Related papers: Local MAP Sampling for Diffusion Models
This paper considers properties of an optimization based sampler for targeting the posterior distribution when the likelihood is intractable and auxiliary statistics are used to summarize information in the data. Our reverse sampler…
Inverse scattering problems have many important applications. In this paper, given limited aperture data, we propose a Bayesian method for the inverse acoustic scattering to reconstruct the shape of an obstacle. The inverse problem is…
We present a novel, training-free approach for textual editing of real images using diffusion models. Unlike prior methods that rely on computationally expensive finetuning, our approach leverages LAtent SPatial Alignment (LASPA) to…
Geophysical inverse problems are often ill-posed and admit multiple solutions. Conventional discriminative methods typically yield a single deterministic solution, which fails to model the posterior distribution, cannot generate diverse…
Reconstructing large-scale latent networks from observed dynamics is crucial for understanding complex systems. However, the existing methods based on compressive sensing are often rendered infeasible in practice by prohibitive…
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…
In the era of big data, graph sampling is indispensable in many settings. Existing sampling methods are mostly designed for static graphs, and aim to preserve basic structural properties of the original graph (such as degree distribution,…
There are several challenges associated with inverse problems in which we seek to reconstruct a piecewise constant field, and which we model using multiple level sets. Adopting a Bayesian viewpoint, we impose prior distributions on both the…
Undoing the image formation process and therefore decomposing appearance into its intrinsic properties is a challenging task due to the under-constraint nature of this inverse problem. While significant progress has been made on inferring…
Robust Bayesian inference using density power divergence (DPD) has emerged as a promising approach for handling outliers in statistical estimation. Although the DPD-based posterior offers theoretical guarantees of robustness, its practical…
The maximum a-posteriori (MAP) perturbation framework has emerged as a useful approach for inference and learning in high dimensional complex models. By maximizing a randomly perturbed potential function, MAP perturbations generate unbiased…
We present a localized a-posteriori error estimate for the localized reduced basis multi-scale (LRBMS) method [Albrecht, Haasdonk, Kaulmann, Ohlberger (2012): The localized reduced basis multiscale method]. The LRBMS is a combination of…
This article proposes diffusion LMS strategies for distributed estimation over adaptive networks that are able to exploit sparsity in the underlying system model. The approach relies on convex regularization, common in compressive sensing,…
Maximum a posteriori (MAP) estimation, like all Bayesian methods, depends on prior assumptions. These assumptions are often chosen to promote specific features in the recovered estimate. The form of the chosen prior determines the shape of…
Limitations on bandwidth and power consumption impose strict bounds on data rates of diagnostic imaging systems. Consequently, the design of suitable (i.e. task- and data-aware) compression and reconstruction techniques has attracted…
A quality-Bayesian approach, combining the direct sampling method and the Bayesian inversion, is proposed to reconstruct the locations and intensities of the unknown acoustic sources using partial data. First, we extend the direct sampling…
As a class of fruitful approaches, diffusion probabilistic models (DPMs) have shown excellent advantages in high-resolution image reconstruction. On the other hand, masked autoencoders (MAEs), as popular self-supervised vision learners,…
It is well-known that the posterior density of linear inverse problems with Gaussian prior and Gaussian likelihood is also Gaussian, hence completely described by its covariance and expectation. Sampling from a Gaussian posterior may be…
We derive a parallel sampling algorithm for computational inverse problems that present an unknown linear forcing term and a vector of nonlinear parameters to be recovered. It is assumed that the data is noisy and that the linear part of…
In a great number of tasks in science and engineering, the goal is to infer an unknown image from a small number of measurements collected from a known forward model describing certain sensing or imaging modality. Due to resource…