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The inversion of linear systems is a fundamental step in many inverse problems. Computational challenges exist when trying to invert large linear systems, where limited computing resources mean that only part of the system can be kept in…
In this paper, we use the Bayesian inversion approach to study the data assimilation problem for a family of tumor growth models described by porous-medium type equations. The models contain uncertain parameters and are indexed by a…
Purpose: Optical imaging is evolving as a key technique for advanced sensing in the operating room. Recent research has shown that machine learning algorithms can be used to address the inverse problem of converting pixel-wise multispectral…
Tomographic reconstruction, despite its revolutionary impact on a wide range of applications, suffers from its ill-posed nature in that there is no unique solution because of limited and noisy measurements. Therefore, in the absence of…
Recent deep learning approaches focus on improving quantitative scores of dedicated benchmarks, and therefore only reduce the observation-related (aleatoric) uncertainty. However, the model-immanent (epistemic) uncertainty is less…
We propose a Bayesian inference framework to estimate uncertainties in inverse scattering problems. Given the observed data, the forward model and their uncertainties, we find the posterior distribution over a finite parameter field…
Existing score-based methods for inverse problems often resort to approximate minimization of the KL divergence between the inversion distribution and the Bayesian posterior. Such an approximation leads to severe mode collapse and…
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…
Schemes for X-ray imaging single protein molecules using new x-ray sources, like x-ray free electron lasers (XFELs), require processing many frames of data that are obtained by taking temporally short snapshots of identical molecules, each…
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…
Computational imaging plays a pivotal role in determining hidden information from sparse measurements. A robust inverse solver is crucial to fully characterize the uncertainty induced by these measurements, as it allows for the estimation…
Beamforming is an essential step in the ultrasound image formation pipeline and has recently attracted growing interest. An important goal of beamforming is to increase the image spatial resolution, or in other words to narrow down the…
We present a computational framework for efficient learning, sampling, and distribution of general Bayesian posterior distributions. The framework leverages a machine learning approach for the construction of normalizing flows for the…
Bayesian imaging inverse problems in astrophysics and cosmology remain challenging, particularly in low-data regimes, due to complex forward operators and the frequent lack of well-motivated priors for non-Gaussian signals. In this paper,…
Faraday tomography (or rotation measure synthesis) is a procedure to convert linear polarization spectra into the Faraday dispersion function, which provides us with unique information of magneto-ionic media along the line of sight.…
The tilted-wave interferometer is a promising technique for the development of a reference measurement system for the highly accurate form measurement of aspheres and freeform surfaces. The technique combines interferometric measurements,…
Bayesian methods are appealing in their flexibility in modeling complex data and ability in capturing uncertainty in parameters. However, when Bayes' rule does not result in tractable closed-form, most approximate inference algorithms lack…
Inverse problems arise in many applications, especially tomographic imaging. We develop a Learned Alternating Minimization Algorithm (LAMA) to solve such problems via two-block optimization by synergizing data-driven and classical…
High-fidelity spectrum cartography is pivotal for spectrum management and wireless situational awareness, yet it remains a challenging ill-posed inverse problem due to the sparsity and irregularity of observations. Furthermore, existing…
We present a Bayesian perspective on quantifying the uncertainty of graph signals estimated or reconstructed from imperfect observations. We show that many conventional methods of graph signal estimation, reconstruction and imputation, can…