Seonho Kim

Seonho Kim, Kiryung Lee

We consider regression of a max-affine model that produces a piecewise linear model by combining affine models via the max function. The max-affine model ubiquitously arises in applications in signal processing and statistics including multiclass classification, auction problems, and convex regression. It also generalizes phase retrieval and learning rectifier linear unit activation functions. We present a non-asymptotic convergence analysis of gradient descent (GD) and mini-batch stochastic gradient descent (SGD) for max-affine regression when the model is observed at random locations following the sub-Gaussianity and an anti-concentration with additive sub-Gaussian noise. Under these assumptions, a suitably initialized GD and SGD converge linearly to a neighborhood of the ground truth specified by the corresponding error bound. We provide numerical results that corroborate the theoretical finding. Importantly, SGD not only converges faster in run time with fewer observations than alternating minimization and GD in the noiseless scenario but also outperforms them in low-sample scenarios with noise.

SiYeoul Lee, SeonHo Kim, Minkyung Seo et al.

This study introduces a motion-based learning network with a global-local self-attention module (MoGLo-Net) to enhance 3D reconstruction in handheld photoacoustic and ultrasound (PAUS) imaging. Standard PAUS imaging is often limited by a narrow field of view and the inability to effectively visualize complex 3D structures. The 3D freehand technique, which aligns sequential 2D images for 3D reconstruction, faces significant challenges in accurate motion estimation without relying on external positional sensors. MoGLo-Net addresses these limitations through an innovative adaptation of the self-attention mechanism, which effectively exploits the critical regions, such as fully-developed speckle area or high-echogenic tissue area within successive ultrasound images to accurately estimate motion parameters. This facilitates the extraction of intricate features from individual frames. Additionally, we designed a patch-wise correlation operation to generate a correlation volume that is highly correlated with the scanning motion. A custom loss function was also developed to ensure robust learning with minimized bias, leveraging the characteristics of the motion parameters. Experimental evaluations demonstrated that MoGLo-Net surpasses current state-of-the-art methods in both quantitative and qualitative performance metrics. Furthermore, we expanded the application of 3D reconstruction technology beyond simple B-mode ultrasound volumes to incorporate Doppler ultrasound and photoacoustic imaging, enabling 3D visualization of vasculature. The source code for this study is publicly available at: https://github.com/guhong3648/US3D

SeonYeong Lee, EonSeung Seong, DongEon Lee et al.

Digital pathology images play a crucial role in medical diagnostics, but their ultra-high resolution and large file sizes pose significant challenges for storage, transmission, and real-time visualization. To address these issues, we propose CLERIC, a novel deep learning-based image compression framework designed specifically for whole slide images (WSIs). CLERIC integrates a learnable lifting scheme and advanced convolutional techniques to enhance compression efficiency while preserving critical pathological details. Our framework employs a lifting-scheme transform in the analysis stage to decompose images into low- and high-frequency components, enabling more structured latent representations. These components are processed through parallel encoders incorporating Deformable Residual Blocks (DRB) and Recurrent Residual Blocks (R2B) to improve feature extraction and spatial adaptability. The synthesis stage applies an inverse lifting transform for effective image reconstruction, ensuring high-fidelity restoration of fine-grained tissue structures. We evaluate CLERIC on a digital pathology image dataset and compare its performance against state-of-the-art learned image compression (LIC) models. Experimental results demonstrate that CLERIC achieves superior rate-distortion (RD) performance, significantly reducing storage requirements while maintaining high diagnostic image quality. Our study highlights the potential of deep learning-based compression in digital pathology, facilitating efficient data management and long-term storage while ensuring seamless integration into clinical workflows and AI-assisted diagnostic systems. Code and models are available at: https://github.com/pnu-amilab/CLERIC.

Minoh Jeong, Seonho Kim, Alfred Hero

Deterministic embeddings learned by contrastive learning (CL) methods such as SimCLR and SupCon achieve state-of-the-art performance but lack a principled mechanism for uncertainty quantification. We propose Variational Contrastive Learning (VCL), a decoder-free framework that maximizes the evidence lower bound (ELBO) by interpreting the InfoNCE loss as a surrogate reconstruction term and adding a KL divergence regularizer to a uniform prior on the unit hypersphere. We model the approximate posterior $q_θ(z|x)$ as a projected normal distribution, enabling the sampling of probabilistic embeddings. Our two instantiation--VSimCLR and VSupCon--replace deterministic embeddings with samples from $q_θ(z|x)$ and incorporate a normalized KL term into the loss. Experiments on multiple benchmarks demonstrate that VCL mitigates dimensional collapse, enhances mutual information with class labels, and matches or outperforms deterministic baselines in classification accuracy, all the while providing meaningful uncertainty estimates through the posterior model. VCL thus equips contrastive learning with a probabilistic foundation, serving as a new basis for contrastive approaches.

Qi Li, Shaheer U. Saeed, Yuliang Huang et al.

