Quantifying Registration Uncertainty with Sparse Bayesian Modelling

International audienceWe investigate uncertainty quantification under a sparse Bayesian model of medical image registration. Bayesian modelling has proven powerful to automate the tuning of registration hyperparameters, such as the trade-off between the data and regularization functionals. Sparsity-inducing priors have recently been used to render the parametrization itself adaptive and data-driven. The sparse prior on transformation parameters effectively favors the use of coarse basis functions to capture the global trends in the visible motion while finer, highly localized bases are introduced only in the presence of coherent image information and motion. In earlier work, approximate inference under the sparse Bayesian model was tackled in an efficient Variational Bayes (VB) framework. In this paper we are interested in the theoretical and empirical quality of uncertainty estimates derived under this approximate scheme vs. under the exact model. We implement an (asymptotically) exact inference scheme based on reversible jump Markov Chain Monte Carlo (MCMC) sampling to characterize the posterior distribution of the transformation and compare the predictions of the VB and MCMC based methods. The true posterior distribution under the sparse Bayesian model is found to be meaningful: orders of magnitude for the estimated uncertainty are quantitatively reasonable, the uncertainty is higher in textureless regions and lower in the direction of strong intensity gradients

Reasoning with Uncertainty in Deep Learning for Safer Medical Image Computing

Deep learning is now ubiquitous in the research field of medical image computing. As such technologies progress towards clinical translation, the question of safety becomes critical. Once deployed, machine learning systems unavoidably face situations where the correct decision or prediction is ambiguous. However, the current methods disproportionately rely on deterministic algorithms, lacking a mechanism to represent and manipulate uncertainty. In safety-critical applications such as medical imaging, reasoning under uncertainty is crucial for developing a reliable decision making system. Probabilistic machine learning provides a natural framework to quantify the degree of uncertainty over different variables of interest, be it the prediction, the model parameters and structures, or the underlying data (images and labels). Probability distributions are used to represent all the uncertain unobserved quantities in a model and how they relate to the data, and probability theory is used as a language to compute and manipulate these distributions. In this thesis, we explore probabilistic modelling as a framework to integrate uncertainty information into deep learning models, and demonstrate its utility in various high-dimensional medical imaging applications. In the process, we make several fundamental enhancements to current methods. We categorise our contributions into three groups according to the types of uncertainties being modelled: (i) predictive; (ii) structural and (iii) human uncertainty. Firstly, we discuss the importance of quantifying predictive uncertainty and understanding its sources for developing a risk-averse and transparent medical image enhancement application. We demonstrate how a measure of predictive uncertainty can be used as a proxy for the predictive accuracy in the absence of ground-truths. Furthermore, assuming the structure of the model is flexible enough for the task, we introduce a way to decompose the predictive uncertainty into its orthogonal sources i.e. aleatoric and parameter uncertainty. We show the potential utility of such decoupling in providing a quantitative “explanations” into the model performance. Secondly, we introduce our recent attempts at learning model structures directly from data. One work proposes a method based on variational inference to learn a posterior distribution over connectivity structures within a neural network architecture for multi-task learning, and share some preliminary results in the MR-only radiotherapy planning application. Another work explores how the training algorithm of decision trees could be extended to grow the architecture of a neural network to adapt to the given availability of data and the complexity of the task. Lastly, we develop methods to model the “measurement noise” (e.g., biases and skill levels) of human annotators, and integrate this information into the learning process of the neural network classifier. In particular, we show that explicitly modelling the uncertainty involved in the annotation process not only leads to an improvement in robustness to label noise, but also yields useful insights into the patterns of errors that characterise individual experts

Image registration via stochastic gradient markov chain monte carlo

We develop a fully Bayesian framework for non-rigid registration of three-dimensional medical images, with a focus on uncertainty quantification. Probabilistic registration of large images along with calibrated uncertainty estimates is difficult for both computational and modelling reasons. To address the computational issues, we explore connections between the Markov chain Monte Carlo by backprop and the variational inference by backprop frameworks in order to efficiently draw thousands of samples from the posterior distribution. Regarding the modelling issues, we carefully design a Bayesian model for registration to overcome the existing barriers when using a dense, high-dimensional, and diffeomorphic parameterisation of the transformation. This results in improved calibration of uncertainty estimates

