Mixed Poisson-Gaussian Noise Research Articles

Bilateral Spectrum Weighted Total Variation for Noisy-Image Super-Resolution and Image Denoising

In this paper, we propose a regularization technique for noisy-image super-resolution and image denoising. Total variation (TV) regularization is adopted in many image processing applications to preserve the local smoothness. However, TV prior is prone to oversmoothness, staircasing effect, and contrast losses. Nonlocal TV (NLTV) mitigates the contrast losses by adaptively weighting the smoothness based on the similarity measure of image patches. Although it suppresses the noise effectively in the flat regions, it might leave residual noise surrounding the edges especially when the image is not oversmoothed. To address this problem, we propose the bilateral spectrum weighted total variation (BSWTV). Specially, we apply a locally adaptive shrink coefficient to the image gradients and employ the eigenvalues of the covariance matrix of the weighted image gradients to effectively refine the weighting map and suppress the residual noise. In conjunction with the data fidelity term derived from a mixed Poisson-Gaussian noise model, the objective function is decomposed and solved by the alternating direction method of multipliers (ADMM) algorithm. In order to remove outliers and facilitate the convergence stability, the weighting map is smoothed by a Gaussian filter with an iteratively decreased kernel width and updated in a momentum-based manner in each ADMM iteration. We benchmark our method with the state-of-the-art approaches on the public real-world datasets for super-resolution and image denoising. Experiments show that the proposed method obtains outstanding performance for super-resolution and achieves promising results for denoising on real-world images.

Mixed Poisson Gaussian noise reduction in fluorescence microscopy images using modified structure of wavelet transform

Mixed Poisson Gaussian noise reduction in fluorescence microscopy images using modified structure of wavelet transform

Bilinear constraint based ADMM for mixed Poisson-Gaussian noise removal

In this paper, we propose new operator-splitting algorithms for the total variation regularized infimal convolution (TV-IC) model [ 6 ] in order to remove mixed Poisson-Gaussian (MPG) noise. In the existing splitting algorithm for TV-IC, an inner loop by Newton method had to be adopted for one nonlinear optimization subproblem, which increased the computation cost per outer loop. By introducing a new bilinear constraint and applying the alternating direction method of multipliers (ADMM), all subproblems of the proposed algorithms named as BCA (short for Bilinear Constraint based ADMM algorithm) and BCA \begin{document}$ _{f} $\end{document} (short for a variant of BCA with \begin{document}$ {\bf f} $\end{document} ully splitting form) can be very efficiently solved. Especially for the proposed BCA \begin{document}$ _{f} $\end{document} , they can be calculated without any inner iterations. The convergence of the proposed algorithms are investigated, where particularly, a Huber type TV regularizer is adopted to guarantee the convergence of BCA \begin{document}$ _f $\end{document} . Numerically, compared to existing primal-dual algorithms for the TV-IC model, the proposed algorithms, with fewer tunable parameters, converge much faster and produce comparable results meanwhile.

Fast Roughness Minimizing Image Restoration Under Mixed Poisson-Gaussian Noise.

Image acquisition in many biomedical imaging modalities is corrupted by Poisson noise followed by additive Gaussian noise. While total variation and related regularization methods for solving biomedical inverse problems are known to yield high quality reconstructions in most situations, such methods mostly use log-likelihood of either Gaussian or Poisson noise models, and rarely use mixed Poisson-Gaussian (PG) noise model. There is a recent work which deals with exact PG likelihood and total variation regularization. This method adapts the primal-dual approach involving gradients steps on the PG log-likelihood, with step size limited by the inverse of its Lipschitz constant. This leads to limitations in the convergence speed. Although the alternating direction method of multipliers (ADMM) algorithm does not have such step size restrictions, ADMM has never been applied for this problem, for the possible reason that PG log-likelihood is quite complex. In this paper, we develop an ADMM based optimization for roughness minimizing image restoration under PG log-likelihood. We achieve this by first developing a novel iterative method for computing the proximal solution of PG log-likelihood, deriving the termination conditions for this iterative method, and then integrating into a provably convergent ADMM scheme. We experimentally demonstrate that the proposed method outperform primal-dual method in most of the cases.

Multi-Frame Star Image Denoising Algorithm Based on Deep Reinforcement Learning and Mixed Poisson-Gaussian Likelihood.

