相关论文: Sparsity promoting reconstructions via hierarchica…
In this paper, we formulate the reconstruction problem in diffuse optical tomography (DOT) in a statistical setting for determining the optical parameters, scattering and absorption, from boundary photon density measurements. A special kind…
Diffuse optical tomography (DOT) utilises near-infrared light for imaging spatially distributed optical parameters, typically the absorption and scattering coefficients. The image reconstruction problem of DOT is an ill-posed inverse…
Score-based diffusion models are a recently developed framework for posterior sampling in Bayesian inverse problems with a state-of-the-art performance for severely ill-posed problems by leveraging a powerful prior distribution learned from…
The electrical impedance tomography (EIT) problem of estimating the unknown conductivity distribution inside a domain from boundary current or voltage measurements requires the solution of a nonlinear inverse problem. Sparsity promoting…
The sparse structure of the solution for an inverse problem can be modelled using different sparsity enforcing priors when the Bayesian approach is considered. Analytical expression for the unknowns of the model can be obtained by building…
Bayesian hierarchical models have been demonstrated to provide efficient algorithms for finding sparse solutions to ill-posed inverse problems. The models comprise typically a conditionally Gaussian prior model for the unknown, augmented by…
Nonlinear parametric inverse problems appear in many applications. Here, we focus on diffuse optical tomography (DOT) in medical imaging to recover unknown images of interest, such as cancerous tissue in a given medium, using a mathematical…
Bayesian hierarchical models can provide efficient algorithms for finding sparse solutions to ill-posed inverse problems. The models typically comprise a conditionally Gaussian prior model for the unknown which is augmented by a generalized…
This paper presents a hierarchical Bayesian model to reconstruct sparse images when the observations are obtained from linear transformations and corrupted by an additive white Gaussian noise. Our hierarchical Bayes model is well suited to…
Hierarchical models with gamma hyperpriors provide a flexible, sparse-promoting framework to bridge $L^1$ and $L^2$ regularizations in Bayesian formulations to inverse problems. Despite the Bayesian motivation for these models, existing…
Variable selection techniques have become increasingly popular amongst statisticians due to an increased number of regression and classification applications involving high-dimensional data where we expect some predictors to be unimportant.…
Achieving high-resolution Direction of Arrival (DoA) recovery typically requires high Signal to Noise Ratio (SNR) and a sufficiently large number of snapshots. This paper presents NUV-DoA algorithm, that augments Bayesian sparse…
The recovery of sparse generative models from few noisy measurements is an important and challenging problem. Many deterministic algorithms rely on some form of $\ell_1$-$\ell_2$ minimization to combine the computational convenience of the…
Many inverse problems are ill-posed and need to be complemented by prior information that restricts the class of admissible models. Bayesian approaches encode this information as prior distributions that impose generic properties on the…
Nonlinear parametric inverse problems appear in several prominent applications; one such application is Diffuse Optical Tomography (DOT) in medical image reconstruction. Such inverse problems present huge computational challenges, mostly…
We present a hierarchical Bayesian learning approach to infer jointly sparse parameter vectors from multiple measurement vectors. Our model uses separate conditionally Gaussian priors for each parameter vector and common gamma-distributed…
Bayesian inference for inverse problems hinges critically on the choice of priors. In the absence of specific prior information, population-level distributions can serve as effective priors for parameters of interest. With the advent of…
We propose a novel hierarchical diffusion planner that embeds task and motion structure directly into the noise model. Unlike standard diffusion-based planners that rely on zero-mean, isotropic Gaussian corruption, we introduce…
Diffuse optical tomography (DOT) has been investigated as an alternative imaging modality for breast cancer detection thanks to its excellent contrast to hemoglobin oxidization level. However, due to the complicated non-linear photon…
The pretrained diffusion model as a strong prior has been leveraged to address inverse problems in a zero-shot manner without task-specific retraining. Different from the unconditional generation, the measurement-guided generation requires…