Discrete versus continuous domain models for disease mapping

The main goal of disease mapping is to estimate disease risk and identify high-risk areas. Such analyses are hampered by the limited geographical resolution of the available data. Typically the available data are counts per spatial unit and the common approach is the Besag--York--Molli{\'e} (BYM) model. When precise geocodes are available, it is more natural to use Log-Gaussian Cox processes (LGCPs). In a simulation study mimicking childhood leukaemia incidence using actual residential locations of all children in the canton of Z\"urich, Switzerland, we compare the ability of these models to recover risk surfaces and identify high-risk areas. We then apply both approaches to actual data on childhood leukaemia incidence in the canton of Z\"urich during 1985-2015. We found that LGCPs outperform BYM models in almost all scenarios considered. Our findings suggest that there are important gains to be made from the use of LGCPs in spatial epidemiology.Comment: 28 pages, 4 figures, 2 Table

Variational data assimilation using targetted random walks

The variational approach to data assimilation is a widely used methodology for both online prediction and for reanalysis (offline hindcasting). In either of these scenarios it can be important to assess uncertainties in the assimilated state. Ideally it would be desirable to have complete information concerning the Bayesian posterior distribution for unknown state, given data. The purpose of this paper is to show that complete computational probing of this posterior distribution is now within reach in the offline situation. In this paper we will introduce an MCMC method which enables us to directly sample from the Bayesian\ud posterior distribution on the unknown functions of interest, given observations. Since we are aware that these\ud methods are currently too computationally expensive to consider using in an online filtering scenario, we frame this in the context of offline reanalysis. Using a simple random walk-type MCMC method, we are able to characterize the posterior distribution using only evaluations of the forward model of the problem, and of the model and data mismatch. No adjoint model is required for the method we use; however more sophisticated MCMC methods are available\ud which do exploit derivative information. For simplicity of exposition we consider the problem of assimilating data, either Eulerian or Lagrangian, into a low Reynolds number (Stokes flow) scenario in a two dimensional periodic geometry. We will show that in many cases it is possible to recover the initial condition and model error (which we describe as unknown forcing to the model) from data, and that with increasing amounts of informative data, the uncertainty in our estimations reduces

Uncertainty quantification in medical image synthesis

Machine learning approaches to medical image synthesis have shown outstanding performance, but often do not convey uncertainty information. In this chapter, we survey uncertainty quantification methods in medical image synthesis and advocate the use of uncertainty for improving clinicians’ trust in machine learning solutions. First, we describe basic concepts in uncertainty quantification and discuss its potential benefits in downstream applications. We then review computational strategies that facilitate inference, and identify the main technical and clinical challenges. We provide a first comprehensive review to inform how to quantify, communicate and use uncertainty in medical synthesis applications

Quantum-inspired computational imaging

Computational imaging combines measurement and computational methods with the aim of forming images even when the measurement conditions are weak, few in number, or highly indirect. The recent surge in quantum-inspired imaging sensors, together with a new wave of algorithms allowing on-chip, scalable and robust data processing, has induced an increase of activity with notable results in the domain of low-light flux imaging and sensing. We provide an overview of the major challenges encountered in low-illumination (e.g., ultrafast) imaging and how these problems have recently been addressed for imaging applications in extreme conditions. These methods provide examples of the future imaging solutions to be developed, for which the best results are expected to arise from an efficient codesign of the sensors and data analysis tools.Y.A. acknowledges support from the UK Royal Academy of Engineering under the Research Fellowship Scheme (RF201617/16/31). S.McL. acknowledges financial support from the UK Engineering and Physical Sciences Research Council (grant EP/J015180/1). V.G. acknowledges support from the U.S. Defense Advanced Research Projects Agency (DARPA) InPho program through U.S. Army Research Office award W911NF-10-1-0404, the U.S. DARPA REVEAL program through contract HR0011-16-C-0030, and U.S. National Science Foundation through grants 1161413 and 1422034. A.H. acknowledges support from U.S. Army Research Office award W911NF-15-1-0479, U.S. Department of the Air Force grant FA8650-15-D-1845, and U.S. Department of Energy National Nuclear Security Administration grant DE-NA0002534. D.F. acknowledges financial support from the UK Engineering and Physical Sciences Research Council (grants EP/M006514/1 and EP/M01326X/1). (RF201617/16/31 - UK Royal Academy of Engineering; EP/J015180/1 - UK Engineering and Physical Sciences Research Council; EP/M006514/1 - UK Engineering and Physical Sciences Research Council; EP/M01326X/1 - UK Engineering and Physical Sciences Research Council; W911NF-10-1-0404 - U.S. Defense Advanced Research Projects Agency (DARPA) InPho program through U.S. Army Research Office; HR0011-16-C-0030 - U.S. DARPA REVEAL program; 1161413 - U.S. National Science Foundation; 1422034 - U.S. National Science Foundation; W911NF-15-1-0479 - U.S. Army Research Office; FA8650-15-D-1845 - U.S. Department of the Air Force; DE-NA0002534 - U.S. Department of Energy National Nuclear Security Administration)Accepted manuscrip