SdCT-GAN: Reconstructing CT from Biplanar X-Rays with Self-driven Generative Adversarial Networks

Computed Tomography (CT) is a medical imaging modality that can generate more informative 3D images than 2D X-rays. However, this advantage comes at the expense of more radiation exposure, higher costs, and longer acquisition time. Hence, the reconstruction of 3D CT images using a limited number of 2D X-rays has gained significant importance as an economical alternative. Nevertheless, existing methods primarily prioritize minimizing pixel/voxel-level intensity discrepancies, often neglecting the preservation of textural details in the synthesized images. This oversight directly impacts the quality of the reconstructed images and thus affects the clinical diagnosis. To address the deficits, this paper presents a new self-driven generative adversarial network model (SdCT-GAN), which is motivated to pay more attention to image details by introducing a novel auto-encoder structure in the discriminator. In addition, a Sobel Gradient Guider (SGG) idea is applied throughout the model, where the edge information from the 2D X-ray image at the input can be integrated. Moreover, LPIPS (Learned Perceptual Image Patch Similarity) evaluation metric is adopted that can quantitatively evaluate the fine contours and textures of reconstructed images better than the existing ones. Finally, the qualitative and quantitative results of the empirical studies justify the power of the proposed model compared to mainstream state-of-the-art baselines

Permutation-invariant Feature Restructuring for Correlation-aware Image Set-based Recognition

We consider the problem of comparing the similarity of image sets with variable-quantity, quality and un-ordered heterogeneous images. We use feature restructuring to exploit the correlations of both inner$\&$inter-set images. Specifically, the residual self-attention can effectively restructure the features using the other features within a set to emphasize the discriminative images and eliminate the redundancy. Then, a sparse/collaborative learning-based dependency-guided representation scheme reconstructs the probe features conditional to the gallery features in order to adaptively align the two sets. This enables our framework to be compatible with both verification and open-set identification. We show that the parametric self-attention network and non-parametric dictionary learning can be trained end-to-end by a unified alternative optimization scheme, and that the full framework is permutation-invariant. In the numerical experiments we conducted, our method achieves top performance on competitive image set/video-based face recognition and person re-identification benchmarks.Comment: Accepted to ICCV 201

Connecting Simple and Precise P-values to Complex and Ambiguous Realities

Mathematics is a limited component of solutions to real-world problems, as it expresses only what is expected to be true if all our assumptions are correct, including implicit assumptions that are omnipresent and often incorrect. Statistical methods are rife with implicit assumptions whose violation can be life-threatening when results from them are used to set policy. Among them are that there is human equipoise or unbiasedness in data generation, management, analysis, and reporting. These assumptions correspond to levels of cooperation, competence, neutrality, and integrity that are absent more often than we would like to believe. Given this harsh reality, we should ask what meaning, if any, we can assign to the P-values, 'statistical significance' declarations, 'confidence' intervals, and posterior probabilities that are used to decide what and how to present (or spin) discussions of analyzed data. By themselves, P-values and CI do not test any hypothesis, nor do they measure the significance of results or the confidence we should have in them. The sense otherwise is an ongoing cultural error perpetuated by large segments of the statistical and research community via misleading terminology. So-called 'inferential' statistics can only become contextually interpretable when derived explicitly from causal stories about the real data generator (such as randomization), and can only become reliable when those stories are based on valid and public documentation of the physical mechanisms that generated the data. Absent these assurances, traditional interpretations of statistical results become pernicious fictions that need to be replaced by far more circumspect descriptions of data and model relations.Comment: 25 pages. Body of text to appear as a rejoinder in the Scandinavian Journal of Statistic

