Tianshun Miao

Bo Zhou, Yu-Jung Tsai, Jiazhen Zhang et al.

Patient motion during PET is inevitable. Its long acquisition time not only increases the motion and the associated artifacts but also the patient's discomfort, thus PET acceleration is desirable. However, accelerating PET acquisition will result in reconstructed images with low SNR, and the image quality will still be degraded by motion-induced artifacts. Most of the previous PET motion correction methods are motion type specific that require motion modeling, thus may fail when multiple types of motion present together. Also, those methods are customized for standard long acquisition and could not be directly applied to accelerated PET. To this end, modeling-free universal motion correction reconstruction for accelerated PET is still highly under-explored. In this work, we propose a novel deep learning-aided motion correction and reconstruction framework for accelerated PET, called Fast-MC-PET. Our framework consists of a universal motion correction (UMC) and a short-to-long acquisition reconstruction (SL-Reon) module. The UMC enables modeling-free motion correction by estimating quasi-continuous motion from ultra-short frame reconstructions and using this information for motion-compensated reconstruction. Then, the SL-Recon converts the accelerated UMC image with low counts to a high-quality image with high counts for our final reconstruction output. Our experimental results on human studies show that our Fast-MC-PET can enable 7-fold acceleration and use only 2 minutes acquisition to generate high-quality reconstruction images that outperform/match previous motion correction reconstruction methods using standard 15 minutes long acquisition data.

Xiaoyu Chen, Zhe Ju, Tianshun Miao et al.

We prove two results on the mixing times of Markov chains for two-spin systems. First, we show that the Glauber dynamics mixes in polynomial time for the Gibbs distributions of antiferromagnetic two-spin systems at the critical threshold of the uniqueness phase transition of the Gibbs measure on infinite regular trees. This completes the computational phase transition picture for antiferromagnetic two-spin systems, which includes near-linear-time optimal mixing in the uniqueness regime [Chen--Liu--Vigoda, STOC '21; Chen--Feng--Yin--Zhang, FOCS '22], NP-hardness of approximate sampling in the non-uniqueness regime [Sly--Sun, FOCS '12], and polynomial-time mixing at criticality (this work). Second, we prove an optimal $O(\log n)$ mixing time bound as well as an optimal $Ω(1)$ spectral gap for the Swendsen--Wang dynamics for the ferromagnetic Ising model with an external field on bounded-degree graphs. To the best of our knowledge, these are the first sharp bounds on the mixing rate of this classical global Markov chain beyond mean-field or strong spatial mixing (SSM) regimes, and resolve a conjecture of [Feng--Guo--Wang, IANDC '23]. A key ingredient in both proofs is a new family of localization schemes that extends the field dynamics of [Chen--Feng--Yin--Zhang, FOCS '21] by tilting general edge (or hyperedge) weights rather than vertex fields. This framework, which subsumes the classical Swendsen--Wang dynamics as a special case, extends the localization framework of [Chen--Eldan, FOCS '22] beyond stochastic and field localizations, and enables controlled tilting of interaction strengths while preserving external fields.