Mixed Poisson–Gaussian noise exists in the star images and is difficult to be effectively suppressed via maximum likelihood estimation (MLE) method due to its complicated likelihood function. In this article, the MLE method is incorporated with a state-of-the-art machine learning algorithm in order to achieve accurate restoration results. By applying the mixed Poisson–Gaussian likelihood function as the reward function of a reinforcement learning algorithm, an agent is able to form the restored image that achieves the maximum value of the complex likelihood function through the Markov Decision Process (MDP). In order to provide the appropriate parameter settings of the denoising model, the key hyperparameters of the model and their influences on denoising results are tested through simulated experiments. The model is then compared with two existing star image denoising methods so as to verify its performance. The experiment results indicate that this algorithm based on reinforcement learning is able to suppress the mixed Poisson–Gaussian noise in the star image more accurately than the traditional MLE method, as well as the method based on the deep convolutional neural network (DCNN).

Approximating the Ideal Observer for Joint Signal Detection and Localization Tasks by use of Supervised Learning Methods.

Medical imaging systems are commonly assessed and optimized by use of objective measures of image quality (IQ). The Ideal Observer (IO) performance has been advocated to provide a figure-of-merit for use in assessing and optimizing imaging systems because the IO sets an upper performance limit among all observers. When joint signal detection and localization tasks are considered, the IO that employs a modified generalized likelihood ratio test maximizes observer performance as characterized by the localization receiver operating characteristic (LROC) curve. Computations of likelihood ratios are analytically intractable in the majority of cases. Therefore, sampling-based methods that employ Markov-Chain Monte Carlo (MCMC) techniques have been developed to approximate the likelihood ratios. However, the applications of MCMC methods have been limited to relatively simple object models. Supervised learning-based methods that employ convolutional neural networks have been recently developed to approximate the IO for binary signal detection tasks. In this paper, the ability of supervised learning-based methods to approximate the IO for joint signal detection and localization tasks is explored. Both background-known-exactly and background-known-statistically signal detection and localization tasks are considered. The considered object models include a lumpy object model and a clustered lumpy model, and the considered measurement noise models include Laplacian noise, Gaussian noise, and mixed Poisson-Gaussian noise. The LROC curves produced by the supervised learning-based method are compared to those produced by the MCMC approach or analytical computation when feasible. The potential utility of the proposed method for computing objective measures of IQ for optimizing imaging system performance is explored.

Multi-frame super-resolution reconstruction based on mixed Poisson–Gaussian noise

In this paper, a non-blind multi-frame super-resolution (SR) model based on mixed Poisson–Gaussian noise (MPGSR) is proposed. Poisson noise arises from the stochastic nature of the photon-counting process. Readout noise and reset noise inherent to the readout circuitry can be modeled by an additive Gaussian noise. Therefore, a mixed Poisson–Gaussian noise model is more appropriate for real imaging system. Instead of deriving the data fidelity term from the perspective of error norms and the corresponding influence functions, we address the multi-frame SR problem based on a statistical noise model. The derived objective function is decomposed into sub-functions and solved by the alternating direction method of multipliers (ADMM) algorithm which allows using techniques of constrained optimization. The validation of the proposed MPGSR was performed quantitatively and qualitatively on natural and X-ray images. In comparison to the optimization-based and learning-based state-of-the-art methods, we have demonstrated the feasibility of MPGSR and the significance of applying a more appropriate noise model on the SR image reconstruction.

An adaptive algorithm for restoring image corrupted by mixed noise

Image denoising is one of the fundamental problems in image processing. Digital images are often contaminated by noise due to the image acquisition process under poor conditions. In this paper, we propose an effective approach to remove mixed Poisson-Gaussian noise in digital images. Particularly, we propose to use a spatially adaptive total variation regularization term in order to enhance the ability of edge preservation. We also propose an instance of the alternating direction algorithm to solve the proposed denoising model as an optimization problem. The experiments on popular natural images demonstrate that our approach achieves superior accuracy than other recent state-of-the-art techniques.

AN ADAPTIVE VARIATIONAL MODEL FOR MEDICAL IMAGES RESTORATION

Abstract. Image denoising is one of the important tasks required by medical imaging analysis. In this work, we investigate an adaptive variation model for medical images restoration. In the proposed model, we have used the first-order total variation combined with Laplacian regularizer to eliminate the staircase effect in the first-order TV model while preserve edges of object in the piecewise constant image. We also propose an instance of Split Bregman method to solve the proposed denoising model as an optimization problem. Experimental results from mixed Poisson-Gaussian noise are given to demonstrate that our proposed approach outperforms the related methods.

Stokes polarimeter performance: general noise model and analysis.

We calculate the photometric Stokes parameter covariance matrices and SNRs estimated by polarimeters exposed to general noise distributions, such as mixed Poisson-Gaussian (PG) noise. The measurement model includes the effects of optical losses and detector quantum efficiency, enabling quantitative comparison of instruments that have different photometric efficiencies. We demonstrate this capability by comparing the performance of many common polarimeter configurations, including diattenuator-based systems, such as Azzam's four-detector polarimeter [Opt. Lett.10, 309 (1985)OPLEDP0146-959210.1364/OL.10.000309] and Kudenov's stacked photovoltaic polarimeter [Opt. Express24, 14737 (2016)OPEXFF1094-408710.1364/OE.24.014737]. Working with the full covariance matrix under mixed PG noise, we also show that instruments optimized under assumptions of Gaussian noise simultaneously exhibit optimal behavior under Poisson noise.

