Image noise severity metric

Digital signals are often contaminated by noise during signal acquisition and transmission for sewage sensing signal treatment such as aeration volume, oxygen content and water transparency etc. Sometimes, noise is a mixed one of gaussian noise and impulse noise. Unfortunately, existing denoising algorithms are often designed for removing single gaussian noise or impulse noise. In this paper, an efficient algorithm for mixed noise removal in signal is proposed, including space impulse noise removal and wavelet Gaussian noise removal. An impulse noise detection algorithm based on median filter is given to filter impulse signal, also a lifting wavelet was constructed by lifting original wavelet. The threshold based on lifting wavelet transform for signal was applied to denoising gaussian noise. Simulations are conducted on the presented algorithm, and the simulation result shows that this algorithm can remove mixed Gaussian and impulse noise in signal efficiently.

Hyperspectral images (HSIs) are frequently corrupted by various types of noise, such as Gaussian noise, impulse noise, stripes, and deadlines due to the atmospheric conditions or imperfect hyperspectral imaging sensors. These types of noise, which are also called mixed noise, severely degrade the HSI and limit the performance of post-processing operations, such as classification, unmixing, target recognition, and so on. The patch-based low-rank and sparse based approaches have shown their ability to remove these types of noise to some extent. In order to remove the mixed noise further, total variation (TV)-based methods are utilized to denoise HSI. In this paper, we propose a group low-rank and spatial-spectral TV (GLSSTV) to denoise HSI. Here, the advantage is twofold. First, group low-rank exploits the local similarity inside patches and non-local similarity between patches which brings extra structural information. Second, SSTV helps in removing Gaussian and sparse noise using the spatial and spectral smoothness of HSI. The extensive simulations show that GLSSTV is effective in removing mixed noise both quantitatively and qualitatively and it outperforms the state-of-the-art low-rank and TV-based methods.

Superpixels have gradually become popular in computer vision and image processing applications. However, no comprehensive study has been performed to evaluate the robustness of superpixel algorithms in regard to common forms of noise in natural images. We evaluated the robustness of 11 recently proposed algorithms to different types of noise. The images were corrupted with various degrees of Gaussian blur, additive white Gaussian noise, and impulse noise that either made the object boundaries weak or added extra information to it. We performed a robustness analysis of simple linear iterative clustering (SLIC), Voronoi Cells (VCells), flooding-based superpixel generation (FCCS), bilateral geodesic distance (Bilateral-G), superpixel via geodesic distance (SSS-G), manifold SLIC (M-SLIC), Turbopixels, superpixels extracted via energy-driven sampling (SEEDS), lazy random walk (LRW), real-time superpixel segmentation by DBSCAN clustering, and video supervoxels using partially absorbing random walks (PARW) algorithms. The evaluation process was carried out both qualitatively and quantitatively. For quantitative performance comparison, we used achievable segmentation accuracy (ASA), compactness, under-segmentation error (USE), and boundary recall (BR) on the Berkeley image database. The results demonstrated that all algorithms suffered performance degradation due to noise. For Gaussian blur, Bilateral-G exhibited optimal results for ASA and USE measures, SLIC yielded optimal compactness, whereas FCCS and DBSCAN remained optimal for BR. For the case of additive Gaussian and impulse noises, FCCS exhibited optimal results for ASA, USE, and BR, whereas Bilateral-G remained a close competitor in ASA and USE for Gaussian noise only. Additionally, Turbopixel demonstrated optimal performance for compactness for both types of noise. Thus, no single algorithm was able to yield optimal results for all three types of noise across all performance measures. Conclusively, to solve real-world problems effectively, more robust superpixel algorithms must be developed.

The central goal of this dissertation is to design and model a smoothing filter based on the random single and mixed noise distribution that would attenuate the effect of noise while preserving edge details. Only then could robust, integrated and resilient edge detection methods be deployed to overcome the ubiquitous presence of random noise in images. Random noise effects are modeled as those that could emanate from impulse noise, Gaussian noise and speckle noise. In the first step, evaluation of methods is performed based on an exhaustive review on the different types of denoising methods which focus on impulse noise, Gaussian noise and their related denoising filters. These include spatial filters (linear, non-linear and a combination of them), transform domain filters, neural network-based filters, numerical-based filters, fuzzy based filters, morphological filters, statistical filters, and supervised learning-based filters. In the second step, switching adaptive median and fixed weighted mean filter (SAMFWMF) which is a combination of linear and non-linear filters, is introduced in order to detect and remove impulse noise. Then, a robust edge detection method is applied which relies on an integrated process including non-maximum suppression, maximum sequence, thresholding and morphological operations. The results are obtained on MRI and natural images. In the third step, a combination of transform domain-based filter which is a combination of dual tree – complex wavelet transform (DT-CWT) and total variation, is introduced in order to detect and remove Gaussian noise as well as mixed Gaussian and Speckle noise. Then, a robust edge detection is applied in order to track the true edges. The results are obtained on medical ultrasound and natural images. In the fourth step, a smoothing filter, which is a feed-forward convolutional network (CNN) is introduced to assume a deep architecture, and supported through a specific learning algorithm, l2 loss function minimization, a regularization method, and batch normalization all integrated in order to detect and remove impulse noise as well as mixed impulse and Gaussian noise. Then, a robust edge detection is applied in order to track the true edges. The results are obtained on natural images for both specific and non-specific noise-level.

