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We study posterior sampling for inverse problems in discrete state spaces using discrete diffusion models as generative priors. While continuous diffusion models have become widely used for inverse problems, their discrete counterparts…
Diffusion models have emerged as powerful learned priors for solving inverse problems. However, current iterative solving approaches which alternate between diffusion sampling and data consistency steps typically require hundreds or…
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…
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…
The Langevin algorithm is a classic method for sampling from a given pdf in a real space. In its basic version, it only requires knowledge of the gradient of the log-density, also called the score function. However, in deep learning, it is…
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…
This paper deals with the resolution of inverse problems in a periodic setting or, in other terms, the reconstruction of periodic continuous-domain signals from their noisy measurements. We focus on two reconstruction paradigms: variational…
While recent years have witnessed a dramatic upsurge of exploiting deep neural networks toward solving image denoising, existing methods mostly rely on simple noise assumptions, such as additive white Gaussian noise (AWGN), JPEG compression…
Diffusion models are powerful tools for sampling from high-dimensional distributions by progressively transforming pure noise into structured data through a denoising process. When equipped with a guidance mechanism, these models can also…
This paper develops a new empirical Bayesian inference algorithm for solving a linear inverse problem given multiple measurement vectors (MMV) of under-sampled and noisy observable data. Specifically, by exploiting the joint sparsity across…
We propose an image deconvolution algorithm when the data is contaminated by Poisson noise. The image to restore is assumed to be sparsely represented in a dictionary of waveforms such as the wavelet or curvelet transforms. Our key…
Plug and play (P&P) algorithms iteratively apply highly optimized image denoisers to impose priors and solve computational image reconstruction problems, to great effect. However, in general the "effective noise", that is the difference…
We propose a new fast algorithm for solving one of the standard approaches to ill-posed linear inverse problems (IPLIP), where a (possibly non-smooth) regularizer is minimized under the constraint that the solution explains the observations…
Gaussian smoothing combined with a probabilistic framework for denoising via the empirical Bayes formalism, i.e., the Tweedie-Miyasawa formula (TMF), are the two key ingredients in the success of score-based generative models in Euclidean…
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…
Deep neural networks (DNNs) have shown very promising results for various image restoration (IR) tasks. However, the design of network architectures remains a major challenging for achieving further improvements. While most existing…
We consider the inpainting problem for noisy images. It is very challenge to suppress noise when image inpainting is processed. An image patches based nonlocal variational method is proposed to simultaneously inpainting and denoising in…
Denoising diffusion models are a powerful type of generative models used to capture complex distributions of real-world signals. However, their applicability is limited to scenarios where training samples are readily available, which is not…
Inverse problems constrained by partial differential equations are often ill-conditioned due to noisy and incomplete data or inherent non-uniqueness. A prominent example is full waveform inversion, which estimates Earth's subsurface…
Many microscopy applications are limited by the total amount of usable light and are consequently challenged by the resulting levels of noise in the acquired images. This problem is often addressed via (supervised) deep learning based…