Poisson-Gaussian Noise Model Research Articles

M-Denoiser: Unsupervised image denoising for real-world optical and electron microscopy data

Real-world microscopy data have a large amount of noise due to the limited light/electron that can be used to capture images. The noise of microscopy data is composed of signal-dependent shot noise and signal-independent read noise, and the Poisson–Gaussian noise model is usually used to describe the noise distribution. Meanwhile, the noise is spatially correlated because of the data acquisition process. Due to the lack of clean ground truth, unsupervised and self-supervised denoising algorithms in computer vision shed new light on tackling such tasks by utilizing paired noisy images or one single noisy image. However, they usually make the assumption that the noise is signal-independent or pixel-wise independent, which contradicts with the actual case. Hence, we propose M-Denoiser for denoising real-world microscopy data in an unsupervised manner. Firstly, the shatter module is used to break the dependency and correlation before denoising. Secondly, a novelly designed unsupervised training loss based on a pair of noisy images is proposed for real-world microscopy data. For evaluation, we train our model on optical and electron microscopy datasets. The experimental results show that M-Denoiser achieves the best performance both quantitatively and qualitatively compared with all the baselines.

Modified denoising method of Raman spectra-based deep learning for Raman semi-quantitative analysis and imaging

Raman spectroscopic technique is a sensitive and non-destructive technique for structural analysis. However, Raman scattering is an unfavorable process, and the signals are weak, resulting in a low signal-to-noise ratio of spectra, making Raman spectroscopy challenging to gain popularity and implement. As a simple and practical approach, denoising techniques could improve the signal-to-noise ratio, which can help researchers extract information more effectively to reflect the configuration, content, and changes of test samples. However, addressing this issue with traditional algorithms is often challenging due to increased complexity and requirements in Raman spectra denoising. While some deep learning–based approaches enhance the signal-to-noise ratio, obtaining excellent performance models with good generalization is not easy when dealing with real-world tasks. This paper proposes a method of good generalization, robust, and denoising performance by using a convolutional neural network based on a new augmented method and a multi-scale feature extraction fusion block called the multi-scale feature extraction denoising (MFED) model. Specifically, first, we addressed insufficient training data using a new augmented approach through simulation of the Raman data acquisition and, in turn, improved generalization of the MFED model. Subsequently, the mixed Poisson-Gaussian noise model showed commendable robustness when dealing with synthetic and real noise data. Finally, a feature extraction block based on a multi-scale fusion significantly improved denoising effects. The comparison results of different denoising methods demonstrated the good applicability and superiority of the proposed approach. More importantly, the main advantage of the proposed MFED model is that it is easily applicable. We demonstrate that applying MFED as a pre-processing technique for Raman spectra can enhance the prediction accuracy of soybean oil concentration in olive oil. Furthermore, despite the integration time dropping from 3 to 1 s, we still yielded good quality images following MFED model denoising processing on point-scan Raman spectral imaging of cervical cancer cells. The proposed MFED model provides an excellent candidate for increasing the Raman SNR, which can contribute substantially to the application of Raman analytics in research and practices.

An adaptive image restoration algorithm based on hybrid total variation regularization

In imaging systems, the mixed Poisson-Gaussian noise (MPGN) model can accurately describe the noise present. Total variation (TV) regularization-based methods have been widely utilized for Poisson-Gaussian removal with edge-preserving. However, TV regularization sometimes causes staircase artifacts with piecewise constants. To overcome this issue, we propose a new model in which the regularization term is represented by a combination of total variation and high-order total variation. We study the existence and uniqueness of the minimizer for the considered model. Numerically, the minimization problem can be efficiently solved by the alternating minimization method. Furthermore, we give rigorous convergence analyses of our algorithm. Experiments results are provided to demonstrate the superiority of our proposed hybrid model and algorithm for deblurring and denoising images simultaneously, in comparison with several state-of-the-art numerical algorithms.

A phantom study on dose efficiency for orthopedic applications: Comparing slot-scanning radiography using ultra-small-angle tomosynthesis to conventional radiography.