Trackerless freehand ultrasound reconstruction aims to reconstruct 3D volumes from sequences of 2D ultrasound images without relying on external tracking systems. By eliminating the need for optical or electromagnetic trackers, this approach offers a low-cost, portable, and widely deployable alternative to more expensive volumetric ultrasound imaging systems, particularly valuable in resource-constrained clinical settings. However, predicting long-distance transformations and handling complex probe trajectories remain challenging. The TUS-REC2024 Challenge establishes the first benchmark for trackerless 3D freehand ultrasound reconstruction by providing a large publicly available dataset, along with a baseline model and a rigorous evaluation framework. By the submission deadline, the Challenge had attracted 43 registered teams, of which 6 teams submitted 21 valid dockerized solutions. The submitted methods span a wide range of approaches, including the state space model, the recurrent model, the registration-driven volume refinement, the attention mechanism, and the physics-informed model. This paper provides a comprehensive background introduction and literature review in the field, presents an overview of the challenge design and dataset, and offers a comparative analysis of submitted methods across multiple evaluation metrics. These analyses highlight both the progress and the current limitations of state-of-the-art approaches in this domain and provide insights for future research directions. All data and code are publicly available to facilitate ongoing development and reproducibility. As a live and evolving benchmark, it is designed to be continuously iterated and improved. The Challenge was held at MICCAI 2024 and is organised again at MICCAI 2025, reflecting its sustained commitment to advancing this field.

Haitham Kanj, Seonho Kim, Kiryung Lee

This paper presents Sparse Gradient Descent as a solution for variable selection in convex piecewise linear regression, where the model is given as the maximum of $k$-affine functions $ x \mapsto \max_{j \in [k]} \langle a_j^\star, x \rangle + b_j^\star$ for $j = 1,\dots,k$. Here, $\{ a_j^\star\}_{j=1}^k$ and $\{b_j^\star\}_{j=1}^k$ denote the ground-truth weight vectors and intercepts. A non-asymptotic local convergence analysis is provided for Sp-GD under sub-Gaussian noise when the covariate distribution satisfies the sub-Gaussianity and anti-concentration properties. When the model order and parameters are fixed, Sp-GD provides an $ε$-accurate estimate given $\mathcal{O}(\max(ε^{-2}σ_z^2,1)s\log(d/s))$ observations where $σ_z^2$ denotes the noise variance. This also implies the exact parameter recovery by Sp-GD from $\mathcal{O}(s\log(d/s))$ noise-free observations. The proposed initialization scheme uses sparse principal component analysis to estimate the subspace spanned by $\{ a_j^\star\}_{j=1}^k$, then applies an $r$-covering search to estimate the model parameters. A non-asymptotic analysis is presented for this initialization scheme when the covariates and noise samples follow Gaussian distributions. When the model order and parameters are fixed, this initialization scheme provides an $ε$-accurate estimate given $\mathcal{O}(ε^{-2}\max(σ_z^4,σ_z^2,1)s^2\log^4(d))$ observations. A new transformation named Real Maslov Dequantization (RMD) is proposed to transform sparse generalized polynomials into sparse max-affine models. The error decay rate of RMD is shown to be exponentially small in its temperature parameter. Furthermore, theoretical guarantees for Sp-GD are extended to the bounded noise model induced by RMD. Numerical Monte Carlo results corroborate theoretical findings for Sp-GD and the initialization scheme.

Seonho Kim, Sohail Bahmani, Kiryung Lee

We consider the multivariate max-linear regression problem where the model parameters $\boldsymbolβ_{1},\dotsc,\boldsymbolβ_{k}\in\mathbb{R}^{p}$ need to be estimated from $n$ independent samples of the (noisy) observations $y = \max_{1\leq j \leq k} \boldsymbolβ_{j}^{\mathsf{T}} \boldsymbol{x} + \mathrm{noise}$. The max-linear model vastly generalizes the conventional linear model, and it can approximate any convex function to an arbitrary accuracy when the number of linear models $k$ is large enough. However, the inherent nonlinearity of the max-linear model renders the estimation of the regression parameters computationally challenging. Particularly, no estimator based on convex programming is known in the literature. We formulate and analyze a scalable convex program given by anchored regression (AR) as the estimator for the max-linear regression problem. Under the standard Gaussian observation setting, we present a non-asymptotic performance guarantee showing that the convex program recovers the parameters with high probability. When the $k$ linear components are equally likely to achieve the maximum, our result shows a sufficient number of noise-free observations for exact recovery scales as {$k^{4}p$} up to a logarithmic factor. { This sample complexity coincides with that by alternating minimization (Ghosh et al., {2021}). Moreover, the same sample complexity applies when the observations are corrupted with arbitrary deterministic noise. We provide empirical results that show that our method performs as our theoretical result predicts, and is competitive with the alternating minimization algorithm particularly in presence of multiplicative Bernoulli noise. Furthermore, we also show empirically that a recursive application of AR can significantly improve the estimation accuracy.}