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The Monotonocity Principle (MP), stating a monotonic relationship between a material property and a proper corresponding boundary operator, is attracting great interest in the field of inverse problems, because of its fundamental role in…

Convolutional Neural Networks (ConvNets) have successfully contributed to improve the accuracy of regression-based methods for computer vision tasks such as human pose estimation, landmark localization, and object detection. The network…

Many datasets can be viewed as a noisy sampling of an underlying space, and tools from topological data analysis can characterize this structure for the purpose of knowledge discovery. One such tool is persistent homology, which provides a…

Topological methods, including persistent homology, are powerful tools for analysis of high-dimensional data sets but these methods rely almost exclusively on thresholding techniques. In noisy data sets, thresholding does not always allow…

Subspace learning is an important problem, which has many applications in image and video processing. It can be used to find a low-dimensional representation of signals and images. But in many applications, the desired signal is heavily…

The piecewise constant Mumford-Shah (PCMS) model and the Rudin-Osher-Fatemi (ROF) model are two important variational models in image segmentation and image restoration, respectively. In this paper, we explore a linkage between these…

In this study, we investigate the inverse source problem arising in bioluminescence tomography, the objective of which is to reconstruct both the support and the intensity of an internal light source from boundary measurements governed by…

Point clouds obtained with 3D scanners or by image-based reconstruction techniques are often corrupted with significant amount of noise and outliers. Traditional methods for point cloud denoising largely rely on local surface fitting (e.g.,…

Methods based on diffusion models (DMs) for solving inverse problems (IPs) have recently achieved remarkable performance. However, DM-based methods typically struggle against outliers, which are common in real-world measurements. In this…

This paper presents a quarter Laplacian filter that can preserve corners and edges during image smoothing. Its support region is $2\times2$, which is smaller than the $3\times3$ support region of Laplacian filter. Thus, it is more local.…

We propose a robust and scalable procedure for general optimization and inference problems on manifolds leveraging the classical idea of `median-of-means' estimation. This is motivated by ubiquitous examples and applications in modern data…

We present a new inner-outer iterative algorithm for edge enhancement in imaging problems. At each outer iteration, we formulate a Tikhonov-regularized problem where the penalization is expressed in the 2-norm and involves a regularization…

Along with recent diffusion models, randomized smoothing has become one of a few tangible approaches that offers adversarial robustness to models at scale, e.g., those of large pre-trained models. Specifically, one can perform randomized…

Establishing the correspondence between two images is an important research direction of computer vision. When estimating the relationship between two images, it is often disturbed by outliers. In this paper, we propose a convolutional…

Ultra-high-definition (UHD) image restoration is vital for applications demanding exceptional visual fidelity, yet existing methods often face a trade-off between restoration quality and efficiency, limiting their practical deployment. In…

Purpose: To develop a synergistic image reconstruction framework that exploits multicontrast (MC), multicoil, and compressed sensing (CS) redundancies in magnetic resonance imaging (MRI). Approach: CS, MC acquisition, and parallel imaging…

This paper investigates a fully unsupervised statistical method for edge preserving image restoration and compression using a spatial decomposition scheme. Smoothed maximum likelihood is used for local estimation of edge pixels from mixture…

In the emerging advancement in the branch of autonomous robotics, the ability of a robot to efficiently localize and construct maps of its surrounding is crucial. This paper deals with utilizing thermal-infrared cameras, as opposed to…

Optimization, a key tool in machine learning and statistics, relies on regularization to reduce overfitting. Traditional regularization methods control a norm of the solution to ensure its smoothness. Recently, topological methods have…

Image deblurring aims to restore the detailed texture information or structures from blurry images, which has become an indispensable step in many computer vision tasks. Although various methods have been proposed to deal with the image…