Xiaoqian Xu

Xiaoqian Xu, Pengxu Wei, Weikai Chen et al.

Due to the sophisticated imaging process, an identical scene captured by different cameras could exhibit distinct imaging patterns, introducing distinct proficiency among the super-resolution (SR) models trained on images from different devices. In this paper, we investigate a novel and practical task coded cross-device SR, which strives to adapt a real-world SR model trained on the paired images captured by one camera to low-resolution (LR) images captured by arbitrary target devices. The proposed task is highly challenging due to the absence of paired data from various imaging devices. To address this issue, we propose an unsupervised domain adaptation mechanism for real-world SR, named Dual ADversarial Adaptation (DADA), which only requires LR images in the target domain with available real paired data from a source camera. DADA employs the Domain-Invariant Attention (DIA) module to establish the basis of target model training even without HR supervision. Furthermore, the dual framework of DADA facilitates an Inter-domain Adversarial Adaptation (InterAA) in one branch for two LR input images from two domains, and an Intra-domain Adversarial Adaptation (IntraAA) in two branches for an LR input image. InterAA and IntraAA together improve the model transferability from the source domain to the target. We empirically conduct experiments under six Real to Real adaptation settings among three different cameras, and achieve superior performance compared with existing state-of-the-art approaches. We also evaluate the proposed DADA to address the adaptation to the video camera, which presents a promising research topic to promote the wide applications of real-world super-resolution. Our source code is publicly available at https://github.com/lonelyhope/DADA.git.

Lei Li, Xiaoqian Xu, Saverio E. Spagnolie

The level set method commonly requires a reinitialization of the level set function due to interface motion and deformation. We extend the traditional technique for reinitializing the level set function to a method that preserves the interface gradient. The gradient of the level set function represents the stretching of the interface, which is of critical importance in many physical applications. The proposed locally gradient-preserving reinitialization (LGPR) method involves the solution of three PDEs of Hamilton-Jacobi type in succession; first the signed distance function is found using a traditional reinitialization technique, then the interface gradient is extended into the domain by a transport equation, and finally the new level set function is achieved with the solution of a generalized reinitialization equation. We prove the well-posedness of the Hamilton-Jacobi equations, with possibly discontinuous Hamiltonians, and propose numerical schemes for their solutions. A subcell resolution technique is used in the numerical solution of the transport equation to extend data away from the interface directly with high accuracy. The reinitialization technique is computationally inexpensive if the PDEs are solved only in a small band surrounding the interface. As an important application, the LGPR method will enable the application of the local level set approach to the Eulerian Immersed boundary method.

Chenyang An, Xiaoqian Xu

We establish explicit lower bounds for advection-diffusion equations in three settings: a polynomial $\dot H^{-1}$ bound for inviscid shears with $u\in L^\infty_t W^{1,1}_y$, a uniform positive lower bound on the mixing scale for diffusive shears, and an exponential $L^2$ bound for rapidly oscillating time-periodic flows. All constants are explicit in the data. The proofs were generated entirely by a multi-agent math proving system, QED, without expert human intervention, serving as a test of AI's capability to produce rigorous mathematics.