Mixed Gaussian-impulse Noise Research Articles

Mixed Gaussian-impulse noise removal using non-convex high-order TV penalty

To restore images with clear edge details and no staircase artifacts from degraded versions, this paper incorporates the ℓ2 plus ℓ0 data fidelity and non-convex high-order total variation regularizer to establish an optimization model for eliminating mixed Gaussian-impulse noise. Among them, the ℓ2 fidelity is adopted to suppress Gaussian noise, while the ℓ0-norm is more suitable for detecting and removing impulse noise. In addition, the non-convex regularization displays excellent performance in overcoming the staircase effect and preserving edge details. Computationally, by using the iteratively reweighted ℓ1 algorithm and variable splitting method, this work designs a modified alternating minimization method to solve the optimization problem we construct. In theory, the convergence proof of our resulting algorithm is also presented. Finally, in the experimental section, we conduct extensive numerical experiments on degraded images and compare with other existing techniques. From the intuitive effects and restoration accuracy, it follows that our newly proposed method is effective and competitive for image deblurring and mixed noise removal.

Lp-norm-based successive denoising approach for hyperspectral images

ABSTRACT Hyperspectral images (HSI) are essentially a data cube containing hundreds of stacked 2-D images collected over a set of adjacent spectral bands with the idea of obtaining a complete spectral information for each pixel in a scene. However, multiple factors contribute to noise, which manifests as grainy textures, dead pixels and stripes in the acquired images, and is classically modelled as a mixture of Gaussian and impulse noise statistics. Denoising therefore forms an important pre-processing task to most HSI applications. In this paper, we propose a novel norm-based successive denoising strategy for the removal of mixed Gaussian-impulse noise in HSI. The image formation model is split into two different parts. The proposed method is a Bayesian-derived variational model designed to handle the removal of Gaussian and impulse noise in a successive manner, and is solved using the half-quadratic split approach. Comparison with various existing HSI denoising techniques, both qualitatively and quantitatively, suggest the superior denoising ability of the proposed method compared to the rest.

A Joint Denoising Technique for Mixed Gaussian–Impulse Noise Removal in HSI

Hyperspectral imaging (HSI) is the procedure of acquiring a scene over a wide range of electromagnetic spectrum for the purpose of detailed analysis and prediction. The occurrence of noise during the acquisition procedure, however, poses a limitation on this imaging system. Noise in HSI is classified as a mixture of Gaussian and impulse noise statistics, and noise removal or denoising forms an integral part of this imaging system. In this paper, we consider the problem of removing this mixed Gaussian-impulse noise from HSI data-sets by formulating a joint optimization problem based on the maximum <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">a posteriori</i> (MAP) estimates for Gaussian and impulse noise distributions. The proposed method is then solved using an efficient minimization strategy realizied through half-quadratic split. Extensive experimentation on synthetic and real HSI data-sets corroborate the effectiveness of the proposed denoising technique.

The Proximity Operator of the Log-Sum Penalty

The log-sum penalty is often adopted as a replacement for the \(\ell _0\) pseudo-norm in compressive sensing and low-rank optimization. The proximity operator of the \(\ell _0\) penalty, i.e., the hard-thresholding operator, plays an essential role in applications; similarly, we require an efficient method for evaluating the proximity operator of the log-sum penalty. Due to the nonconvexity of this function, its proximity operator is commonly computed through the iteratively reweighted \(\ell _1\) method, which replaces the log-sum term with its first-order approximation. This paper reports that the proximity operator of the log-sum penalty actually has an explicit expression. With it, we show that the iteratively reweighted \(\ell _1\) solution disagrees with the true proximity operator in certain regions. As a by-product, the iteratively reweighted \(\ell _1\) solution is precisely characterized in terms of the chosen initialization. We also give the explicit form of the proximity operator for the composition of the log-sum penalty with the singular value function, as seen in low-rank applications. These results should be useful in the development of efficient and accurate algorithms for optimization problems involving the log-sum penalty. We present applications to solving compressive sensing problems and to mixed additive Gaussian white noise and impulse noise removal.