Methods for Optimization and Regularization of Generative Models

This thesis studies the problem of regularizing and optimizing generative models, often using insights and techniques from kernel methods. The work proceeds in three main themes. Conditional score estimation. We propose a method for estimating conditional densities based on a rich class of RKHS exponential family models. The algorithm works by solving a convex quadratic problem for fitting the gradient of the log density, the score, thus avoiding the need for estimating the normalizing constant. We show the resulting estimator to be consistent and provide convergence rates when the model is well-specified. Structuring and regularizing implicit generative models. In a first contribution, we introduce a method for learning Generative Adversarial Networks, a class of Implicit Generative Models, using a parametric family of Maximum Mean Discrepancies (MMD). We show that controlling the gradient of the critic function defining the MMD is vital for having a sensible loss function. Moreover, we devise a method to enforce exact, analytical gradient constraints. As a second contribution, we introduce and study a new generative model suited for data with low intrinsic dimension embedded in a high dimensional space. This model combines two components: an implicit model, which can learn the low-dimensional support of data, and an energy function, to refine the probability mass by importance sampling on the support of the implicit model. We further introduce algorithms for learning such a hybrid model and for efficient sampling. Optimizing implicit generative models. We first study the Wasserstein gradient flow of the Maximum Mean Discrepancy in a non-parametric setting and provide smoothness conditions on the trajectory of the flow to ensure global convergence. We identify cases when this condition does not hold and propose a new algorithm based on noise injection to mitigate this problem. In a second contribution, we consider the Wasserstein gradient flow of generic loss functionals in a parametric setting. This flow is invariant to the model's parameterization, just like the Fisher gradient flows in information geometry. It has the additional benefit to be well defined even for models with varying supports, which is particularly well suited for implicit generative models. We then introduce a general framework for approximating the Wasserstein natural gradient by leveraging a dual formulation of the Wasserstein pseudo-Riemannian metric that we restrict to a Reproducing Kernel Hilbert Space. The resulting estimator is scalable and provably consistent as it relies on Nystrom methods

Learning and inference with Wasserstein metrics

Thesis: Ph. D., Massachusetts Institute of Technology, Department of Brain and Cognitive Sciences, 2018.Cataloged from PDF version of thesis.Includes bibliographical references (pages 131-143).This thesis develops new approaches for three problems in machine learning, using tools from the study of optimal transport (or Wasserstein) distances between probability distributions. Optimal transport distances capture an intuitive notion of similarity between distributions, by incorporating the underlying geometry of the domain of the distributions. Despite their intuitive appeal, optimal transport distances are often difficult to apply in practice, as computing them requires solving a costly optimization problem. In each setting studied here, we describe a numerical method that overcomes this computational bottleneck and enables scaling to real data. In the first part, we consider the problem of multi-output learning in the presence of a metric on the output domain. We develop a loss function that measures the Wasserstein distance between the prediction and ground truth, and describe an efficient learning algorithm based on entropic regularization of the optimal transport problem. We additionally propose a novel extension of the Wasserstein distance from probability measures to unnormalized measures, which is applicable in settings where the ground truth is not naturally expressed as a probability distribution. We show statistical learning bounds for both the Wasserstein loss and its unnormalized counterpart. The Wasserstein loss can encourage smoothness of the predictions with respect to a chosen metric on the output space. We demonstrate this property on a real-data image tagging problem, outperforming a baseline that doesn't use the metric. In the second part, we consider the probabilistic inference problem for diffusion processes. Such processes model a variety of stochastic phenomena and appear often in continuous-time state space models. Exact inference for diffusion processes is generally intractable. In this work, we describe a novel approximate inference method, which is based on a characterization of the diffusion as following a gradient flow in a space of probability densities endowed with a Wasserstein metric. Existing methods for computing this Wasserstein gradient flow rely on discretizing the underlying domain of the diffusion, prohibiting their application to problems in more than several dimensions. In the current work, we propose a novel algorithm for computing a Wasserstein gradient flow that operates directly in a space of continuous functions, free of any underlying mesh. We apply our approximate gradient flow to the problem of filtering a diffusion, showing superior performance where standard filters struggle. Finally, we study the ecological inference problem, which is that of reasoning from aggregate measurements of a population to inferences about the individual behaviors of its members. This problem arises often when dealing with data from economics and political sciences, such as when attempting to infer the demographic breakdown of votes for each political party, given only the aggregate demographic and vote counts separately. Ecological inference is generally ill-posed, and requires prior information to distinguish a unique solution. We propose a novel, general framework for ecological inference that allows for a variety of priors and enables efficient computation of the most probable solution. Unlike previous methods, which rely on Monte Carlo estimates of the posterior, our inference procedure uses an efficient fixed point iteration that is linearly convergent. Given suitable prior information, our method can achieve more accurate inferences than existing methods. We additionally explore a sampling algorithm for estimating credible regions.by Charles Frogner.Ph. D