Bayesian Inference on Multiscale Models for Poisson Intensity Estimation: Applications to Photon-Limited Image Denoising

@article{Lefkimmiatis2009BayesianIO,  title={Bayesian Inference on Multiscale Models for Poisson Intensity Estimation: Applications to Photon-Limited Image Denoising},  author={Stamatios Lefkimmiatis and Petros Maragos and George Papandreou},  journal={IEEE Transactions on Image Processing},  year={2009},  volume={18},  pages={1724-1741},  url={https://api.semanticscholar.org/CorpusID:859561}}
An improved statistical model for analyzing Poisson processes is presented, adopting a multiscale representation of the Poisson process in which the ratios of the underlying Poisson intensities in adjacent scales are modeled as mixtures of conjugate parametric distributions.

83 Citations

Poisson-Gaussian Noise Reduction Using the Hidden Markov Model in Contourlet Domain for Fluorescence Microscopy Images

An effective denoising algorithm for Poisson-Gaussian noise is proposed using the contourlet transform, hidden Markov models and noise estimation in the transform domain and is supplemented by cycle spinning and Wiener filtering for further improvements.

Fast Bayesian Restoration of Poisson Corrupted Images with INLA

This study proposes a Bayesian restoration method of Poisson corrupted image using Integrated Nested Laplace Approximation (INLA), which is a computational method to evaluate marginalized posterior distributions of latent Gaussian models (LGMs).

Poisson Noise Reduction with Higher-Order Natural Image Prior Model

This paper considers a variational modeling to integrate the so-called fields of experts (FoE) image prior, that has proven an effective higher-order Markov random fields model for many classic image restoration problems.

Image Denoising in Mixed Poisson–Gaussian Noise

The denoising process is expressed as a linear expansion of thresholds (LET) that is optimized by relying on a purely data-adaptive unbiased estimate of the mean-squared error (MSE) derived in a non-Bayesian framework (PURE: Poisson-Gaussian unbiased risk estimate).

Poisson-Haar Transform: A nonlinear multiscale representation for photon-limited image denoising

The proposed Poisson-Haar transform is well-suited for analyzing images degraded by signal-dependent Poisson noise, allowing efficient estimation of their underlying intensity by means of multiscale Bayesian schemes.

Reducing Poisson noise and baseline drift in x-ray spectral images with bootstrap Poisson regression and robust nonparametric regression

This work proposes a novel algorithm to promote the signal-to-noise ratio (SNR) of x-ray spectral images that have low photon counts through the bootstrap resampling method and a robust local nonparametric regression method to improve the SNR of the data.

Poisson image denoising by piecewise principal component analysis and its application in single-particle X-ray diffraction imaging

It is shown that the resolution of three-dimensional reconstruction from XFEL diffraction images is improved when the data are preprocessed with PWPCA, and the first application of such approaches to single-particle X-ray free-electron laser (XFEL) data is shown.

Exact Unbiased Inverse of the Anscombe Transformation and its Poisson-Gaussian Generalization

Image denoising aims at removing or attenuating signal-dependent noise from the captured image, in order to provide an estimate of the underlying ideal noise-free image, and uses an indirect three-step variance-stabilization approach.

Fast and Accurate Poisson Denoising with Optimized Nonlinear Diffusion

This study exploits the newly-developed trainable nonlinear reaction diffusion model which has proven an extremely fast image restoration approach with performance surpassing recent state-of-the-arts, and proposes an efficient Poisson denoising model with both high computational efficiency and recovery quality.

Poisson Image Reconstruction With Hessian Schatten-Norm Regularization

This paper proposes an efficient framework for Poisson image reconstruction, under a regularization approach, which depends on matrix-valued regularization operators and derives a link that relates the proximal map of an lp norm with the proximate map of a Schatten matrix norm of order p.
...

44 References

Photon-limited image denoising by inference on multiscale models

An improved statistical model of Poisson processes is presented, adopting a multiscale representation of the Poisson process in which the ratios of the underlying Poisson intensities in adjacent scales are modeled as mixtures of conjugate parametric distributions.

Multiscale Modeling and Estimation of Poisson Processes with Application to Photon-Limited Imaging

A new Bayesian approach to Poisson intensity estimation based on the Haar wavelet transform is applied to photon-limited image estimation, and its potential to improve nuclear medicine imaging is examined.

Bayesian Multiscale Models for Poisson Processes

Abstract I introduce a class of Bayesian multiscale models (BMSM's) for one-dimensional inhomogeneous Poisson processes. The focus is on estimating the (discretized) intensity function underlying the

Pairwise likelihood estimation for multivariate mixed Poisson models generated by Gamma intensities

A maximum pairwise likelihood approach to estimate the parameters of multivariate mixed Poisson models when the mixing distribution is a multivariate Gamma distribution is studied and the consistency and asymptotic normality of this estimator are derived.

Wavelet-domain filtering for photon imaging systems

A novel gedankenexperiment is performed to devise a new wavelet-domain filtering procedure for noise removal in photon imaging systems that is simultaneously optimal in a small-sample predictive sum of squares sense and asymptotically optimal in the mean-square-error sense.

WAVELET SHRINKAGE ESTIMATION OF CERTAIN POISSON INTENSITY SIGNALS USING CORRECTED THRESHOLDS

An approach to estimating intensity functions for a certain class of "burst-like" Poisson processes using wavelet shrink- age based on the shrinkage of wavelet coefficients of the original count data, as opposed to the current approach of pre-processing the data using Anscombe's square root transform and working with the resulting data in a Gaussian framework.

Improved Poisson intensity estimation: denoising application using Poisson data

This work generates training data from the observed data and compute maximum likelihood estimates of all of the beta-mixture parameters and considers a denoising application using Poisson data.

Discrete Markov image modeling and inference on the quadtree

An extension of the Viterbi algorithm is introduced which enables exact maximum a posteriori (MAP) estimation on the quadtree, and two expectation-maximization (EM)-type algorithms, allowing unsupervised inference with these models are defined.

Multiscale Hidden Markov Models for Bayesian Image Analysis

    R. Nowak
    Computer Science, Mathematics
  • 1999
This chapter focuses on a probabilistic graph model called the multiscale hidden Markov model (MHMM), which captures the key inter-scale dependencies present in natural signals and images.

Related Papers

Showing 1 through 3 of 0 Related Papers