Related papers: Utilizing variational autoencoders in the Bayesian…
We propose a novel adaptive importance sampling scheme for Bayesian inversion problems where the inference of the variables of interest and the power of the data noise is split. More specifically, we consider a Bayesian analysis for the…
In this work, a method for obtaining pixel-wise error bounds in Bayesian regularization of inverse imaging problems is introduced. The proposed method employs estimates of the posterior variance together with techniques from conformal…
We investigate the problem of producing diverse solutions to an image super-resolution problem. From a probabilistic perspective, this can be done by sampling from the posterior distribution of an inverse problem, which requires the…
Feedforward neural networks are widely used as universal predictive models to fit data distribution. Common gradient-based learning, however, suffers from many drawbacks making the training process ineffective and time-consuming.…
This paper considers a Bayesian approach for inclusion detection in nonlinear inverse problems using two known and popular push-forward prior distributions: the star-shaped and level set prior distributions. We analyze the convergence of…
In just three years, Variational Autoencoders (VAEs) have emerged as one of the most popular approaches to unsupervised learning of complicated distributions. VAEs are appealing because they are built on top of standard function…
This paper provides an analysis of the linearized inverse problem in multifrequency electrical impedance tomography. We consider an isotropic conductivity distribution with a finite number of unknown inclusions with different frequency…
We consider the problem of learning Variational Autoencoders (VAEs), i.e., a type of deep generative model, from data with missing values. Such data is omnipresent in real-world applications of machine learning because complete data is…
Photoacoustic tomography (PAT) is a rapidly-evolving medical imaging modality that combines optical absorption contrast with ultrasound imaging depth. One challenge in PAT is image reconstruction with inadequate acoustic signals due to…
We propose using Probabilistic Cellular Automata (PCA) to address inverse problems with the Bayesian approach. In particular, we use PCA to sample from an approximation of the posterior distribution. The peculiar feature of PCA is their…
Characterizing statistical properties of solutions of inverse problems is essential for decision making. Bayesian inversion offers a tractable framework for this purpose, but current approaches are computationally unfeasible for most…
Recent studies have explored the use of deep generative models of speech spectra based of variational autoencoders (VAEs), combined with unsupervised noise models, to perform speech enhancement. These studies developed iterative algorithms…
Learning from an imbalanced distribution presents a major challenge in predictive modeling, as it generally leads to a reduction in the performance of standard algorithms. Various approaches exist to address this issue, but many of them…
This paper is concerned with inverse acoustic scattering problem of inferring the position and shape of a sound-soft obstacle from phaseless far-field data. We propose the Bayesian approach to recover sound-soft disks, line cracks and…
The inverse source problem arising in photoacoustic tomography and in several other coupled-physics modalities is frequently solved by iterative algorithms. Such algorithms are based on the minimization of a certain cost functional. In…
In this paper, first a great number of inverse problems which arise in instrumentation, in computer imaging systems and in computer vision are presented. Then a common general forward modeling for them is given and the corresponding…
In this paper, we study a fast approximate inference method based on expectation propagation for exploring the posterior probability distribution arising from the Bayesian formulation of nonlinear inverse problems. It is capable of…
In a variety of scientific applications we wish to characterize a physical system using measurements or observations. This often requires us to solve an inverse problem, which usually has non-unique solutions so uncertainty must be…
The problem of mixed signals occurs in many different contexts; one of the most familiar being acoustics. The forward problem in acoustics consists of finding the sound pressure levels at various detectors resulting from sound signals…
Bayesian methods have become a popular way to incorporate prior knowledge and a notion of uncertainty into machine learning models. At the same time, the complexity of modern machine learning makes it challenging to comprehend a model's…