A Variational Bayesian Approach for Image Restoration—Application to Image Deblurring With Poisson–Gaussian Noise

In this paper, a methodology is investigated for signal recovery in the presence of non-Gaussian noise. In contrast with regularized minimization approaches often adopted in the literature, in our algorithm the regularization parameter is reliably estimated from the observations. As the posterior density of the unknown parameters is analytically intractable, the estimation problem is derived in a variational Bayesian framework where the goal is to provide a good approximation to the posterior distribution in order to compute posterior mean estimates. Moreover, a majorization technique is employed to circumvent the difficulties raised by the intricate forms of the non-Gaussian likelihood and of the prior density. We demonstrate the potential of the proposed approach through comparisons with state-of-the-art techniques that are specifically tailored to signal recovery in the presence of mixed Poisson–Gaussian noise. Results show that the proposed approach is efficient and achieves performance comparable with other methods where the regularization parameter is manually tuned from the ground truth.

Bayesian dictionary learning for hyperspectral image super resolution in mixed Poisson–Gaussian noise

This paper develops a Bayesian dictionary learning method for hyperspectral image super resolution in the presence of mixed Poisson–Gaussian noise. A likelihood function is first designed to deal with the mixed Poisson–Gaussian noise. A fusion optimization model is then introduced, including the data-fidelity term capturing the statistics of mixed Poisson–Gaussian noise, and a beta process analysis-based sparse representation regularization term. In order to implement the proposed method, we use alternating direction method of multipliers (ADMM) for simultaneous Bayesian nonparametric dictionary learning and image estimation. Compared with conventional dictionary learning methods, the introduced dictionary learning method is based on a popular beta process factor analysis (BPFA) for an adaptive learning performance. Simulation results illustrate that the proposed method has a better performance than several well-known methods in terms of quality indices and reconstruction visual effects.

Poisson noise removal of images on graphs using tight wavelet frames

After many years of study, the subject of image denoising on the flat domain is well developed. However, many practical problems arising from different areas, such as computer vision, computer graphics, geometric modeling and medical imaging, involve images on the irregular domain sets such as graphs. In this paper, we consider Poisson and mixed Poisson–Gaussian noise removal of images on graphs. Based on the statistical characteristic of the observed noisy images, we propose a wavelet frame-based variational model to restore images on graphs. The model contains a weighted $$\ell _2$$ fidelity term and an $$\ell _1$$ -regularized term which makes additional use of the tight wavelet frame transform on graphs in order to preserve key features such as textures and edges of images. We then apply the popular alternating direction method of multipliers (ADMM) to solve the model. Finally, we provide supporting numerical experiments on graphs and compare with other denoising methods. The results on some image denoising tasks indicate the effectiveness of our method.

Fourier ptychographic microscopy using a generalized Anscombe transform approximation of the mixed Poisson-Gaussian likelihood.

Fourier ptychographic microscopy (FPM) is a novel computational microscopy technique that provides intensity images with both wide field-of-view (FOV) and high-resolution (HR). By combining ideas from synthetic aperture and phase retrieval, FPM iteratively stitches together a number of variably illuminated, low-resolution (LR) intensity images in Fourier space to reconstruct an HR complex sample image. In practice, however, the reconstruction of FPM is sensitive to the input noise, including Gaussian noise, Poisson shot noise or mixed Poisson-Gaussian noise. To efficiently address these noises, we developed a novel FPM reconstruction method termed generalized Anscombe transform approximation Fourier ptychographic (GATFP) reconstruction. The method utilizes the generalized Anscombe transform (GAT) approximation for the noise model, and a maximum likelihood theory is employed for formulating the FPM optimization problem. We validated the proposed method with both simulated data for quantitative evaluation and real experimental data captured using FPM setup. The results show that the proposed method achieves state-of-the-art performance in comparison with other approaches.

