Sunghwan Moon

Markus Haltmeier, Sunghwan Moon

Recovering a function from its spherical Radon transform with centers of spheres of integration restricted to a hypersurface is at the heart of several modern imaging technologies, including SAR, ultrasound imaging, and photo- and thermoacoustic tomography. In this paper we study an inversion of the spherical Radon transform with centers of integration restricted to cylindrical surfaces of the form $Γ\times \mathbb{R}^m$, where $Γ$ is a hypersurface in $\mathbb{R}^n$. We show that this transform can be decomposed into two lower dimensional spherical Radon transforms, one with centers on $Γ$ and one with a planar center-set in $\mathbb{R}^{m+1}$. Together with explicit inversion formulas for the spherical Radon transform with a planar center-set and existing algorithms for inverting the spherical Radon transform with a center-set $\mathbb{R}$, this yields reconstruction procedures for general cylindrical domains. In the special case of spherical or elliptical cylinders we obtain novel explicit inversion formulas. For three spatial dimensions, these inversion formulas can be implemented efficiently by backprojection type algorithms only requiring $\mathcal O(N^{4/3})$ floating point operations, where $N$ is the total number of unknowns to be recovered. We present numerical results demonstrating the efficiency of the derived algorithms.

Sunghwan Moon, Joonghyeok Heo

In recent years, many types of elliptical Radon transforms that integrate functions over various sets of ellipses/ellipsoids have been considered, relating to studies in bistatic synthetic aperture radar, ultrasound reflection tomography, radio tomography, and migration imaging. In this article, we consider the transform that integrates a given function in $\mathbf R^n$ over a set of ellipses (when $n=2$) or ellipsoids of rotation (when $n\geq 3$) with foci restricted to a hyperplane. We show a relation between this elliptical Radon transform and the regular Radon transform, and provide the inversion formula for the elliptical Radon transform using this relation. Numerical simulations are performed to demonstrate the suggested algorithms in two dimensions, and these simulations are also provided in this article.

Sunghwan Moon, Anwesa Dey, Souvik Roy

In photoacoustic tomography (PAT), a hybrid imaging modality that is based on the acoustic detection of optical absorption from biological tissue exposed to a pulsed laser, a short pulse laser generates an initial pressure proportional to the absorbed optical energy, which then propagates acoustically and is measured on the boundary. To account for the significant signal distortion caused by acoustic attenuation in biological tissue, we model PAT in heterogeneous media using a damped wave equation featuring spatially varying sound speed and a time-dependent damping term. Under natural assumptions, we show that the initial pressure is uniquely determined by the boundary measurements using a harmonic extension of the boundary data with energy decay. For constant damping, an expansion in Dirichlet eigenfunctions of $-c^2(\xx)Δ$ leads to an explicit series reconstruction formula for the initial pressure. Finally, we develop a gradient free numerical method based on the Pontryagin's maximum principle to provide a robust and computationally viable approach to image reconstruction in attenuating PAT.

Mingyu Sung, Vikas Palakonda, Suhwan Im et al.

Large language models (LLMs) have achieved near-human performance across diverse reasoning tasks, yet their deployment on resource-constrained Internet-of-Things (IoT) devices remains impractical due to massive parameter footprints and memory-intensive autoregressive decoding. While split computing offers a promising solution by partitioning model execution between edge devices and cloud servers, existing approaches fail to address the unique challenges of autoregressive inference, particularly the iterative token generation process and expanding key-value (KV) cache requirements. This work introduces the first autoregressive-aware split computing framework designed explicitly for LLM deployment on edge devices. Our approach makes three key contributions. First, we develop one-point split compression (OPSC), a mixed-precision quantization scheme that prevents out-of-memory failures by strategically partitioning models into front-end and back-end segments with different precision levels. Second, we propose a two-stage intermediate compression pipeline that combines threshold splitting (TS) and token-wise adaptive bit quantization (TAB-Q) to preserve accuracy-critical activations while dramatically reducing communication overhead. Third, we formulate a unified optimization framework that jointly selects optimal split points, quantization settings, and sequence lengths to satisfy strict memory and latency constraints. Extensive evaluations across diverse LLMs and hardware platforms demonstrate superior performance compared to state-of-the-art quantization methods, including SmoothQuant, OmniQuant, and Atom. The framework achieves a 1.49 inference speedup and significant communication overhead reduction while maintaining or improving model accuracy.

Jae-Mo Kang, Sunghwan Moon

Neural networks have shown high successful performance in a wide range of tasks, but further studies are needed to improve its performance. We analyze the approximation error of the specific neural network architecture with a local connection and higher application than one with the full connection because the local-connected network can be used to explain diverse neural networks such as CNNs. Our error estimate depends on two parameters: one controlling the depth of the hidden layer, and the other, the width of the hidden layers.

Markus Haltmeier, Sunghwan Moon, Daniela Schiefeneder

The Compton camera is a promising alternative to the Anger camera for imaging gamma radiation, with the potential to significantly increase the sensitivity of SPECT. Two-dimensional Compton camera image reconstruction can be implemented by inversion of the V-line transform, which integrates the emission distribution over V-lines (unions of two half-lines), that have vertices on a surrounding detector array. Inversion of the V-line transform without attenuation has recently been addressed by several authors. However, it is well known from standard SPECT that ignoring attenuation can significantly degrade the quality of the reconstructed image. In this paper we address this issue and study the attenuated V-line transform accounting for attenuation of photons in SPECT with Compton cameras. We derive an analytic inversion approach based on circular harmonics expansion, and show uniqueness of reconstruction for the attenuated V-line transform. We further develop a discrete image reconstruction algorithm based on our analytic studies, and present numerical results that demonstrate the effectiveness of our algorithm.