Tootfinder

Regularization of Inverse Problems by Filtered Diagonal Frame Decomposition under general source
Dang Duc Trong, Nguyen Dang Minh, Luu Xuan Thang, Luu Dang Khoa
https://arxiv.org/abs/2507.23651

Regularization of Inverse Problems by Filtered Diagonal Frame Decomposition under general source
Let $X$ and $Y$ be Hilbert spaces, and $\mathbf{K}: \text{dom} \mathbf{K} \subset X \to Y$ a bounded linear operator. This paper addresses the inverse problem $\mathbf{K}x = y$, where exact data $y$ is replaced by noisy data $y^δ$ satisfying $\|y^δ- y\|_Y \leq δ$. Due to the ill-posedness of such problems, we employ regularization methods to stabilize solutions. While singular value decomposition (SVD) provides a classical approach, its computation can be costly and impractical for…

TotalRegistrator: Towards a Lightweight Foundation Model for CT Image Registration
Xuan Loc Pham, Gwendolyn Vuurberg, Marjan Doppen, Joey Roosen, Tip Stille, Thi Quynh Ha, Thuy Duong Quach, Quoc Vu Dang, Manh Ha Luu, Ewoud J. Smit, Hong Son Mai, Mattias Heinrich, Bram van Ginneken, Mathias Prokop, Alessa Hering
https://arxiv.org/abs/2508.0…

TotalRegistrator: Towards a Lightweight Foundation Model for CT Image Registration
Image registration is a fundamental technique in the analysis of longitudinal and multi-phase CT images within clinical practice. However, most existing methods are tailored for single-organ applications, limiting their generalizability to other anatomical regions. This work presents TotalRegistrator, an image registration framework capable of aligning multiple anatomical regions simultaneously using a standard UNet architecture and a novel field decomposition strategy. The model is lightweight…

Recovery of initial displacement and velocity in anisotropic elastic systems by the time dimensional reduction method
Trong D. Dang, Chanh V. Le, Khoa D. Luu, Loc H Nguyen
https://arxiv.org/abs/2506.13000

Recovery of initial displacement and velocity in anisotropic elastic systems by the time dimensional reduction method
We introduce a time-dimensional reduction method for the inverse source problem in linear elasticity, where the goal is to reconstruct the initial displacement and velocity fields from partial boundary measurements of elastic wave propagation. The key idea is to employ a novel spectral representation in time, using an orthonormal basis composed of Legendre polynomials weighted by exponential functions. This Legendre polynomial-exponential basis enables a stable and accurate decomposition in the…