39 research outputs found

    Faster PET reconstruction with non-smooth priors by randomization and preconditioning

    Get PDF
    Uncompressed clinical data from modern positron emission tomography (PET) scanners are very large, exceeding 350 million data points (projection bins). The last decades have seen tremendous advancements in mathematical imaging tools many of which lead to non-smooth (i.e. non-differentiable) optimization problems which are much harder to solve than smooth optimization problems. Most of these tools have not been translated to clinical PET data, as the state-of-the-art algorithms for non-smooth problems do not scale well to large data. In this work, inspired by big data machine learning applications, we use advanced randomized optimization algorithms to solve the PET reconstruction problem for a very large class of non-smooth priors which includes for example total variation, total generalized variation, directional total variation and various different physical constraints. The proposed algorithm randomly uses subsets of the data and only updates the variables associated with these. While this idea often leads to divergent algorithms, we show that the proposed algorithm does indeed converge for any proper subset selection. Numerically, we show on real PET data (FDG and florbetapir) from a Siemens Biograph mMR that about ten projections and backprojections are sufficient to solve the MAP optimisation problem related to many popular non-smooth priors; thus showing that the proposed algorithm is fast enough to bring these models into routine clinical practice

    Deep learning as optimal control problems

    Get PDF
    We briefly review recent work where deep learning neural networks have been interpreted as discretisations of an optimal control problem subject to an ordinary differential equation constraint. We report here new preliminary experiments with implicit symplectic Runge-Kutta methods. In this paper, we discuss ongoing and future research in this area

    On Learned Operator Correction in Inverse Problems

    Get PDF
    We discuss the possibility of learning a data-driven explicit model correction for inverse problems and whether such a model correction can be used within a variational framework to obtain regularized reconstructions. This paper discusses the conceptual difficulty of learning such a forward model correction and proceeds to present a possible solution as a forward-adjoint correction that explicitly corrects in both data and solution spaces. We then derive conditions under which solutions to the variational problem with a learned correction converge to solutions obtained with the correct operator. The proposed approach is evaluated on an application to limited view photoacoustic tomography and compared to the established framework of the Bayesian approximation error method

    Calibrating the dice loss to handle neural network overconfidence for biomedical image segmentation

    Get PDF
    The Dice similarity coefficient (DSC) is both a widely used metric and loss function for biomedical image segmentation due to its robustness to class imbalance. However, it is well known that the DSC loss is poorly calibrated, resulting in overconfident predictions that cannot be usefully interpreted in biomedical and clinical practice. Performance is often the only metric used to evaluate segmentations produced by deep neural networks, and calibration is often neglected. However, calibration is important for translation into biomedical and clinical practice, providing crucial contextual information to model predictions for interpretation by scientists and clinicians. In this study, we provide a simple yet effective extension of the DSC loss, named the DSC++ loss, that selectively modulates the penalty associated with overconfident, incorrect predictions. As a standalone loss function, the DSC++ loss achieves significantly improved calibration over the conventional DSC loss across six well-validated open-source biomedical imaging datasets, including both 2D binary and 3D multi-class segmentation tasks. Similarly, we observe significantly improved calibration when integrating the DSC++ loss into four DSC-based loss functions. Finally, we use softmax thresholding to illustrate that well calibrated outputs enable tailoring of recall-precision bias, which is an important post-processing technique to adapt the model predictions to suit the biomedical or clinical task. The DSC++ loss overcomes the major limitation of the DSC loss, providing a suitable loss function for training deep learning segmentation models for use in biomedical and clinical practice. Source code is available at https://github.com/mlyg/DicePlusPlus

    ADI splitting schemes for a fourth-order nonlinear partial differential equation from image processing

    Get PDF
    We present directional operator splitting schemes for the numerical solution of a fourth-order, nonlinear partial differential evolution equation which arises in image processing. This equation constitutes the H−1-gradient flow of the total variation and represents a prototype of higher-order equations of similar type which are popular in imaging for denoising, deblurring and inpainting problems. The efficient numerical solution of this equation is very challenging due to the stiffness of most numerical schemes. We show that the combination of directional splitting schemes with implicit time-stepping provides a stable and computationally cheap numerical realisation of the equation

    Optical flow analysis reveals that Kinesin-mediated advection impacts on the orientation of microtubules in the Drosophila oocyte.

    Get PDF
    The orientation of microtubule networks is exploited by motors to deliver cargoes to specific intracellular destinations, and is thus essential for cell polarity and function. Reconstituted in vitro systems have largely contributed to understanding the molecular framework regulating the behavior of microtubule filaments. In cells however, microtubules are exposed to various biomechanical forces that might impact on their orientation, but little is known about it. Oocytes, which display forceful cytoplasmic streaming, are excellent model systems to study the impact of motion forces on cytoskeletons in vivo. Here we implement variational optical flow analysis as a new approach to analyze the polarity of microtubules in the Drosophila oocyte, a cell that displays distinct Kinesin-dependent streaming. After validating the method as robust for describing microtubule orientation from confocal movies, we find that increasing the speed of flows results in aberrant plus end growth direction. Furthermore, we find that in oocytes where Kinesin is unable to induce cytoplasmic streaming, the growth direction of microtubule plus ends is also altered. These findings lead us to propose that cytoplasmic streaming - and thus motion by advection - contributes to the correct orientation of MTs in vivo. Finally, we propose a possible mechanism for a specialised cytoplasmic actin network (the actin mesh) to act as a regulator of flow speeds; to counteract the recruitment of Kinesin to microtubules. [Media: see text] [Media: see text] [Media: see text] [Media: see text] [Media: see text] [Media: see text] [Media: see text] [Media: see text] [Media: see text] [Media: see text]
    corecore