This paper studies the abilities of a twin-robotic x-ray slot-scanning system for orthopedic imaging to reduce dose by scatter rejection compared to conventional digital radiography. We investigate the dose saving capabilities, especially in terms of the signal- and the contrast-to-noise ratio, as well as the scatter-to-primary ratio of the proposed slot-scanning method in comparison to the state-of-the-art method for length-extended imaging. As a baseline, we use x-ray parameters of two clinically established acquisition protocols that provide the same detector entrance dose but are profoundly different in patient dose. To obtain an estimate of the photon-related noise directly from an x-ray image, we implement a Poisson-Gaussian noise model. This model is used to compare the dose efficiency of two settings and combined with the well-known to determine the transmission parameters. We present a method with an associated measurement protocol, utilizing the robotic capabilities of the used system to automatically obtain quasi-scatter-free ground-truth data with exact geometric correspondence to full-field and slot acquisitions. In total, we investigate two body regions (thoracic spine and lumbar spine) in anterior-posterior view with two patient sizes (BMI = 22 and 30) in two acquisition modes (conventional and slot scan with a flat-panel detector) with and without anti-scatter grid using an anthropomorphic upper-body phantom. We have shown that it is feasible to combine the proposed approach with the for the determination of scatter rejection parameters. The use of an anti-scatter grid is indicated for full-field acquisitions allowing for dose savings up to 46% compared to their gridless counterparts. When changing the acquisition mode to the investigated slot scan, the use of an anti-scatter grid has no major impact on the image quality in terms of dose efficiency, in particular for patients with a BMI of 22. However, an increased contrast improvement factor was found. For normal-sized patients, up to 53% of dose can be saved additionally in comparison to full-field acquisitions with grid. Moreover, we could demonstrate that a slot size of 5cm and air gap of 10cm is sufficient to achieve scatter-to-primary ratios, which are equal or better compared to those of the full-field acquisitions with a grid. We have shown, that the slot-scanning approach is always superior to the conventional full-field acquisition in terms of signal-to-noise and scatter-to-primary ratios. Compared to the state-of-the-art acquisition protocols with a grid, dose savings up to 53% are possible due to the scatter rejection without compromising the SNR. Hence, the use of the slot-scanning method is indicated, especially when it comes to regularly carried-out follow-up acquisitions, for example, in the case of scoliosis monitoring.

Toward blind joint demosaicing and denoising of raw color filter array data

Raw color-filter-array (CFA) data collected in the real world are often noisy and signal-dependent, which makes it difficult to recover the full-resolution noise-free color image. Denoising and demosaicing are two popular tools developed for noisy CFA data in modern color imaging pipeline. However, most existing works on joint demosaicing and denoising (JDD) are based on ad hoc assumptions about image degradation process; while in practice little is known about noise statistics (e.g., noise level) and processing pipeline (e.g., gamma correction). We advocate a blind formulation of joint demosaicing and denoising (bJDD) problem in this paper and present a novel divide-and-conquer approach toward blind reconstruction from noisy raw CFA data. Instead of making over-simplified assumptions about noise statistics, we propose to develop a more realistic Poisson-Gaussian noise model for simulating noisy raw CFA data in the real world. We also introduce a sub-network to adaptively estimate the noise level map from the noisy input, which will provide supplementary information to the deep model for non-blind JDD. Finally, we have adopted a generative adversarial network (GAN) based network for further perceptual optimization. Our extensive experimental results have shown convincingly improved performance over existing state-of-the-art methods in terms of both subjective and objective quality metrics.

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.

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 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.

Variance-stabilization-based compressive inversion under Poisson or Poisson–Gaussian noise with analytical bounds

Most existing bounds for signal reconstruction from compressive measurements make the assumption of additive signal-independent noise. However in many compressive imaging systems, the noise statistics are more accurately represented by Poisson or Poisson–Gaussian noise models. In this paper, we derive upper bounds for signal reconstruction error from compressive measurements which are corrupted by Poisson or Poisson–Gaussian noise. The features of our bounds are as follows: (1) the bounds are derived for a computationally tractable convex estimator with statistically motivated parameter selection. The estimator penalizes signal sparsity subject to a constraint that imposes a novel statistically motivated upper bound on a term based on variance stabilization transforms to approximate the Poisson or Poisson–Gaussian distributions by distributions with (nearly) constant variance. (2) The bounds are applicable to signals that are sparse as well as compressible in any orthonormal basis, and are derived for compressive systems obeying realistic constraints such as non-negativity and flux-preservation. Our bounds are motivated by several properties of the variance stabilization transforms that we develop and analyze. We present extensive numerical results for signal reconstruction under varying number of measurements and varying signal intensity levels. Ours is the first piece of work to derive bounds on compressive inversion for the Poisson–Gaussian noise model. We also use the properties of the variance stabilizer to develop a principle for selection of the regularization parameter in penalized estimators for Poisson and Poisson–Gaussian inverse problems.

RENOIR – A dataset for real low-light image noise reduction

Image denoising algorithms are evaluated using images corrupted by artificial noise, which may lead to incorrect conclusions about their performances on real noise. In this paper we introduce a dataset of color images corrupted by natural noise due to low-light conditions, together with spatially and intensity-aligned low noise images of the same scenes. We also introduce a method for estimating the true noise level in our images, since even the low noise images contain small amounts of noise. We evaluate the accuracy of our noise estimation method on real and artificial noise, and investigate the Poisson-Gaussian noise model. Finally, we use our dataset to evaluate six denoising algorithms: Active Random Field, BM3D, Bilevel-MRF, Multi-Layer Perceptron, and two versions of NL-means. We show that while the Multi-Layer Perceptron, Bilevel-MRF, and NL-means with soft threshold outperform BM3D on gray images with synthetic noise, they lag behind on our dataset.

