Mixed Poisson-Gaussian Noise Research Articles

Distortion Correction and Denoising of Light Sheet Fluorescence Images.

Light Sheet Fluorescence Microscopy (LSFM) has emerged as a valuable tool for neurobiologists, enabling the rapid and high-quality volumetric imaging of mice brains. However, inherent artifacts and distortions introduced during the imaging process necessitate careful enhancement of LSFM images for optimal 3D reconstructions. This work aims to correct images slice by slice before reconstructing 3D volumes. Our approach involves a three-step process: firstly, the implementation of a deblurring algorithm using the work of K. Becker; secondly, an automatic contrast enhancement; and thirdly, the development of a convolutional denoising auto-encoder featuring skip connections to effectively address noise introduced by contrast enhancement, particularly excelling in handling mixed Poisson-Gaussian noise. Additionally, we tackle the challenge of axial distortion in LSFM by introducing an approach based on an auto-encoder trained on bead calibration images. The proposed pipeline demonstrates a complete solution, presenting promising results that surpass existing methods in denoising LSFM images. These advancements hold potential to significantly improve the interpretation of biological data.

MULTISPECTRAL IMAGE RESTORATION USING A VECTOR-VALUED REACTION-DIFFUSION BASED MIXED NOISE REMOVAL TECHNIQUE

Abstract. A novel multispectral image filtering technique is proposed in this article. Since the multispectral images are often corrupted by mixed Poisson-Gaussian noise during the sensing and acquisition process, a nonlinear anisotropic diffusion-based restoration approach that deals efficiently with this type of noise mixture is considered here. A second-order vector-valued reaction-diffusion model that leads to a system of well-posed single-valued anisotropic diffusion equations coupled by correlation terms is introduced for this purpose. A finite difference method-based fast-converging approximation algorithm that solves numerically this nonlinear diffusion-based system is then proposed. This iterative numerical approximation scheme is successfully used for removing both the additive Gaussian and quantum noises while preserving the essential features of the multi-valued image. The effectiveness of the described mixed denoising technique is illustrated by the results of the restoration experiments and method comparisons that are also presented here. The proposed restoration approach enhances considerably the spectral image quality, making it well-prepared for the further MSI analysis and computer vision processes, such as the geospatial and remote sensing image analysis.

Maximum-likelihood estimation in ptychography in the presence of Poisson-Gaussian noise statistics.

Optical measurements often exhibit mixed Poisson-Gaussian noise statistics, which hampers the image quality, particularly under low signal-to-noise ratio (SNR) conditions. Computational imaging falls short in such situations when solely Poissonian noise statistics are assumed. In response to this challenge, we define a loss function that explicitly incorporates this mixed noise nature. By using a maximum-likelihood estimation, we devise a practical method to account for a camera readout noise in gradient-based ptychography optimization. Our results, based on both experimental and numerical data, demonstrate that this approach outperforms the conventional one, enabling enhanced image reconstruction quality under challenging noise conditions through a straightforward methodological adjustment.

Mixed Poisson-Gaussian noise reduction using a time-space fractional differential equations

Images are frequently corrupted by various sorts of mixed or unrecognized noise, including mixed Poisson-Gaussian noise, rather than just a single kind of noise. In this work, we propose a time-space fractional differential equation to remove mixed Poisson-Gaussian noise. Combining fixed- and variable-order fractional derivatives allows us to maintain an image's high- and low-frequency components while eliminating noise. The current model, although primarily intended for mixed noise reduction, can indeed be utilized with great efficacy on images that have been solely degraded by Gaussian noise. In addition to this, a stable discretization strategy is presented. The illustrative results demonstrate that our scheme performs better than earlier models, reduces the staircase effect, and is applicable to electron microscopy and CT images.

First-order primal–dual algorithm for image restoration corrupted by mixed Poisson–Gaussian noise

The total variation infimal convolution (TV-IC) model combining Kullback–Leibler and ℓ2-norm data fidelity term works well for the inverse problem of mixed Poisson–Gaussian noise. Most existing algorithms for solving the TV-IC model rely on the Newton method to solve a nonlinear optimization subproblem, which inevitably increases the computation burden. In this study, we apply the first-order primal–dual Chambolle–Pock algorithm to solve the TV-IC model. In particular, we present an effective algorithm to solve the subproblem of the joint proximal operator with the Kullback–Leibler divergence and ℓ2-norm, which is based on the bilinear constraint alternating direction multiplier method. Numerical experiment results demonstrate that the proposed algorithm outperforms the state-of-the-art methods for mixed Poisson–Gaussian denoising and deblurring problems.

