Related papers: Fast Scalable Image Restoration using Total Variat…
In this paper we propose a new approach for tomographic reconstruction with spatially varying regularization parameter. Our work is based on the SA-TV image restoration model proposed in [3] where an automated parameter selection rule for…
Latent Gaussian models have a rich history in statistics and machine learning, with applications ranging from factor analysis to compressed sensing to time series analysis. The classical method for maximizing the likelihood of these models…
A class of mixed-order \emph{PDE}-constraint regularizer for image processing problem is proposed, generalizing the standard first order total variation $(TV)$. A semi-supervised (bilevel) training scheme, which provides a simultaneous…
We show that a probabilistic version of the classical forward-stepwise variable inclusion procedure can serve as a general data-augmentation scheme for model space distributions in (generalized) linear models. This latent variable…
Numerous total variation (TV) regularizers, engaged in image restoration problem, encode the gradients by means of simple $[-1,1]$ FIR filter. Despite its low computational processing, this filter severely deviates signal's high frequency…
In this paper we focus on learning optimized partial differential equation (PDE) models for image filtering. In this approach, the grey-scaled images are represented by a vector field of two real-valued functions and the image restoration…
Large-scale precision matrix estimation is of fundamental importance yet challenging in many contemporary applications for recovering Gaussian graphical models. In this paper, we suggest a new approach of innovated scalable efficient…
Modern methods for Bayesian regression beyond the Gaussian response setting are often computationally impractical or inaccurate in high dimensions. In fact, as discussed in recent literature, bypassing such a trade-off is still an open…
We present a variational Bayesian method of joint image reconstruction and point spread function (PSF) estimation when the PSF of the imaging device is only partially known. To solve this semi-blind deconvolution problem, prior…
We introduce a probabilistic approach to ptychographic reconstruction in computational imaging. Ptychography is an imaging method where the complex amplitude of an object is estimated from a sequence of diffraction measurements. We…
Algorithms for automatically selecting a scalar or locally varying regularization parameter for total variation models with an $L^{\tau}$-data fidelity term, $\tau\in \{1,2\}$, are presented. The automated selection of the regularization…
Characterizing the phase transitions of convex optimizations in recovering structured signals or data is of central importance in compressed sensing, machine learning and statistics. The phase transitions of many convex optimization signal…
Image reconstruction based on indirect, noisy, or incomplete data remains an important yet challenging task. While methods such as compressive sensing have demonstrated high-resolution image recovery in various settings, there remain issues…
This paper presents an adaptive and intelligent sparse model for digital image sampling and recovery. In the proposed sampler, we adaptively determine the number of required samples for retrieving image based on space-frequency-gradient…
Bayesian inference provides principled uncertainty quantification, but accurate posterior sampling with MCMC can be computationally prohibitive for modern applications. Variational inference (VI) offers a scalable alternative and often…
Natural image statistics exhibit hierarchical dependencies across multiple scales. Representing such prior knowledge in non-factorial latent tree models can boost performance of image denoising, inpainting, deconvolution or reconstruction…
Signal recovery from unitarily invariant measurements is investigated in this paper. A message-passing algorithm is formulated on the basis of expectation propagation (EP). A rigorous analysis is presented for the dynamics of the algorithm…
The problem of image blurring is one of the most studied topics in the field of image processing. Image blurring is caused by various factors such as hand or camera shake. To restore the blurred image, it is necessary to know information…
This paper introduces a Bayesian image segmentation algorithm based on finite mixtures. An EM algorithm is developed to estimate parameters of the Gaussian mixtures. The finite mixture is a flexible and powerful probabilistic modeling tool.…
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…