Mixed noise removal based on Stokes residual noise removal for division of focal plane polarimetric images

The division of focal plane (DoFP) polarimeter has the advantages of simultaneous imaging and compact optical structure. It is inevitable to introducing the noise in the process of micro-polarizer array integration, polarization image acquisition and transmission. In this paper, we propose a novel mixed noise suppression method based on Stokes residual noise removal (SRNR) for mixed additive white Gaussian noise (AWGN) and impulse noise (IN) removal in DoFP polarimetric images. The Laplacian scale mixture (LSM) model is introduced to estimate the IN and the nonlocal low-rank regularization (NLR) is adopted to enhance the denoising performance. The residual noise of the Stokes parameters is taken into consideration. This crucial processing achieves the acquisition of high-quality polarization data. The experiments demonstrate the superior denoising performance for polarimetric imagery in terms of objective assessment and visual evaluation.

A GPU-accelerated light-field super-resolution framework based on mixed noise model and weighted regularization

Light-field (LF) super-resolution (SR) plays an essential role in alleviating the current technology challenge in the acquisition of a 4D LF, which assembles both high-density angular and spatial information. Due to the algorithm complexity and data-intensive property of LF images, LFSR demands a significant computational effort and results in a long CPU processing time. This paper presents a GPU-accelerated computational framework for reconstructing high-resolution (HR) LF images under a mixed Gaussian-Impulse noise condition. The main focus is on developing a high-performance approach considering processing speed and reconstruction quality. From a statistical perspective, we derive a joint ell ^1-ell ^2 data fidelity term for penalizing the HR reconstruction error taking into account the mixed noise situation. For regularization, we employ the weighted non-local total variation approach, which allows us to effectively realize LF image prior through a proper weighting scheme. We show that the alternating direction method of the multipliers algorithm (ADMM) can be used to simplify the computation complexity and results in a high-performance parallel computation on the GPU Platform. An extensive experiment is conducted on both synthetic 4D LF dataset and natural image dataset to validate the proposed SR model’s robustness and evaluate the accelerated optimizer’s performance. The experimental results show that our approach achieves better reconstruction quality under severe mixed-noise conditions as compared to the state-of-the-art approaches. In addition, the proposed approach overcomes the limitation of the previous work in handling large-scale SR tasks. While fitting within a single off-the-shelf GPU, the proposed accelerator provides an average speedup of 2.46{times } and 1.57{times } for {times }2 and {times }3 SR tasks, respectively. In addition, a speedup of 77{times } is achieved as compared to CPU execution.

An efficient method to remove mixed Gaussian and random-valued impulse noise.

Mixed Gaussian and Random-valued impulse noise (RVIN) removal is still a big challenge in the field of image denoising. Existing denoising algorithms have defects in denoising performance and computational complexity. Based on the improved “detecting then filtering” strategy and the idea of inpainting, this paper proposes an efficient method to remove mixed Gaussian and RVIN. The proposed algorithm contains two phases: noise classification and noise removal. The noise classifier is based on Adaptive center-weighted median filter (ACWMF), three-sigma rule and extreme value processing. Different from the traditional “detecting then filtering” strategy, a preliminary RVIN removal step is added to the noise removal phase, which leads to three steps in this phase: preliminary RVIN removal, Gaussian noise removal and final RVIN removal. Firstly, RVIN is processed to obtain a noisy image approximately corrupted by Gaussian noise only. Subsequently, Gaussian noise is re-estimated and then denoised by Block Matching and 3D filtering method (BM3D). At last, the idea of inpainting is introduced to further remove RVIN. Extensive experimental results demonstrate that the proposed method outperforms quantitatively and visually to the state-of-the-art mixed Gaussian and RVIN removal methods. In addition, it greatly shortens the computation time.

