Related papers: Centroidal Voronoi Refinement in the Geometric Ref…
Purpose: The purpose of this work is to investigate the hypothesis that uniform sampling measurements that are endowed with antipodal symmetry play an important role when the raw data and image data are related through the Fourier…
The reconstruction of images from their corresponding noisy Radon transform is a typical example of an ill-posed linear inverse problem as arising in the application of computerized tomography (CT). As the (naive) solution does not depend…
Vision Transformer (ViT) architectures represent images as collections of high-dimensional vectorized tokens, each corresponding to a rectangular non-overlapping patch. This representation trades spatial granularity for embedding…
Owing to the natural interpretation and various desirable mathematical properties, centroidal Voronoi tessellations (CVT) have found a wide range of applications and correspondingly a vast development in their literature. However the…
Language models operate on discrete tokens but compute in continuous vector spaces, inducing a Voronoi tessellation over the representation manifold. We study this tessellation empirically on Qwen3.5-4B-Base, making two contributions.…
Shack Hartmann wavefront sensor is a two dimensional array of lenslets which is used to detect the incoming phase distorted wavefront through local tilt measurements made by recording the spot pattern near the focal plane. Wavefront…
We present a new solution framework to solve the generalized trust region subproblem (GTRS) of minimizing a quadratic objective over a quadratic constraint. More specifically, we derive a convex quadratic reformulation (CQR) via minimizing…
Vision Transformers (ViTs) achieve state-of-the-art performance on challenging vision tasks, but their deployment on edge devices is severely hindered by the computational complexity and global reduction bottleneck imposed by layer…
In this paper we develop a numerical method for solving a class of optimization problems known as optimal location or quantization problems. The target energy can be written either in terms of atomic measures and the Wasserstein distance or…
Gersho's conjecture in 3D asserts the asymptotic periodicity and structure of the optimal centroidal Voronoi tessellation. This relatively simple crystallization problem remains to date open. We prove bounds on the geometric complexity of…
Large pre-trained models have demonstrated extensive applications across various fields. However, fine-tuning these models for specific downstream tasks demands significant computational resources and storage. One fine-tuning method,…
The Voronoi Covariance Measure of a compact set K of R^d is a tensor-valued measure that encodes geometric information on K and which is known to be resilient to Hausdorff noise but sensitive to outliers. In this article, we generalize this…
Low-dose computed tomography (LDCT) reconstruction is fundamentally challenged by severe noise and compromised data fidelity under reduced radiation exposure. Most existing methods operate either in the image or post-log projection domain,…
Regularization is critical for solving ill-posed geophysical inverse problems. Explicit regularization is often used, but there are opportunities to explore the implicit regularization effects that are inherent in a Neural Network…
We propose a novel approach for 3D mesh reconstruction from multi-view images. Our method takes inspiration from large reconstruction models like LRM that use a transformer-based triplane generator and a Neural Radiance Field (NeRF) model…
Lost image areas with different size and arbitrary shape can occur in many scenarios such as error-prone communication, depth-based image rendering or motion compensated wavelet lifting. The goal of image reconstruction is to restore these…
Measurement-critical ultrasound tasks often depend on a small anatomical region, making global reconstruction metrics an unreliable proxy for clinical fidelity. We propose an ROI-aware representation learning framework and instantiate it…
Wavelet-based grid adaptation methods use multiresolution analysis for error estimation, offering a mathematically rigorous approach to adaptive grid refinement when solving Partial Differential Equations (PDEs). However, applying these…
Proximal gradient-based optimization is one of the most common strategies to solve inverse problem of images, and it is easy to implement. However, these techniques often generate heavy artifacts in image reconstruction. One of the most…
The iterative refinement method (IRM) has been very successfully applied in many different fields for examples the modern quantum chemical calculation and CT image reconstruction. It is proved that the refinement method can create an exact…