Related papers: NF-ULA: Langevin Monte Carlo with Normalizing Flow…
We propose a sampling algorithm to perform system identification from a set of input-output graph signal pairs. The dynamics of the systems we study are given by a partially known adjacency matrix and a generic parametric graph filter of…
Inverse problems arise almost everywhere in science and engineering where we need to infer on a quantity from indirect observation. The cases of medical, biomedical, and industrial imaging systems are the typical examples. A very high…
Recently it has been shown that using diffusion models for inverse problems can lead to remarkable results. However, these approaches require a closed-form expression of the degradation model and can not support complex degradations. To…
Deep learning based image compression has recently witnessed exciting progress and in some cases even managed to surpass transform coding based approaches that have been established and refined over many decades. However, state-of-the-art…
Normalizing flow (NF) has gained popularity over traditional maximum likelihood based methods due to its strong capability to model complex data distributions. However, the standard approach, which maps the observed data to a normal…
Deep convolutional networks have become a popular tool for image generation and restoration. Generally, their excellent performance is imputed to their ability to learn realistic image priors from a large number of example images. In this…
Normalizing flows have emerged as an important family of deep neural networks for modelling complex probability distributions. In this note, we revisit their coupling and autoregressive transformation layers as probabilistic graphical…
We propose a new method for solving imaging inverse problems using text-to-image latent diffusion models as general priors. Existing methods using latent diffusion models for inverse problems typically rely on simple null text prompts,…
The main contribution of this paper is to develop a hierarchical Bayesian formulation of PINNs for linear inverse problems, which is called BPINN-IP. The proposed methodology extends PINN to account for prior knowledge on the nature of the…
We present the first framework to solve linear inverse problems leveraging pre-trained latent diffusion models. Previously proposed algorithms (such as DPS and DDRM) only apply to pixel-space diffusion models. We theoretically analyze our…
Inverse scattering is a fundamental challenge in many imaging applications, ranging from microscopy to remote sensing. Solving this problem often requires jointly estimating two unknowns -- the image and the scattering field inside the…
In this work, we deepen on the use of normalizing flows for causal reasoning. Specifically, we first leverage recent results on non-linear ICA to show that causal models are identifiable from observational data given a causal ordering, and…
We present a new class of Langevin based algorithms, which overcomes many of the known shortcomings of popular adaptive optimizers that are currently used for the fine tuning of deep learning models. Its underpinning theory relies on recent…
Using diffusion priors to solve inverse problems in imaging have significantly matured over the years. In this chapter, we review the various different approaches that were proposed over the years. We categorize the approaches into the more…
We study Bayesian inverse problems with mixed noise, modeled as a combination of additive and multiplicative Gaussian components. While traditional inference methods often assume fixed or known noise characteristics, real-world…
Inverse problems are ubiquitous because they formalize the integration of data with mathematical models. In many scientific applications the forward model is expensive to evaluate, and adjoint computations are difficult to employ; in this…
Ill-posed linear inverse problems arise frequently in various applications, from computational photography to medical imaging. A recent line of research exploits Bayesian inference with informative priors to handle the ill-posedness of such…
We adopt Bayesian approach to consider the inverse problem of estimate a function from noisy observations. One important component of this approach is the prior measure. Total variation prior has been proved with no discretization invariant…
We study a normalizing flow in the latent space of a top-down generator model, in which the normalizing flow model plays the role of the informative prior model of the generator. We propose to jointly learn the latent space normalizing flow…
Classical model-based imaging methods for ultrasound elasticity inverse problem require prior constraints about the underlying elasticity patterns, while finding the appropriate hand-crafted prior for each tissue type is a challenge. In…