Mixed Gaussian-Impulse noise robust face hallucination via noise suppressed low-and-high resolution space-based neighbor representation

Mixed Gaussian-Impulse noise robust face hallucination via noise suppressed low-and-high resolution space-based neighbor representation

Partial Differential Equation (PDE) based Hybrid Diffusion Filters for Enhancing Noise Performance of Point of Care Ultrasound (POCUS) Images

A hybrid filter is developed by combining smoothing and edge preservation properties of anisotropic diffusion (AD) filters and noise reduction features of median filtering. Mixed Gaussian Impulse noise and speckle noise are considered for analysis. The performance of this hybrid filter is verified using ultrasound images. The effectiveness of this filter is assessed with Point of Care Ultrasound (POCUS) images to verify whether the algorithm developed is applicable to them. POCUS refers to a handheld portable ultrasound instrument that can be used at patient bedside. Quantitative analysis with COVID-19 POCUS images, in terms of SNR, SSIM and MSE is performed. Results demonstrate that for all test images, the proposed filter has the best SNR, least MSE, and highest SSIM. Significant improvement in image quality is thus observed both qualitatively and quantitatively. The novelty of suggested technique is its effectiveness in reducing both mixed Gaussian impulse noise and speckle noise in ultrasound as well as POCUS images without the need for separate filters. POCUS has played a significant role in the diagnosis and management of pulmonary, cardiac and vascular pathologies associated with COVID-19. Automatic segmentation of these images and subsequent automatic detection and diagnosis are becoming increasingly popular due to the rapid development of artificial intelligence technologies. These results are useful in implementing better pre-processing prior to segmentation of ultrasound images to facilitate improved patient care.

A spatially adaptive hybrid total variation model for image restoration under Gaussian plus impulse noise

In this paper, a spatially adaptive hybrid total variation model is proposed to recover blurred images corrupted by mixed Gaussian-impulse noise. The model consists of a combined L1/L2 data fidelity term and two regularization terms including total variation and high-order total variation. The spatially adaptive parameters with multiple windows are utilized by the model to adequately smooth homogeneous areas while preserving small features. A strategy for adaptively selecting the locally varying parameters together with a solver of the constituted optimisation problem are presented. Experimental results demonstrate the excellent performance of the new approach compared with current state-of-the-art methods with respect to digital indicators and visual quality.

Nonlocal low-rank regularized two-phase approach for mixed noise removal

Removing mixed noise in images is a difficult problem which has been discussed in many recent papers. In this paper, we tackle the problem of having mixed additive Gaussian white noise and impulse noise. We propose to remove this mixed noise through a nonlocal low-rank regularized two-phase approach. In the first phase, we identify and label the pixels that are likely to be corrupted by the impulse noise. In the second phase, the image is restored through the unlabeled observed data. The restored image is achieved via solving an optimization problem whose objective function has an ℓ 1/ℓ 2 combined content-dependent fidelity term and a nonconvex nonlocal low-rank regularization term. Both terms are built on patch matrices formed from similar patches. Each patch matrix is considered to be low-rank according to the prior knowledge of images. We solve this nonconvex optimization through an iterative adaptive nuclear norm minimization algorithm and provide its convergence analysis. Our experiments show the proposed method outperforms the existing state-of-the-art algorithms in terms of three quantitative metrics, namely, the peak signal-to-noise ratio, the structural similarity and the feature similarity, and visual quality of the restored images.

Image restoration and contrast enhancement based on a nonlinear reaction-diffusion mathematical model and divide &amp; conquer technique

In this article, we present a new algorithm for digital image processing noised by mixed Gaussian-impulse noise. Our mathematical model is based on the divide-conquer technique coupled with a reaction-diffusion system. We first decompose our image into low and high-frequency components by convolving each with a predefined convolutional filter. Further, we use a simple scheme of different weights to integrate and collect these processed sub-images into a filtered image. Finally, we apply our Reaction-Diffusion system to increase the contrast in the image. A number of experimental results are described to illustrate the performance of our algorithm and show that it is very effective in eliminating mixed Gaussian-impulse noise, increasing the contrast of the image and preserving the edges.