General error model for analysis of laser-induced incandescence signals.

This paper presents a novel error model for TiRe-LII signals and illustrates how the model can be used to diagnose a detection system, quantify uncertainties in TiRe-LII, and characterize fluctuations in the measured process. Noise in a single TiRe-LII measurement shot obeys a Poisson-Gaussian noise model. Variation in the aerosol results in shot-to-shot fluctuations in the measured signals. These fluctuations induce a quadratic relationship between the mean and variance of a set of signals. We show how this model can elucidate aspects of the measurement system and fundamental properties of the aerosol, by comparing the noise model to four sets of experimental data.

Signal-dependent noise removal for color videos using temporal and cross-channel priors

Noise widely exists in video acquisition, and is especially large under low illumination conditions. Existing video denoising methods are usually at the risk of losing perceptually crucial scene details and introducing unpleasant artifacts. Inspired by high sensitivity of human vision system to thin structures and color aberration in natural images, we incorporate two video priors into a joint optimization framework besides the constraint from the adopted Poisson–Gaussian noise model: (i) we force the motion compensated frames to be a low rank matrix to separate thin structures from large noise. (ii) we utilize the consistency of image pixel gradients in different color channels as a cross channel prior to eliminate color fringing artifacts. To solve this non-convex optimization model, we derive a numerical algorithm via the augmented Lagrangian multiplier method. The effectiveness of our approach is validated by a series of experiments, with both objective and subjective evaluations.

Medical image denoising using simple form of MMSE estimation in Poisson–Gaussian noise model

Poisson–Gaussian noise is the basis of image formation for a great number of imaging systems used in variety of applications, including medical and astronomical imaging. In wavelet domain, the application of Bayesian estimation method with generalized Anscombe transform in Poisson–Gaussian noise reduction algorithm has shown remarkable success over the last decade. The generalized Anscombe transform is exerted to convert the Poisson–Gaussian noise into an additive white Gaussian noise (AWGN). So, the resulting data can be denoised with any algorithm designed for the removal of AWGN. Here, we present simple form of minimum mean square error (MMSE) estimator for logistic distribution in Poisson–Gaussian noise. The experimental results show that the proposed method yields good denoising results.

Removal of horizontal and vertical scratches for a new class of wavelet and log energy bounded Wiener estimation over Poisson-Gaussian noise model

Generally Gaussian noise model is taken into account in image processing applications. However its presence in charge coupled device (CCD) enabled cameras. Off let photon noise as packet of energy came up from statistical nature of electromagnetic radiation from object of interest. Photon noise with poison distribution also exists with Gaussian noise. Certainly, Poisson-Gaussian noise model is often essential gradients for image processing to achieve acceptable visual appearance and strengthen the recipient signal. Proposed work demonstrated the Poisson-Gaussian noise model and its implementation in the new soft shrinkage algorithm, which is based on wavelet scaling coefficients and log energy transformation of detail coefficients in Wiener estimation. The significance of the proposed method in digital image processing is only and only for providing pure visual cortex of the recipient signal. Proposed work demonstrated the automated sub band adaptive statistical estimation of standard deviation of noisy wavelet coefficients. Further the proposed extended filter minimises the problem of horizontal and vertical scratches which arose in jointly processed wavelet transform and log energy-based Wiener filter. A significant improvement in PSNR using peak tube voltage was reported for guaranteed pure image restoration and also deployed structural similarity index (SSIM) for high quality visual assurance.

Practical signal-dependent noise parameter estimation from a single noisy image.

The additive white Gaussian noise is widely assumed in many image processing algorithms. However, in the real world, the noise from actual cameras is better modeled as signal-dependent noise (SDN). In this paper, we focus on the SDN model and propose an algorithm to automatically estimate its parameters from a single noisy image. The proposed algorithm identifies the noise level function of signal-dependent noise assuming the generalized signal-dependent noise model and is also applicable to the Poisson-Gaussian noise model. The accuracy is achieved by improved estimation of local mean and local noise variance from the selected low-rank patches. We evaluate the proposed algorithm with both synthetic and real noisy images. Experiments demonstrate that the proposed estimation algorithm outperforms the state-of-the-art methods.

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.

Simplified noise model parameter estimation for signal-dependent noise

In this paper, we present a noise parameter estimation method using a simplified signal-dependent noise model. The generic Poisson–Gaussian noise model is simplified to a Gaussian–Gaussian noise model. From the simplified noise model, we experimentally verify that the value obtained by the robust median estimator is almost the same as the mean of the noise standard deviation. Based on this property, the noise model parameters are estimated by the least square method. Simulation results show that the estimation performance using our proposed algorithm is compatible with the performance of the existing method. Our method can generate good parameter estimation results with reduced computational complexity.