computing power, deep learning architectures, and expert labelled datasets have spurred the development of medical imaging artificial intelligence systems that rival clinical experts in a variety of scenarios. The National Institutes of Health in 2018 identified key focus areas for the future of artificial intelligence in medical imaging, creating a foundational roadmap for research in image acquisition, algorithms, data standardization, and translatable clinical decision support systems. Among the key issues raised in the report: data availability, need for novel computing architectures and explainable AI algorithms, are still relevant despite the tremendous progress made over the past few years alone. Furthermore, translational goals of data sharing, validation of performance for regulatory approval, generalizability and mitigation of unintended bias must be accounted for early in the development process. In this perspective paper we explore challenges unique to high dimensional clinical imaging data, in addition to highlighting some of the technical and ethical considerations in developing high-dimensional, multi-modality, machine learning systems for clinical decision support.
In this work we introduce a novel stochastic algorithm dubbed SNIPS, which draws samples from the posterior distribution of any linear inverse problem, where the observation is assumed to be contaminated by additive white Gaussian noise. Our solution incorporates ideas from Langevin dynamics and Newtons method, and exploits a pre-trained minimum mean squared error (MMSE) Gaussian denoiser. The proposed approach relies on an intricate derivation of the posterior score function that includes a singular value decomposition (SVD) of the degradation operator, in order to obtain a tractable iterative algorithm for the desired sampling. Due to its stochasticity, the algorithm can produce multiple high perceptual quality samples for the same noisy observation. We demonstrate the abilities of the proposed paradigm for image deblurring, super-resolution, and compressive sensing. We show that the samples produced are sharp, detailed and consistent with the given measurements, and their diversity exposes the inherent uncertainty in the inverse problem being solved.
Quantification of anatomical shape changes currently relies on scalar global indexes which are largely insensitive to regional or asymmetric modifications. Accurate assessment of pathology-driven anatomical remodeling is a crucial step for the diagnosis and treatment of many conditions. Deep learning approaches have recently achieved wide success in the analysis of medical images, but they lack interpretability in the feature extraction and decision processes. In this work, we propose a new interpretable deep learning model for shape analysis. In particular, we exploit deep generative networks to model a population of anatomical segmentations through a hierarchy of conditional latent variables. At the highest level of this hierarchy, a two-dimensional latent space is simultaneously optimised to discriminate distinct clinical conditions, enabling the direct visualisation of the classification space. Moreover, the anatomical variability encoded by this discriminative latent space can be visualised in the segmentation space thanks to the generative properties of the model, making the classification task transparent. This approach yielded high accuracy in the categorisation of healthy and remodelled left ventricles when tested on unseen segmentations from our own multi-centre dataset as well as in an external validation set, and on hippocampi from healthy controls and patients with Alzheimers disease when tested on ADNI data. More importantly, it enabled the visualisation in three-dimensions of both global and regional anatomical features which better discriminate between the conditions under exam. The proposed approach scales effectively to large populations, facilitating high-throughput analysis of normal anatomy and pathology in large-scale studies of volumetric imaging.
Deep neural networks have been applied successfully to a wide variety of inverse problems arising in computational imaging. These networks are typically trained using a forward model that describes the measurement process to be inverted, which is often incorporated directly into the network itself. However, these approaches are sensitive to changes in the forward model: if at test time the forward model varies (even slightly) from the one the network was trained for, the reconstruction performance can degrade substantially. Given a network trained to solve an initial inverse problem with a known forward model, we propose two novel procedures that adapt the network to a change in the forward model, even without full knowledge of the change. Our approaches do not require access to more labeled data (i.e., ground truth images). We show these simple model adaptation approaches achieve empirical success in a variety of inverse problems, including deblurring, super-resolution, and undersampled image reconstruction in magnetic resonance imaging.
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