A Parallel Fuzzy Algorithm for Real-Time Medical Image Enhancement

Medical images may be corrupted by noise. This noise affects the image quality and can obscure important information required for accurate diagnosis. Effectively apply filtering techniques can facilitate diagnosis or reduce radiation exposure. In this paper, we introduce a parallel method designed to reduce mixed Gaussian-impulse noise from digital images. The method uses fuzzy logic and the fuzzy peer group concept. Implementations of the method on multi-core interface using the open multi-processing (OpenMP) and on graphics processing units (GPUs) using CUDA are presented. Efficiency is measured in terms of execution time and in terms of MAE, PSNR and SSIM over medical images from the mini-MIAS database and over computed radiography (CR) images generated at different exposure levels. These images have been contaminated with impulsive and/or Gaussian noise. Experiments show that the proposed method obtains good performance in terms of the above mentioned objective quality measures. After applying multi-core and GPUs optimization strategies, the observed time shows that the new filter allows to remove mixed Gaussian-impulse noise in real-time.

Noise Robust Face Hallucination via Outlier Regularized Least Square and Neighbor Representation

In surveillance scenario the captured face may be of small size, low-quality, low-resolution and noisy. Noise introduces outliers in the captured face images which cause problems in similarity matching, an essential component in attaining the face reconstruction constraints. The situation becomes even more complicated when face images are corrupted by mixed Gaussian-Impulse noise (MIXGIN). To address this problem, a novel outlier regularized least square and neighbor representation (ORLSNR) based face hallucination method is proposed here. The proposed method starts with the detection of the outliers in an input face and performs outlier regularization to reduce the impact of outliers on the reconstruction produce. This assists in achieving the sparsity and locality simultaneously by allowing the selection of the most relevant patches for reconstruction of the high-resolution face. Experimental results performed on public FEI, CMU+MIT face databases, and surveillance videos reflect that the proposed method is computationally efficient and demonstrate better performance than the existing state-of-the-art face hallucination methods.

Hyperspectral Image Denoising via Matrix Factorization and Deep Prior Regularization.

Deep learning has been successfully introduced for 2D-image denoising, but it is still unsatisfactory for hyperspectral image (HSI) denosing due to the unacceptable computational complexity of the end-to-end training process and the difficulty of building a universal 3D-image training dataset. In this paper, instead of developing an end-to-end deep learning denoising network, we propose a hyperspectral image denoising framework for the removal of mixed Gaussian impulse noise, in which the denoising problem is modeled as a convolutional neural network (CNN) constrained non-negative matrix factorization problem. Using the proximal alternating linearized minimization, the optimization can be divided into three steps: the update of the spectral matrix, the update of the abundance matrix and the estimation of the sparse noise. Then, we design the CNN architecture and proposed two training schemes, which can allow the CNN to be trained with a 2D-image dataset. Compared with the state-of-the-art denoising methods, the proposed method has relatively good performance on the removal of the Gaussian and mixed Gaussian impulse noises. More importantly, the proposed model can be only trained once by a 2D-image dataset, but can be used to denoise HSIs with different numbers of channel bands.

Adaptation Strategies for Applying AWGN-Based Denoiser to Realistic Noise

Discriminative learning based denoising model trained with Additive White Gaussian Noise (AWGN) performs well on synthesized noise. However, realistic noise can be spatialvariant, signal-dependent and a mixture of complicated noises. In this paper, we explore multiple strategies for applying an AWGN-based denoiser to realistic noise. Specifically, we trained a deep network integrating noise estimating and denoiser with mixed Gaussian (AWGN) and Random Value Impulse Noise (RVIN). To adapt the model to realistic noises, we investigated multi-channel, multi-scale and super-resolution approaches. Our preliminary results demonstrated the effectiveness of the newly-proposed noise model and adaptation strategies.

Robust Mesh Denoising via Triple Sparsity.

