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It is highly desirable to know how uncertain a model's predictions are, especially for models that are complex and hard to understand as in deep learning. Although there has been a growing interest in using deep learning methods in…
Motivated by single-particle cryo-electron microscopy, multi-reference alignment (MRA) models the task of recovering an unknown signal from multiple noisy observations corrupted by random rotations. The standard approach,…
Video processing solutions for motion analysis are key tasks in many computer vision applications, ranging from human activity recognition to object detection. In particular, speed estimation algorithms may be relevant in contexts such as…
Linear inverse problems $A \mu = \delta$ with Poisson noise and non-negative unknown $\mu \geq 0$ are ubiquitous in applications, for instance in Positron Emission Tomography (PET) in medical imaging. The associated maximum likelihood…
A pre-trained unconditional diffusion model, combined with posterior sampling or maximum a posteriori (MAP) estimation techniques, can solve arbitrary inverse problems without task-specific training or fine-tuning. However, existing…
This paper proposes Incremental Seeded Expectation Maximization, an algorithm that improves upon the traditional Expectation Maximization computational flow for clusterwise or finite mixture linear regression tasks. The proposed method…
With fluid antenna system (FAS) gradually establishing itself as a possible enabling technology for next generation wireless communications, channel estimation for FAS has become a pressing issue. Existing methodologies however face…
In this paper, we provide a multiscale perspective on the problem of maximum marginal likelihood estimation. We consider and analyse a diffusion-based maximum marginal likelihood estimation scheme using ideas from multiscale dynamics. Our…
In this paper, Bayesian parameter estimation through the consideration of the Maximum A Posteriori (MAP) criterion is revisited under the prism of the Expectation-Maximization (EM) algorithm. By incorporating a sparsity-promoting penalty…
Purpose: The Unadjusted Langevin Algorithm (ULA) in combination with diffusion models can generate high quality MRI reconstructions with uncertainty estimation from highly undersampled k-space data. However, sampling methods such as…
The present study proposes incorporating non-parametric knowledge into the diffusion least-mean-squares algorithm in the framework of a maximum a posteriori (MAP) estimation. The proposed algorithm leads to a robust estimation of an unknown…
Minimum mean squared error (MMSE) estimators of signals from samples corrupted by jitter (timing noise) and additive noise are nonlinear, even when the signal prior and additive noise have normal distributions. This paper develops a…
Inverse problems have many applications in science and engineering. In Computer vision, several image restoration tasks such as inpainting, deblurring, and super-resolution can be formally modeled as inverse problems. Recently, methods have…
Diffusion models have indeed shown great promise in solving inverse problems in image processing. In this paper, we propose a novel, problem-agnostic diffusion model called the maximum a posteriori (MAP)-based guided term estimation method…
Knowledge of the noise distribution in diffusion MRI is the centerpiece to quantify uncertainties arising from the acquisition process. Accurate estimation beyond textbook distributions often requires information about the acquisition…
While energy-based models (EBMs) exhibit a number of desirable properties, training and sampling on high-dimensional datasets remains challenging. Inspired by recent progress on diffusion probabilistic models, we present a diffusion…
This work proposes diffusion normalized least mean M-estimate algorithm based on the modified Huber function, which can equip distributed networks with robust learning capability in the presence of impulsive interference. In order to…
Mutual information (MI) is one of the most general ways to measure relationships between random variables, but estimating this quantity for complex systems is challenging. Denoising diffusion models have recently set a new bar for density…
Diffusion-based generative models (DBGMs) perturb data to a target noise distribution and reverse this process to generate samples. The choice of noising process, or inference diffusion process, affects both likelihoods and sample quality.…
We propose a multi-hop diffusion strategy for a sensor network to perform distributed least mean-squares (LMS) estimation under local and network-wide energy constraints. At each iteration of the strategy, each node can combine intermediate…