A non–convex total generalized variation model for image denoising

We propose an effective regularization model based on second–order total generalized variation for image restoration with mixed Poisson–Gaussian noise. An efficient alternating minimization algorithm is employed to solve the considered model. Finally, provided numerical results show that our proposed model can preserve more details and get higher image visual quality than recent state-of-the-art methods.

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.

Compressed sensing based on L1 and TGV regularization for low-light-level images denoising

Compressed sensing has been applied to image denoising in recent years, and it shows strong noise suppression ability for image corrupted by Gaussian noise. However, the noise contained in low-light-level image is extensive and complex and is modeled as mixed Poisson-Gaussian noise. In this paper, to enable the compressed sensing method to handle such the noise model, the variance-stabilizing transformation and its inverse transformation are used before and after denoising. The total generalized variation constraint term is introduced into the L1 regularization model to maintain the image's structure information, and the alternating direction method of multiplier is used to solve the proposed model. Each subproblem has a closed-form solution. Numerical experiments on artificially degraded and raw low-light-level images show that the proposed method achieves superior performance in terms of visual effects and objective evaluation indices compared with several existing methods.

Deep external and internal learning for noisy compressive sensing

Reconstructing natural image from its corresponding compressive sensing (CS) measurements is an ill-posed problem. Learning accurate prior of desirable image is essential to solve this inverse problem in high quality, especially for CS reconstruction from noisy measurements. The existing learning-based methods cannot effectively simulate whole potential noise in the testing data during external learning, and cannot effectively exploit the information from internal testing data. In this paper, we present an effective convolutional neural network (CNN) based method for CS reconstruction from noisy measurements, which learns the deep prior from an external dataset and internal noisy testing data with Stein’s unbiased risk estimator (SURE). Specifically, we first pre-train an arbitrary CNN for CS reconstruction with an external dataset to learn a common prior. Then, we utilize meta learning to find a generic initial parameter that is suitable for fast internal learning and adaption to various noisy measurements. Finally, we customize the learned network to learn a specific prior for each internal testing data under Gaussian noise or more general mixed Poisson-Gaussian noise. Experimental results show that the proposed method outperforms the state-of-the-art methods under both comprehensively quantitative metrics and perceptive quality.

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.

Least-squares and maximum-likelihood in computed tomography.

Purpose: Existing maximum-likelihood (ML) methods in computed tomography usually require significant computing resources to implement, and/or are limited to particular measurement noise models that are representative of the simplest theoretical archetypes. There is an absence of general procedures to produce rapid ML methods that account precisely for the noise model of a given experiment. We investigate a mathematical-computational procedure of producing constrained quadratic optimization reconstruction algorithms that fill this niche, requiring less computing resources than the exact (expectation-maximization) procedures and having comparable performance with least-squares iterative methods. This allows high-fidelity reconstructions to be practically achievable for largely arbitrary noise models. Approach: We identify a systematic mathematical procedure to produce constrained quadratic optimization methods that maximize tomogram likelihood under arbitrary noise models, which are tunable to specific characteristics of the experiment. This procedure is applied to a general theory of mixed Poisson-Gaussian noise in transmission tomography, and to a theory of invertible linear transformations of measurement intensity subject to Poisson noise. We perform tomographic reconstructions of a very highly attenuating two-dimensional object phantom and compare the speed and fidelity of reconstruction with alternative quadratic metrics ( -minimization among others). Results: Quantitative metrics reveal that reconstructions under our systematically produced quadratic methods achieved significantly greater reconstruction fidelity with less computation than the optimized conventional, untuned quadratic metrics with a comparable procedure. Conclusion: Constrained quadratic optimization methods appear to apply sufficiently good approximations to achieve a high reconstruction fidelity with a simple quadratic metric amenable to a broad class of minimization methods. These preliminary simulation-based results are very promising and suggest that such methods may be used to produce high-fidelity reconstructions with less computation than many other statistical methods. By design, these quadratic methods are also explicit and quantitative in their description, allowing fine-tuning according to the specific uncertainties and noise model of the experiment. Further research is required to ascertain the full practical potential of these methods.

