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Image noise can often be accurately fitted to a Poisson-Gaussian distribution. However, estimating the distribution parameters from a noisy image only is a challenging task. Here, we study the case when paired noisy and noise-free samples…

Denoising diffusion probabilistic models have recently received much research attention since they outperform alternative approaches, such as GANs, and currently provide state-of-the-art generative performance. The superior performance of…

Classification is a vital tool that is important for modelling many complex numerical models. A model or system may be such that, for certain areas of input space, the output either does not exist, or is not in a quantifiable form. Here, we…

This paper introduces a Bayesian framework to detect multiple signals embedded in noisy observations from a sensor array. For various states of knowledge on the communication channel and the noise at the receiving sensors, a marginalization…

Despite substantial progress in signal source separation, results for richly structured data continue to contain perceptible artifacts. In contrast, recent deep generative models can produce authentic samples in a variety of domains that…

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…

Astronomical images in the Poisson regime are typically characterized by a spatially varying cosmic background, large variety of source morphologies and intensities, data incompleteness, steep gradients in the data, and few photon counts…

Learning segmentation from noisy labels is an important task for medical image analysis due to the difficulty in acquiring highquality annotations. Most existing methods neglect the pixel correlation and structural prior in segmentation,…

We present a flexible Bayesian semiparametric mixed model for longitudinal data analysis in the presence of potentially high-dimensional categorical covariates. Building on a novel hidden Markov tensor decomposition technique, our proposed…

We propose a Bayesian approach to joint source separation and restoration for astrophysical diffuse sources. We constitute a prior statistical model for the source images by using their gradient maps. We assume a t-distribution for the…

Denoising diffusion probabilistic models and score-matching models have proven to be very powerful for generative tasks. While these approaches have also been applied to the generation of discrete graphs, they have, so far, relied on…

This paper presents a novel Bayesian approach for hyperspectral image unmixing. The observed pixels are modeled by a linear combination of material signatures weighted by their corresponding abundances. A spike-and-slab abundance prior is…

The semantic segmentation task aims at dense classification at the pixel-wise level. Deep models exhibited progress in tackling this task. However, one remaining problem with these approaches is the loss of spatial precision, often produced…

We address the challenge of incorporating document-level metadata into topic modeling to improve topic mixture estimation. To overcome the computational complexity and lack of theoretical guarantees in existing Bayesian methods, we extend…

Image segmentation is a fundamental step for the interpretation of Remote Sensing Images. Clustering or segmentation methods usually precede the classification task and are used as support tools for manual labeling. The most common…

System identification is of special interest in science and engineering. This article is concerned with a system identification problem arising in stochastic dynamic systems, where the aim is to estimate the parameters of a system along…

This paper proposes a novel two-stage method for the classification of hyperspectral images. Pixel-wise classifiers, such as the classical support vector machine (SVM), consider spectral information only; therefore they would generate noisy…

Noisy labels are ubiquitous in real-world datasets, especially in the large-scale ones derived from crowdsourcing and web searching. It is challenging to train deep neural networks with noisy datasets since the networks are prone to…

Noisy labels can significantly affect the performance of deep neural networks (DNNs). In medical image segmentation tasks, annotations are error-prone due to the high demand in annotation time and in the annotators' expertise. Existing…

Image foreground extraction is a classical problem in image processing and vision, with a large range of applications. In this dissertation, we focus on the extraction of text and graphics in mixed-content images, and design novel…