Related papers: Random matrix route to image denoising

We study the high-dimensional inference of a rank-one signal corrupted by sparse noise. The noise is modelled as the adjacency matrix of a weighted undirected graph with finite average connectivity in the large size limit. Using the replica…

This paper investigates the classical statistical signal processing problem of detecting a signal in the presence of colored noise with an unknown covariance matrix. In particular, we consider a scenario where m-dimensional p possible…

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,…

The details of an image with noise may be restored by removing noise through a suitable image de-noising method. In this research, a new method of image de-noising based on using median filter (MF) in the wavelet domain is proposed and…

Deep image denoising networks have achieved impressive success with the help of a considerably large number of synthetic train datasets. However, real-world denoising is a still challenging problem due to the dissimilarity between…

We present a comparison between various algorithms of inference of covariance and precision matrices in small datasets of real vectors, of the typical length and dimension of human brain activity time series retrieved by functional Magnetic…

Image denoising can be described as the problem of mapping from a noisy image to a noise-free image. The best currently available denoising methods approximate this mapping with cleverly engineered algorithms. In this work we attempt to…

Here we consider the problem of denoising features associated to complex data, modeled as signals on a graph, via a smoothness prior. This is motivated in part by settings such as single-cell RNA where the data is very high-dimensional, but…

We propose a novel probabilistic method for detection of objects in noisy images. The method uses results from percolation and random graph theories. We present an algorithm that allows to detect objects of unknown shapes in the presence of…

We propose a novel approach to video anomaly detection: we treat feature vectors extracted from videos as realizations of a random variable with a fixed distribution and model this distribution with a neural network. This lets us estimate…

Deep neural networks have been successfully applied to a broad range of problems where overparametrization yields weight matrices which are partially random. A comparison of weight matrix singular vectors to the Porter-Thomas distribution…

Supervised training for real-world denoising presents challenges due to the difficulty of collecting large datasets of paired noisy and clean images. Recent methods have attempted to address this by utilizing unpaired datasets of clean and…

Image denoising is a fundamental problem in computer vision and medical imaging. However, real-world images are often degraded by structured noise with strong anisotropic correlations that existing methods struggle to remove. Most…

A new image denoising algorithm to deal with the additive Gaussian white noise model is given. Like the non-local means method, the filter is based on the weighted average of the observations in a neighborhood, with weights depending on the…

Random matrix theory (RMT) combined with principal component analysis has resulted in a widely used MPPCA noise mapping and denoising algorithm, that utilizes the redundancy in multiple acquisitions and in local image patches. RMT-based…

We propose a data-dependent denoising procedure to restore noisy images. Different from existing denoising algorithms which search for patches from either the noisy image or a generic database, the new algorithm finds patches from a…

Deconvolution is a statistical inverse problem to estimate the distribution of a random variable based on its noisy observations. Despite the extensive studies on the topic, deconvolution with unknown noise distribution remains as a…

Removal or cancellation of noise has wide-spread applications for imaging and acoustics. In every-day-life applications, denoising may even include generative aspects, which are unfaithful to the ground truth. For scientific use, however,…

The original contributions of this paper are twofold: a new understanding of the influence of noise on the eigenvectors of the graph Laplacian of a set of image patches, and an algorithm to estimate a denoised set of patches from a noisy…

Sampling and quantization are standard practices in signal and image processing, but a theoretical understanding of their impact is incomplete. We consider discrete image registration when the underlying function is a one-dimensional…