Sparse reconstructions from few noisy data: analysis of hierarchical Bayesian models with generalized gamma hyperpriors
Solving inverse problems with sparsity promoting regularizing penalties can be recast in the
Bayesian framework as finding a maximum a posteriori (MAP) estimate with sparsity …
Bayesian framework as finding a maximum a posteriori (MAP) estimate with sparsity …
Maximum likelihood estimation of regularization parameters in high-dimensional inverse problems: An empirical bayesian approach part i: Methodology and …
Many imaging problems require solving an inverse problem that is ill-conditioned or ill-
posed. Imaging methods typically address this difficulty by regularizing the estimation …
posed. Imaging methods typically address this difficulty by regularizing the estimation …
[图书][B] Bayesian scientific computing
D Calvetti, E Somersalo - 2023 - Springer
Fifteen years ago, when the idea of using probability to model unknown parameters to be
estimated computationally was a less commonly accepted idea than it is today, writing a …
estimated computationally was a less commonly accepted idea than it is today, writing a …
Computationally efficient sampling methods for sparsity promoting hierarchical Bayesian models
D Calvetti, E Somersalo - SIAM/ASA Journal on Uncertainty Quantification, 2024 - SIAM
Bayesian hierarchical models have been demonstrated to provide efficient algorithms for
finding sparse solutions to ill-posed inverse problems. The models comprise typically a …
finding sparse solutions to ill-posed inverse problems. The models comprise typically a …
Generalized sparse Bayesian learning and application to image reconstruction
Image reconstruction based on indirect, noisy, or incomplete data remains an important yet
challenging task. While methods such as compressive sensing have demonstrated high …
challenging task. While methods such as compressive sensing have demonstrated high …
Sparsity promoting hybrid solvers for hierarchical Bayesian inverse problems
The recovery of sparse generative models from few noisy measurements is an important and
challenging problem. Many deterministic algorithms rely on some form of \ell_1-\ell_2 …
challenging problem. Many deterministic algorithms rely on some form of \ell_1-\ell_2 …
Horseshoe priors for edge-preserving linear Bayesian inversion
In many large-scale inverse problems, such as computed tomography and image deblurring,
characterization of sharp edges in the solution is desired. Within the Bayesian approach to …
characterization of sharp edges in the solution is desired. Within the Bayesian approach to …
Hierarchical ensemble Kalman methods with sparsity-promoting generalized gamma hyperpriors
This paper introduces a computational framework to incorporate flexible regularization
techniques in ensemble Kalman methods for nonlinear inverse problems. The proposed …
techniques in ensemble Kalman methods for nonlinear inverse problems. The proposed …
Bayesian sparsity and class sparsity priors for dictionary learning and coding
Dictionary learning methods continue to gain popularity for the solution of challenging
inverse problems. In the dictionary learning approach, the computational forward model is …
inverse problems. In the dictionary learning approach, the computational forward model is …
Empirical Bayesian inference using a support informed prior
J Zhang, A Gelb, T Scarnati - SIAM/ASA Journal on Uncertainty Quantification, 2022 - SIAM
This paper develops a new empirical Bayesian inference algorithm for solving a linear
inverse problem given multiple measurement vectors of noisy observable data. Specifically …
inverse problem given multiple measurement vectors of noisy observable data. Specifically …