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This paper proposes a method for estimating a surface that contains a given set of points from noisy measurements. More precisely, by assuming that the surface is described by the zero set of a function in the span of a given set of…
We consider the problem of identifying the support of the block signal in a sequence when both the length and the location of the block signal are unknown. The multivariate version of this problem is also considered, in which we try to…
This article investigates the use of a model-based neural-network for the traffic reconstruction problem using noisy measurements coming from probe vehicles. The traffic state is assumed to be the density only, modeled by a partial…
We present a new idea that allows us to detect gravitational waves without being disturbed by any kind of displacement noise, based on the fact that gravitational waves and test-mass motions affect the propagations of light differently. We…
Object detection and recognition are important problems in computer vision. Since these problems are meta-heuristic, despite a lot of research, practically usable, intelligent, real-time, and dynamic object detection/recognition methods are…
Scattering obscures information carried by wave by producing a speckle pattern, posing a common challenge across various fields, including microscopy and astronomy. Traditional methods for extracting information from speckles often rely on…
This paper deals with impulse noise removal from color images. The proposed noise removal algorithm employs a novel approach with morphological filtering for color image denoising; that is, detection of corrupted pixels and removal of the…
Image denoising is a typical ill-posed problem due to complex degradation. Leading methods based on normalizing flows have tried to solve this problem with an invertible transformation instead of a deterministic mapping. However, the…
A new algorithm is developed to jointly recover a temporal sequence of images from noisy and under-sampled Fourier data. Specifically, we consider the case where each data set is missing vital information that prevents its (individual)…
Artificial objects usually have very stable shape features, which are stable, persistent properties in geometry. They can provide evidence for object recognition. Shape features are more stable and more distinguishing than appearance…
In this paper, we study a mixed variational problem subject to perturbations, where the noise term is modelled by means of a bilinear form that has to be understood to be "small" in some sense. Indeed, we consider a family of such problems…
In this paper we introduce and study a new feature-preserving nonlinear anisotropic diffusion for denoising signals. The proposed partial differential equation is based on a novel diffusivity coefficient that uses a nonlocal automatically…
This paper develops a new mathematical framework for denoising in blind two-dimensional (2D) super-resolution upon using the atomic norm. The framework denoises a signal that consists of a weighted sum of an unknown number of time-delayed…
Since time immemorial, noise has been a constant source of disturbance to the various entities known to mankind. Noise models of different kinds have been developed to study noise in more detailed fashion over the years. Image processing,…
We consider the problem of positioning a cloud of points in the Euclidean space $\mathbb{R}^d$, using noisy measurements of a subset of pairwise distances. This task has applications in various areas, such as sensor network localization and…
Symmetries are ubiquitous across all kinds of objects, whether in nature or in man-made creations. While these symmetries may seem intuitive to the human eye, detecting them with a machine is nontrivial due to the vast search space.…
Noise is a significant challenge in imaging. Conventional intensity-based techniques mitigate noise through various filtering methods, but they often require prior knowledge of noise characteristics and struggle, especially under low-light…
Diffusion models have found valuable applications in anomaly detection by capturing the nominal data distribution and identifying anomalies via reconstruction. Despite their merits, they struggle to localize anomalies of varying scales,…
The problem studied in this paper is ultrasound image reconstruction from frequency-domain measurements of the scattered field from an object with contrast in attenuation and sound speed. The case where the object has uniform but unknown…
In practice, images can contain different amounts of noise for different color channels, which is not acknowledged by existing super-resolution approaches. In this paper, we propose to super-resolve noisy color images by considering the…