A new approach for reduction of the noise from microscopy images using Fourier decomposition

In this paper, an efficient method based on the Fourier decomposition method (FDM) is presented for noise removal of medical microscopic images. We propose an adaptive thresholding technique based FDM for denoising of heavily degraded images. An accurate image deconvolution is done with variance stabilization transformation and multi-scale Wiener filtering as a pre-processing step. The different series of frequency intrinsic band functions (FIBF’s) obtained with FDM which are further separated into noise and signal-significant FIBF’s based on cosine similarity index. The FDM adaptive thresholding technique is used to filter-out the unwanted frequency coefficients related to mixed Poisson-Gaussian noise (MPG). The thresholded FIBF’s and signal significant FIBF’s are combined to obtained reconstructed output. Finally, the optimization is done using mixed noise unbiased risk estimate (MNURE). To evaluate the effectiveness of proposed scheme, we have compared the results of the proposed scheme with six different state-of-the-art techniques. The simulation results verify, the effectiveness of proposed method. The proposed algorithm achieves better performance in terms of four quantitative evaluation measures by reducing the effect of noise.

Real-time image denoising of mixed Poisson–Gaussian noise in fluorescence microscopy images using ImageJ

Fluorescence microscopy imaging speed is fundamentally limited by the measurement signal-to-noise ratio (SNR). To improve image SNR for a given image acquisition rate, computational denoising techniques can be used to suppress noise. However, common techniques to estimate a denoised image from a single frame either are computationally expensive or rely on simple noise statistical models. These models assume Poisson or Gaussian noise statistics, which are not appropriate for many fluorescence microscopy applications that contain quantum shot noise and electronic Johnson–Nyquist noise, therefore a mixture of Poisson and Gaussian noise. In this paper, we show convolutional neural networks (CNNs) trained on mixed Poisson and Gaussian noise images to overcome the limitations of existing image denoising methods. The trained CNN is presented as an open-source ImageJ plugin that performs real-time image denoising (within tens of milliseconds) with superior performance (SNR improvement) compared to conventional fluorescence microscopy denoising methods. The method is validated on external datasets with out-of-distribution noise, contrast, structure, and imaging modalities from the training data and consistently achieves high-performance ( > --> 8 d B ) denoising in less time than other fluorescence microscopy denoising methods.

Noise reduction in two-photon laser scanned microscopic images by singular value decomposition with copula threshold

Multi-photon laser scanning microscopy is an advantageous technique for layered imaging in thick tissue samples. It enables reduced phototoxicity as the region of fluorescence excitation is limited. But, the small number and stochastic nature of detected photons require the multifold acquisition of each image so the photodamage may accumulate. This paper aims to reduce the number of repeated image acquisitions, proposing a denoising technique based on singular value decomposition with a novel two-stage copula threshold, thus the name SVD-COPULA. The first stage defines the referent noise level based on copula analysis. Following the comparative analysis of classical techniques and different copula families, Frank's copula is selected to determine the regions for noise estimation. The second threshold stage analyzes the stationarity of the singular values and adjusts the number of the eigenimages necessary for reconstruction, an issue important for images without the distinctive background regions. A problem of the mixed discrete-continual nature of pixel values is noticed and resolved. The procedure is fully automatic, with the built-in set of parameters and without the necessity for prior image analysis. The proposed method, together with twelve state-of-the-art denoising methods, are tested using the microscopic images from the proprietary and open databases, and the test images with simulated mixed Poisson-Gaussian noise. It is shown that the performance of SVD-COPULA is consistently good for all investigated images.

A practical residual block-based no-reference quality metric for neutron radiographic images

Objective image quality metric is a challenging problem for neutron radiography due to the lack of reference images. The existing no-reference image quality metric (NR-IQM) method designed for neutron radiographic images (NRIs) still exists two main shortcomings. Firstly, the limited L/D of the collimator would inevitably lead to geometric blur in the NRIs. However, the special distortion type of mixed Poisson–Gaussian noise is merely considered but ignores the blur distortion. Secondly, the distortion levels of Poisson noise added to an image cannot be adjusted. In order to address these two issues, a more practical objective NR-IQM method is proposed to predict the perceptual quality of NRIs in this paper. Experimental results demonstrate that the proposed method shows good consistency with the quality of authentic NRIs and also performs well in reflecting the tiny quality difference of enhanced NRIs, thus demonstrating its application potential in neutron radiography.

