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We consider the problem of finding the subset of order statistics that contains the most information about a sample of random variables drawn independently from some known parametric distribution. We leverage information-theoretic…
In the study of condensed matter physics, spectral information plays an important role for understand the mechanism of materials. However, it is difficult to obtain the spectrum directly through experiments or simulation. For example, the…
Fully supervised deep-learning based denoisers are currently the most performing image denoising solutions. However, they require clean reference images. When the target noise is complex, e.g. composed of an unknown mixture of primary…
We consider the inverse problem of recovering a continuous-domain function from a finite number of noisy linear measurements. The unknown signal is modeled as the sum of a slowly varying trend and a periodic or quasi-periodic seasonal…
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,…
Tweedie distributions are a special case of exponential dispersion models, which are often used in classical statistics as distributions for generalized linear models. Here, we reveal that Tweedie distributions also play key roles in modern…
When capturing and storing images, devices inevitably introduce noise. Reducing this noise is a critical task called image denoising. Deep learning has become the de facto method for image denoising, especially with the emergence of…
Density estimation is a fundamental problem that arises in many areas of astronomy, with applications ranging from selecting quasars using color distributions to characterizing stellar abundances. Astronomical observations are inevitably…
We consider the very challenging task of restoring images (i) which have a large number of missing pixels, (ii) whose existing pixels are corrupted by noise and (iii) the ideal image to be restored contains both cartoon and texture…
Digital sensors can lead to noisy results under many circumstances. To be able to remove the undesired noise from images, proper noise modeling and an accurate noise parameter estimation is crucial. In this project, we use a…
This paper demonstrates a practical method that can correct spatial varying blur from a set of images of the same object. The algorithm jointly estimates the object and local point spread functions~(PSF). The method prioritizes sections…
We propose a variational regularisation approach for the problem of template-based image reconstruction from indirect, noisy measurements as given, for instance, in X-ray computed tomography. An image is reconstructed from such measurements…
Diffusion models have recently achieved success in solving Bayesian inverse problems with learned data priors. Current methods build on top of the diffusion sampling process, where each denoising step makes small modifications to samples…
In this paper, we propose a new method of Bayesian measurement for spectral deconvolution, which regresses spectral data into the sum of unimodal basis function such as Gaussian or Lorentzian functions. Bayesian measurement is a framework…
Variations of deep neural networks such as convolutional neural network (CNN) have been successfully applied to image denoising. The goal is to automatically learn a mapping from a noisy image to a clean image given training data consisting…
Owing to the edge preserving ability and low computational cost of the total variation (TV), variational models with the TV regularization have been widely investigated in the field of multiplicative noise removal. The key points of the…
We study a blind deconvolution problem on graphs, which arises in the context of localizing a few sources that diffuse over networks. While the observations are bilinear functions of the unknown graph filter coefficients and sparse input…
Acquired images for medical and other purposes can be affected by noise from both the equipment used in the capturing or the environment. This can have adverse effect on the information therein. Thus, the need to restore the image to its…
This paper addresses the challenge of audio-visual single-microphone speech separation and enhancement in the presence of real-world environmental noise. Our approach is based on generative inverse sampling, where we model clean speech and…
Multireference alignment (MRA) problem is to estimate an underlying signal from a large number of noisy circularly-shifted observations. The existing methods are always proposed under the hypothesis of a single Gaussian noise. However, the…