Santiago Lopez-Tapia

Jiaqi Guo, Santiago Lopez-Tapia, Wing Shun Li et al.

Computed tomography is a widely used imaging modality with applications ranging from medical imaging to material analysis. One major challenge arises from the lack of scanning information at certain angles, resulting in distortion or artifacts in the reconstructed images. This is referred to as the Limited Angle Computed Tomography (LACT) reconstruction problem. To address this problem, we propose the use of Residual Null-Space Diffusion Stochastic Differential Equations (RN-SDEs), which are a variant of diffusion models that characterize the diffusion process with mean-reverting (MR) stochastic differential equations. To demonstrate the generalizability of RN-SDEs, we conducted experiments with two different LACT datasets, ChromSTEM and C4KC-KiTS. Through extensive experiments, we demonstrate that by leveraging learned MR-SDEs as a prior and emphasizing data consistency using Range-Null Space Decomposition (RNSD) based rectification, we can recover high-quality images from severely degraded ones and achieve state-of-the-art performance in most LACT tasks. Additionally, we present a quantitative comparison of RN-SDE with other networks, in terms of computational complexity and runtime efficiency, highlighting the superior effectiveness of our proposed approach.

Manuel Ballester, Santiago Lopez-Tapia, Seth Gossage et al.

Stellar astrophysics relies critically on accurate descriptions of the physical conditions inside stars. Traditional solvers such as \texttt{MESA} (Modules for Experiments in Stellar Astrophysics), which employ adaptive finite-difference methods, can become computationally expensive and challenging to scale for large stellar population synthesis ($>10^9$ stars). In this work, we present an self-supervised physics-informed neural network (PINN) framework that provides a mesh-free and fully differentiable approach to solving the stellar structure equations under hydrostatic and thermal equilibrium. The model takes as input the stellar boundary conditions (at the center and surface) together with the chemical composition, and learns continuous radial profiles for mass $M_r(r)$, pressure $P(r)$, density $ρ(r)$, temperature $T(r)$, and luminosity $L_r(r)$ by enforcing the governing structure equations through physics-based loss terms. To incorporate realistic microphysics, we introduce auxiliary neural networks that approximate the equation of state and opacity tables as smooth, differentiable functions of the local thermodynamic state. These surrogates replace traditional tabulated inputs and enable end-to-end training. Once trained for a given star, the model produces continuous solutions across the entire radial domain without requiring discretization or interpolation. Validation against benchmark \texttt{MESA} models across a range of stellar masses yields a Mean Relative Absolute Error of $3.06\%$ and an average $R^2$ score of $99.98\%$. To our knowledge, this is the first demonstration that the stellar structure equations can be solved in a fully self-supervised and data-free fashion employing PINNs. This work establishes a foundation for scalable, physics-informed emulation of stellar interiors and opens the door to future extensions toward time-dependent stellar evolution.

Zhihao Huang, Santiago Lopez-Tapia, Aggelos K. Katsaggelos

Video deblurring is a challenging task that aims to recover sharp sequences from blur and noisy observations. The image-formation model plays a crucial role in traditional model-based methods, constraining the possible solutions. However, this is only the case for some deep learning-based methods. Despite deep-learning models achieving better results, traditional model-based methods remain widely popular due to their flexibility. An increasing number of scholars combine the two to achieve better deblurring performance. This paper proposes introducing knowledge of the image-formation model into a deep learning network by using the pseudo-inverse of the blur. We use a deep network to fit the blurring and estimate pseudo-inverse. Then, we use this estimation, combined with a variational deep-learning network, to deblur the video sequence. Notably, our experimental results demonstrate that such modifications can significantly improve the performance of deep learning models for video deblurring. Furthermore, our experiments on different datasets achieved notable performance improvements, proving that our proposed method can generalize to different scenarios and cameras.

Jiaqi Guo, Santiago Lopez-Tapia, Aggelos K. Katsaggelos

Limited Angle Computed Tomography (LACT) often faces significant challenges due to missing angular information. Unlike previous methods that operate in the image domain, we propose a new method that focuses on sinogram inpainting. We leverage MR-SDEs, a variant of diffusion models that characterize the diffusion process with mean-reverting stochastic differential equations, to fill in missing angular data at the projection level. Furthermore, by combining distillation with constraining the output of the model using the pseudo-inverse of the inpainting matrix, the diffusion process is accelerated and done in a step, enabling efficient and accurate sinogram completion. A subsequent post-processing module back-projects the inpainted sinogram into the image domain and further refines the reconstruction, effectively suppressing artifacts while preserving critical structural details. Quantitative experimental results demonstrate that the proposed method achieves state-of-the-art performance in both perceptual and fidelity quality, offering a promising solution for LACT reconstruction in scientific and clinical applications.

Alice Lucas, Santiago Lopez-Tapia, Rafael Molina et al.

While Convolutional Neural Networks (CNNs) trained for image and video super-resolution (SR) regularly achieve new state-of-the-art performance, they also suffer from significant drawbacks. One of their limitations is their lack of robustness to unseen image formation models during training. Other limitations include the generation of artifacts and hallucinated content when training Generative Adversarial Networks (GANs) for SR. While the Deep Learning literature focuses on presenting new training schemes and settings to resolve these various issues, we show that one can avoid training and correct for SR results with a fully self-supervised fine-tuning approach. More specifically, at test time, given an image and its known image formation model, we fine-tune the parameters of the trained network and iteratively update them using a data fidelity loss. We apply our fine-tuning algorithm on multiple image and video SR CNNs and show that it can successfully correct for a sub-optimal SR solution by entirely relying on internal learning at test time. We apply our method on the problem of fine-tuning for unseen image formation models and on removal of artifacts introduced by GANs.