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We propose a general framework for conditional sampling in PDE-based inverse problems, targeting the recovery of whole solutions from extremely sparse or noisy measurements. This is accomplished by a function-space diffusion model and…
This article addresses the issue of estimating observation parameters (response and error parameters) in inverse problems. The focus is on cases where regularization is introduced in a Bayesian framework and the prior is modeled by a…
Generative diffusion models can provide powerful prior probability models for inverse problems in imaging, but existing implementations suffer from two key limitations: $(i)$ the prior density is represented implicitly, and $(ii)$ they rely…
Inverting visual representations within deep neural networks (DNNs) presents a challenging and important problem in the field of security and privacy for deep learning. The main goal is to invert the features of an unidentified target image…
In recent years we have witnessed a growth in mathematics for deep learning, which has been used to solve inverse problems of partial differential equations (PDEs). However, most deep learning-based inversion methods either require paired…
We present a principled Bayesian framework for signal reconstruction, in which the signal is modelled by basis functions whose number (and form, if required) is determined by the data themselves. This approach is based on a Bayesian…
Diffusion models (DMs) have shown promising results on single-image super-resolution and other image-to-image translation tasks. Benefiting from more computational resources and longer inference times, they are able to yield more realistic…
Diffusion models, known for their powerful generative capabilities, play a crucial role in addressing real-world super-resolution challenges. However, these models often focus on improving local textures while neglecting the impacts of…
Diffusion Posterior Sampling (DPS) can be used in Computed Tomography (CT) reconstruction by leveraging diffusion-based generative models for unconditional image synthesis while matching the observations (data) of a CT scan. Of particular…
Data limitation is a significant challenge in applying deep learning to medical images. Recently, the diffusion probabilistic model (DPM) has shown the potential to generate high-quality images by converting Gaussian random noise into…
Satellites are widely used to estimate and monitor ground cover, providing critical information to address the challenges posed by climate change. High-resolution satellite images help to identify smaller features on the ground and…
Recovering degraded low-resolution text images is challenging, especially for Chinese text images with complex strokes and severe degradation in real-world scenarios. Ensuring both text fidelity and style realness is crucial for…
In this work, we address the limitations of denoising diffusion models (DDMs) in image restoration tasks, particularly the shape and color distortions that can compromise image quality. While DDMs have demonstrated a promising performance…
In this paper, a Bayesian fusion technique for remotely sensed multi-band images is presented. The observed images are related to the high spectral and high spatial resolution image to be recovered through physical degradations, e.g.,…
We solve the inverse problem of deblurring a pixelized image of Jupiter using regularized deconvolution and by sample-based Bayesian inference. By efficiently sampling the marginal posterior distribution for hyperparameters, then the full…
This work addresses image restoration tasks through the lens of inverse problems using unpaired datasets. In contrast to traditional approaches -- which typically assume full knowledge of the forward model or access to paired degraded and…
Denoising Diffusion Probabilistic Models (DDPMs) have achieved impressive performance on various generation tasks. By modeling the reverse process of gradually diffusing the data distribution into a Gaussian distribution, generating a…
By decomposing the image formation process into a sequential application of denoising autoencoders, diffusion models (DMs) achieve state-of-the-art synthesis results on image data and beyond. Additionally, their formulation allows for a…
The ability to obtain reliable point estimates of model parameters is of crucial importance in many fields of physics. This is often a difficult task given that the observed data can have a very high number of dimensions. In order to…
In recent years, the ascendance of diffusion modeling as a state-of-the-art generative modeling approach has spurred significant interest in their use as priors in Bayesian inverse problems. However, it is unclear how to optimally integrate…