Infrared star image denoising using regions with deep reinforcement learning

Efficient and accurate extraction and restoration of star targets in infrared star images with small number of frames is a growing need for optical adaptive image processing. Among the various noise in star images, mixed Poisson-Gaussian noise is difficult to be accurately suppressed due to its complicated distribution function. Aiming at obtaining the true value of star targets’ signal intensity in infrared images, a novel star target extraction and denoising model called regions with deep reinforcement learning (RDRL) is designed and developed in this study. This fully-automatic model contains two modules: (1) star region extraction module (SREM) that generates star regions within the image through an iterative algorithm based on geometric centroid method (GCM); (2) denoising module that performs an iterative denoising process on the star regions based on deep reinforcement learning. The denoising algorithm is tested on infrared star images, and the experiment results indicate that the proposed RDRL denoising model is able to achieve more accurate restoration with a smaller number of calculations than existing star image denoising methods.

Single-pixel image reconstruction from experimental data using neural networks.

Single-pixel cameras that measure image coefficients have various promising applications, in particular for hyper-spectral imaging. Here, we investigate deep neural networks that when fed with experimental data can output high-quality images in real time. Assuming that the measurements are corrupted by mixed Poisson-Gaussian noise, we propose to map the raw data from the measurement domain to the image domain based on a Tikhonov regularization. This step can be implemented as the first layer of a deep neural network, followed by any architecture of layers that acts in the image domain. We also describe a framework for training the network in the presence of noise. In particular, our approach includes an estimation of the image intensity and experimental parameters, together with a normalization scheme that allows varying noise levels to be handled during training and testing. Finally, we present results from simulations and experimental acquisitions with varying noise levels. Our approach yields images with improved peak signal-to-noise ratios, even for noise levels that were foreseen during the training of the networks, which makes the approach particularly suitable to deal with experimental data. Furthermore, while this approach focuses on single-pixel imaging, it can be adapted for other computational optics problems.

Second-order total generalized variation based model for restoring images with mixed Poisson — Gaussian noise

Introduction: A common problem in image restoration is image denoising. Among many noise models, the mixed Poisson-Gaussian model has recently aroused considerable interest. Purpose: Development of a model for denoising images corrupted by mixed Poisson-Gaussian noise, along with an algorithm for solving the resulting minimization problem. Results: We proposed a new total variation model for restoring an image with mixed Poisson-Gaussian noise, based on second-order total generalized variation. In order to solve this problem, an efficient alternating minimization algorithm is used. To illustrate its comparison with related methods, experimental results are presented, demonstrating the high efficiency of the proposed approach. Practical relevance: The proposed model allows you to remove mixed Poisson-Gaussian noise in digital images, preserving the edges. The presented numerical results demonstrate the competitive features of the proposed model.

Infrared image denoising based on the variance-stabilizing transform and the dual-domain filter

In the past decades, image denoising has been widely studied as a basic technology for image processing. However, most denoising methods are designed for Gaussian noise, while few researches focus on the suppression of mixed Poisson-Gaussian noise, which usually found in infrared images. In order to remove the mixed noise in infrared images, this paper proposes a denoising method based on the variance-stabilizing transform (VST) and the dual-domain filter (DDF). We transform the mixed noise data into an approximate Gaussian distribution with uniform variance through the VST and then adopt the improved DDF to denoise the transformed data. Finally, we apply the closed approximation inverse of the VST to the denoised data for the final denoising estimate. The denoising results of infrared images with different intensity all effectively suppress the mixed noise and retain abundant details. The quality and quantity comparisons with nine other methods reveal that our method can achieve a superior performance.

A Non-Local Superpatch-Based Algorithm Exploiting Low Rank Prior for Restoration of Hyperspectral Images.

We propose a novel algorithm for the restoration of a degraded hyperspectral image. The proposed algorithm exploits the spatial as well as the spectral redundancy of a degraded hyperspectral image in order to restore it without having any prior knowledge about the type of degradation present. Our work uses superpatches to exploit the spatial and spectral redundancies. We formulate a restoration algorithm incorporating structural similarity index measure as the data fidelity term and nuclear norm as the regularization term. The proposed algorithm is able to cope with additive Gaussian noise, signal dependent Poisson noise, mixed Poisson-Gaussian noise and can restore a hyperspectral image corrupted by dead lines and stripes. As we demonstrate with the aid of extensive experiments, our algorithm is capable of recovering the spectra even in the case of severe degradation. A comparison with the state-of-the-art low rank hyperspectral image restoration methods via experiments with real world and simulated data establishes the competitiveness of the proposed algorithm with the existing methods.