High temporal resolution total-body dynamic PET/CT imaging based on third-order Hermite interpolation

Dynamic positron emission tomography (dPET) is currently a widely used medical imaging technique for the clinical diagnosis, staging and therapy guidance of all kinds of human cancers. Higher temporal imaging resolution for the early stage of radiotracer metabolism is desired; however, in this case, the reconstructed images with short frame durations always suffer from a limited image signal-to-noise ratio (SNR), which results in unsatisfactory image spatial resolution. In this work, we proposed a dPET processing method that denoises images with short frame durations via pixel-level time-activity curve (TAC) correction based on third-order Hermite interpolation (Pitch-In). The proposed method was validated using total-body dynamic PET image data and compared to several state-of-the-art methods to demonstrate its superior performance in terms of high temporal resolution dPET image noise reduction and imaging contrast. Higher stability and feasibility of the proposed Pitch-In method for future clinical application with high temporal resolution (HTR) dPET imaging can be expected.

Self-training Converts Weak Learners to Strong Learners in Mixture Models

We consider a binary classification problem when the data comes from a mixture of two rotationally symmetric distributions satisfying concentration and anti-concentration properties enjoyed by log-concave distributions among others. We show that there exists a universal constant $C_{mathrm{err}}>0$ such that if a pseudolabeler $boldsymbol{beta}_{mathrm{pl}}$ can achieve classification error at most $C_{mathrm{err}}$, then for any $varepsilon>0$, an iterative self-training algorithm initialized at $boldsymbol{beta}_0 := boldsymbol{beta}_{mathrm{pl}}$ using pseudolabels $hat y = mathrm{sgn}(langle boldsymbol{beta}_t, mathbf{x}rangle)$ and using at most $tilde O(d/varepsilon^2)$ unlabeled examples suffices to learn the Bayes-optimal classifier up to $varepsilon$ error, where $d$ is the ambient dimension. That is, self-training converts weak learners to strong learners using only unlabeled examples. We additionally show that by running gradient descent on the logistic loss one can obtain a pseudolabeler $boldsymbol{beta}_{mathrm{pl}}$ with classification error $C_{mathrm{err}}$ using only $O(d)$ labeled examples (i.e., independent of $varepsilon$). Together our results imply that mixture models can be learned to within $varepsilon$ of the Bayes-optimal accuracy using at most $O(d)$ labeled examples and $tilde O(d/varepsilon^2)$ unlabeled examples by way of a semi-supervised self-training algorithm.

Almost Optimal Algorithms for Two-player Markov Games with Linear Function Approximation

We study reinforcement learning for two-player zero-sum Markov games with simultaneous moves in the finite-horizon setting, where the transition kernel of the underlying Markov games can be parameterized by a linear function over the current state, both players actions and the next state. In particular, we assume that we can control both players and aim to find the Nash Equilibrium by minimizing the duality gap. We propose an algorithm Nash-UCRL-VTR based on the principle Optimism-in-Face-of-Uncertainty. Our algorithm only needs to find a Coarse Correlated Equilibrium (CCE), which is computationally very efficient. Specifically, we show that Nash-UCRL-VTR can provably achieve an $tilde{O}(dHsqrt{T})$ regret, where $d$ is the linear function dimension, $H$ is the length of the game and $T$ is the total number of steps in the game. To access the optimality of our algorithm, we also prove an $tilde{Omega}( dHsqrt{T})$ lower bound on the regret. Our upper bound matches the lower bound up to logarithmic factors, which suggests the optimality of our algorithm.

Stein Neural Sampler

We propose two novel samplers to generate high-quality samples from a given (un-normalized) probability density. Motivated by the success of generative adversarial networks, we construct our samplers using deep neural networks that transform a reference distribution to the target distribution. Training schemes are developed to minimize two variations of the Stein discrepancy, which is designed to work with un-normalized densities. Once trained, our samplers are able to generate samples instantaneously. We show that the proposed methods are theoretically sound and experience fewer convergence issues compared with traditional sampling approaches according to our empirical studies.