Mesh denoising is to recover high quality meshes from noisy inputs scanned from the real world. It is a crucial step in geometry processing, computer vision, computer-aided design, etc. Yet, state-of-the-art denoising methods still fall short of handling meshes containing both sharp features and fine details. Besides, some of the methods usually introduce undesired staircase effects in smoothly curved regions. These issues become more severe when a mesh is corrupted by various kinds of noise, including Gaussian, impulsive, and mixed Gaussian–impulsive noise. In this paper, we present a novel optimization method for robustly denoising the mesh. The proposed method is based on a triple sparsity prior: a double sparse prior on first order and second order variations of the face normal field and a sparse prior on the residual face normal field. Numerically, we develop an efficient algorithm based on variable-splitting and augmented Lagrange method to solve the problem. The proposed method can not only effectively recover various features (including sharp features, fine details, smoothly curved regions, etc), but also be robust against different kinds of noise. We testify effectiveness of the proposed method on synthetic meshes and a broad variety of scanned data produced by the laser scanner, Kinect v1, Kinect v2, and Kinect-fusion. Intensive numerical experiments show that our method outperforms all of the compared select-of-the-art methods qualitatively and quantitatively.

Evolutionary multiobjective multiple description wavelet based image coding in the presence of mixed noise in images

In this paper, a novel method for generation of multiple description (MD) wavelet based image coding is proposed by using Multi-Objective Evolutionary Algorithms (MOEAs). Complexity of the multimedia transmission problem has been increased for MD coders if an input image is affected by any type of noise. In this case, it is necessary to solve two different problems which are designing the optimal side quantizers and estimating optimal parameters of the denoising filter. Existing MD coding (MDC) generation methods are capable of solving only one problem which is to design side quantizers from the given noise-free image but they can fail reducing any type of noise on the descriptions if they applied to the given noisy image and this will cause bad quality of multimedia transmission in networks. Proposed method is used to overcome these difficulties to provide effective multimedia transmission in lossy networks. To achieve it, Dual Tree-Complex Wavelet Transform (DT-CWT) is first applied to the noisy image to obtain the subbands or set of coefficients which are used as a search space in the optimization problem. After that, two different objective functions are simultaneously employed in the MOEA to find pareto optimal solutions with the minimum costs by evolving the initial individuals through generations. Thus, optimal quantizers are created for MDCs generation and obtained optimum parameters are used in the image filter to remove the mixed Gaussian impulse noise on the descriptions effectively. The results demonstrate that proposed method is robust to the mixed Gaussian impulse noise, and offers a significant improvement of optimal side quantizers for balanced MDCs generation at different bitrates.

Mixed Gaussian-impulse noise reduction from images using convolutional neural network

The removal of mixed-noise is an ill-posed problem due to high level of non-linearity in the distribution of noise. Most commonly encountered mixed-noise is the combination of additive white Gaussian noise (AWGN) and impulse noise (IN) that have contrasting characteristics. A number of methods from the cascade of IN and AWGN reduction to the state-of-the-art sparse representation have been reported to reduce this common form of mixed-noise. In this paper, a new learning-based algorithm using the convolutional neural network (CNN) model is proposed to reduce the mixed Gaussian-impulse noise from images. The proposed CNN model adopts computationally efficient transfer learning approach to obtain an end-to-end map from noisy image to noise-free image. The model has a small structure yet it is capable of providing performance superior to that of the well established methods. Experimental results on different settings of mixed-noise show that the proposed CNN-based denoising method performs significantly better than the sparse representation and patch-based methods do both in terms of accuracy and robustness. Moreover, due to the lightweight structure, the denoising operation of the proposed CNN-based method is computationally faster than that of the previously reported methods.

Sparse Technique for Images Corrupted by Mixed Gaussian-Impulsive Noise

In this paper, a novel framework is presented for denoising images that have been corrupted by a mixture of additive and impulsive noise. The proposed method consists of three main stages: impulsive noise suppression, additive noise suppression and post-processing. In the first stage, a pixel that has been contaminated by impulsive noise is detected and filtered. In the next stage, filtering is based on sparse representation and 3D-processing using discrete cosine transform. Finally, the post-processing stage increases the filtering quality by using a bilateral filter and an edge restoration technique. Evaluation is performed using objective criteria (PSNR and SSIM) and subjective human visual perception to confirm the methods performance compared with state-of-the-art techniques.