Gyeongha Hwang

Yucheol Jung, Hyomin Kim, Gyeongha Hwang et al.

In 3D shape reconstruction based on template mesh deformation, a regularization, such as smoothness energy, is employed to guide the reconstruction into a desirable direction. In this paper, we highlight an often overlooked property in the regularization: the vertex density in the mesh. Without careful control on the density, the reconstruction may suffer from under-sampling of vertices near shape details. We propose a novel mesh density adaptation method to resolve the under-sampling problem. Our mesh density adaptation energy increases the density of vertices near complex structures via deformation to help reconstruction of shape details. We demonstrate the usability and performance of mesh density adaptation with two tasks, inverse rendering and non-rigid surface registration. Our method produces more accurate reconstruction results compared to the cases without mesh density adaptation.

Markus Haltmeier, Lukas Neumann, Nadja Gruber et al.

Machine learning has achieved impressive performance in tomographic reconstruction, but supervised training requires paired measurements and ground-truth images that are often unavailable. This has motivated self-supervised approaches, which have primarily addressed denoising and, more recently, linear inverse problems. We address nonlinear inverse problems and introduce SPLIT (Self-supervised Partitioning for Learned Inversion in Nonlinear Tomography), a self-supervised machine-learning framework for reconstructing images from nonlinear, incomplete, and noisy projection data without any samples of ground-truth images. SPLIT enforces cross-partition consistency and measurement-domain fidelity while exploiting complementary information across multiple partitions. Our main theoretical result shows that, under mild conditions, the proposed self-supervised objective is equivalent to its supervised counterpart in expectation. We regularize training with an automatic stopping rule that halts optimization when a no-reference image-quality surrogate saturates. As a concrete application, we derive SPLIT variants for multispectral computed tomography. Experiments on sparse-view acquisitions demonstrate high reconstruction quality and robustness to noise, surpassing classical iterative reconstruction and recent self-supervised baselines.

Markus Haltmeier, Nadja Gruber, Gyeongha Hwang

Photoacoustic tomography (PAT) is an emerging imaging modality that combines the complementary strengths of optical contrast and ultrasonic resolution. A central task is image reconstruction, where measured acoustic signals are used to recover the initial pressure distribution. For ideal point-like or line-like detectors, several efficient and fast reconstruction algorithms exist, including Fourier methods, filtered backprojection, and time reversal. However, when applied to data acquired with finite-size detectors, these methods yield systematically blurred images. Although sharper images can be obtained by compensating for finite-detector effects, supervised learning approaches typically require ground-truth images that may not be available in practice. We propose a self-supervised reconstruction method based on Noisier2Inverse that addresses finite-size detector effects without requiring ground-truth data. Our approach operates directly on noisy measurements and learns to recover high-quality PAT images in a ground-truth-free manner. Its key components are: (i) PAT-specific modeling that recasts the problem as angular deblurring; (ii) a Noisier2Inverse formulation in the polar domain that leverages the known angular point-spread function; and (iii) a novel, statistically grounded early-stopping rule. In experiments, the proposed method consistently outperforms alternative approaches that do not use supervised data and achieves performance close to supervised benchmarks, while remaining practical for real acquisitions with finite-size detectors.

Gyeongha Hwang, Bradley Thomas Wolfe, Naima Naheed

This paper documents the implementation and evaluation of a self-supervised denoising framework on Inertial Confinement Fusion (ICF) images corrupted by Multiplicative Uniform noise: the \emph{Log-Domain Noisier2Inverse} framework. This framework is developed and analysed in this work; the key theoretical result -- that minimising the log-domain self-supervised loss is equivalent to supervised learning in the transformed domain -- is presented with full proof. We document significant implementation challenges arising from the unique characteristics of ICF imagery, describe the fixes applied at each stage, and report final quantitative results. The log-domain approach with per-image JSON Uniform noise loading (Variant~B) achieves the best result: a mean PSNR of $21.41\db$ and SSIM of $0.8358$, a $+19.46\db$ improvement over the noisy input baseline of $1.95\db$, substantially outperforming BM3D log-domain ($4.47\db$, SSIM $0.5181$) and Noise2Self ($4.75\db$, SSIM $0.0177$). Variant~A, using fixed Gaussian noise loading, achieves $21.39\db$ PSNR and SSIM $0.8436$. Of the three evaluated methods, Log-Domain Noisier2Inverse and Noise2Self are entirely self-supervised during training, requiring no clean ground truth data; BM3D is a classical filter-based method requiring no training at all. The clean reference images are used solely for quantitative evaluation of all three methods.

Markus Haltmeier, Gyeongha Hwang

Inverse problems are inherently ill-posed, suffering from non-uniqueness and instability. Classical regularization methods provide mathematically well-founded solutions, ensuring stability and convergence, but often at the cost of reduced flexibility or visual quality. Learned reconstruction methods, such as convolutional neural networks, can produce visually compelling results, yet they typically lack rigorous theoretical guarantees. DC (DC) networks address this gap by enforcing the measurement model within the network architecture. In particular, null-space networks combined with a classical regularization method as an initial reconstruction define a convergent regularization method. This approach preserves the theoretical reliability of classical schemes while leveraging the expressive power of data-driven learning, yielding reconstructions that are both accurate and visually appealing.