Self-adapting denoising, alignment and reconstruction in electron tomography in materials science

An automatic procedure for electron tomography is presented. This procedure is adapted for specimens that can be fashioned into a needle-shaped sample and has been evaluated on inorganic samples. It consists of self-adapting denoising, automatic and accurate alignment including detection and correction of tilt axis, and 3D reconstruction. We propose the exploitation of a large amount of information of an electron tomography acquisition to achieve robust and automatic mixed Poisson–Gaussian noise parameter estimation and denoising using undecimated wavelet transforms. The alignment is made by mixing three techniques, namely (i) cross-correlations between neighboring projections, (ii) common line algorithm to get a precise shift correction in the direction of the tilt axis and (iii) intermediate reconstructions to precisely determine the tilt axis and shift correction in the direction perpendicular to that axis. Mixing alignment techniques turns out to be very efficient and fast. Significant improvements are highlighted in both simulations and real data reconstructions of porous silicon in high angle annular dark field mode and agglomerated silver nanoparticles in incoherent bright field mode. 3D reconstructions obtained with minimal user-intervention present fewer artefacts and less noise, which permits easier and more reliable segmentation and quantitative analysis. After careful sample preparation and data acquisition, the denoising procedure, alignment and reconstruction can be achieved within an hour for a 3D volume of about a hundred million voxels, which is a step toward a more routine use of electron tomography.

A reweighted $l^2$ method for image restoration with Poisson and mixed Poisson-Gaussian noise

We study weighted $l^2$ fidelity in variational models for Poisson noise related image restoration problems. Gaussian approximation to Poisson noise statistic is adopted to deduce weighted $l^2$ fidelity. Different from the traditional weighted $l^2$ approximation, we propose a reweighted $l^2$ fidelity with sparse regularization by wavelet frame. Based on the split Bregman algorithm introduced in [21], the proposed numerical scheme is composed of three easy subproblems that involve quadratic minimization, soft shrinkage and matrix vector multiplications. Unlike usual least square approximation of Poisson noise, we dynamically update the underlying noise variance from previous estimate. The solution of the proposed algorithm is shown to be the same as the one obtained by minimizing Kullback-Leibler divergence fidelity with the same regularization. This reweighted $l^2$ formulation can be easily extended to mixed Poisson-Gaussian noise case. Finally, the efficiency and quality of the proposed algorithm compared to other Poisson noise removal methods are demonstrated through denoising and deblurring examples. Moreover, mixed Poisson-Gaussian noise tests are performed on both simulated and real digital images for further illustration of the performance of the proposed method.

Efficient interference cancellation detector for asynchronous upstream optical code division multiple access‐passive optical network with mixed Poisson–Gaussian noise

Optical code division multiple access (OCDMA) is a promising candidate for next generation passive optical networks (NG-PON). OCDMA-PON can potentially provide all customers with a Gb/s-class BW upstream with inherent flexibility. Unfortunately OCDMA suffers from multiple access interference (MAI) and various detection noises. In this study, the authors consider developing efficient interference cancellation detection under mixed Poisson-Gaussian noise. The latter is more realistic than considering Gaussian or Poisson noise alone. The authors first start by developing a maximum likelihood framework of the detection process under Gaussian, Poisson and Poisson-Gaussian noises, respectively. Then, the authors develop the proposed interference cancellation detector for the Poisson-Gaussian noise case after deriving the conventional expectation-maximisation (EM) detector for the Poisson noise case. Finally, the authors simulate the proposed detector and compare it to the projected parallel interference cancellation, EM and other detectors to validate its superiority and enhanced performance.

An Unbiased Risk Estimator for Image Denoising in the Presence of Mixed Poisson–Gaussian Noise

The behavior and performance of denoising algorithms are governed by one or several parameters, whose optimal settings depend on the content of the processed image and the characteristics of the noise, and are generally designed to minimize the mean squared error (MSE) between the denoised image returned by the algorithm and a virtual ground truth. In this paper, we introduce a new Poisson-Gaussian unbiased risk estimator (PG-URE) of the MSE applicable to a mixed Poisson-Gaussian noise model that unifies the widely used Gaussian and Poisson noise models in fluorescence bioimaging applications. We propose a stochastic methodology to evaluate this estimator in the case when little is known about the internal machinery of the considered denoising algorithm, and we analyze both theoretically and empirically the characteristics of the PG-URE estimator. Finally, we evaluate the PG-URE-driven parametrization for three standard denoising algorithms, with and without variance stabilizing transforms, and different characteristics of the Poisson-Gaussian noise mixture.

Image Denoising in Mixed Poisson–Gaussian Noise

We propose a general methodology (PURE-LET) to design and optimize a wide class of transform-domain thresholding algorithms for denoising images corrupted by mixed Poisson-Gaussian noise. We express the denoising process as a linear expansion of thresholds (LET) that we optimize 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). We provide a practical approximation of this theoretical MSE estimate for the tractable optimization of arbitrary transform-domain thresholding. We then propose a pointwise estimator for undecimated filterbank transforms, which consists of subband-adaptive thresholding functions with signal-dependent thresholds that are globally optimized in the image domain. We finally demonstrate the potential of the proposed approach through extensive comparisons with state-of-the-art techniques that are specifically tailored to the estimation of Poisson intensities. We also present denoising results obtained on real images of low-count fluorescence microscopy.