For the problem of denoising incomplete phenomenon appeared in the existing wavelet threshold methods, a new kind of threshold function and denoising method of parameter adjustable wavelet threshold is proposed. The traditional hard threshold and soft threshold wavelet had problems such as continuity and constant deviation. Firstly, to construct a new threshold function and theoretically proves the superiority of this new threshold function, as long as choosing the suitable parameter, the new threshold function has a better denoising effect than traditional thresholding function. Secondly, to reduce the deviation between wavelet coefficients and the original, the threshold value is changed with the change of decomposition scale. The experimental results demonstrate that by using the proposed method, whether the Gaussian noise or impulse noise, the signal-to-noise ratio (SNR) of image and the peak signal to noise ratio (PSNR) of image can be greatly improved and the mean square error (MSE) of the image was reduced, the denoising effect is better than other algorithms.

Wide variety of medical images are degraded by different types of noise such as Impulse noise, Gaussian noise, Poisson or a mixed of all. These noise disruptions typically result from sensor malfunctions, transmission issues, or environmental factors [1]. They provide an essential basis for clinical diagnosis and treatment. Unlike natural photographs, medical images often contain significant signal-related noise during their creation, resulting in lower contrast and more visible noise [3].No single method or procedure is effective for noise removal hence care should be taken before cleaning noisy area of image. Factors such as type of image (CT scan, Ultrasound, MRI etc) and type of noise such as (Gaussian, the impulsive and speckle noise etc) should be identified and based on the type of input, an appropriate method should be selected. For accurate segmentation of medical images through the automatic means,it is necessary to remove the noise from the images. There are many methods such as learning based (traditional methods) and non-learning based methods(using various types neural networks).To measure the denoising accuracy, parameters like Signal-to-Noise Ratio (SNR), Peak Signal-to-Noise Ratio (PSNR) and Structural Similarity Index Measure (SSIM) are used. This paper discusses the results obtained through the various methods and their comparison in terms of PSNR,SSIM. Removing noise is crucial for accurate segmentation of medical images. These noise-less images are to be treated as pre-processed images for the segmentation task.

Hyspectral images (HSIs) are inevitably degraded by a mixture of different types of noise, such as Gaussian noise, impulse noise, stripes, and deadlines. Traditional methods exploit the global low-rankness and local smoothness by using two separate regularization terms for HSI denoising, which may be highly affected by the trade-off parameters between the two regularizers. In this paper, we propose to utilize the three directional tensor correlated total variation (3DTCTV) to explore the global low-rankness and local smoothness of HSIs simultaneously. More specifically, the three directional transformed tensor nuclear norm is employed to the gradient domain of the underlying HSIs along the spatial and spectral dimensions. And the tensor ℓ<sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> norm is used to characterize the sparsity of the noisy tensor. Moreover, a nonconvex approach is proposed to characterize the low-rankness of the underlying HSIs and enhance the sparsity of noisy tensor further for HSI denoising, where a family of nonconvex functions are employed onto the singular values of the three directional gradient tensors along spatial-spectral dimensions in the transformed domain and each entry of the sparse tensor, respectively. An alternating direction method of multipliers is developed to solve the resulting models and its convergence for the nonconvex model is established under some conditions. Extensive numerical experiments on simulated and real HSI datasets demonstrate that the proposed methods outperform various state-of-the-art methods both visually and quantitatively.

In this paper a new approach to reduction of a mixture of Gaussian and random impulse noises in color images is presented. The proposed filtering scheme is based on the application of the Bilateral Filter in order to address the problem of impulse noise reduction by determining the rate of region homogeneity, for calculating the weights needed for the Non-Local Means (NLM) averaging operation. Gaussian Mixture Model approach is applied for determining similarity between local image regions. The proposed solution is capable to successfully suppress the mixed noise of various intensities, at a lower computational cost than NLM method, due to the adaptive choice of size of search window for similar local neighborhoods. Experimental results prove that the introduced design yields better results than the Non-Local Means and Anisotropic Diffusion techniques in the case of color images contaminated by strong mixed Gaussian and impulsive noise.

In this paper, we propose an effective noise reduction method for image sequences corrupted by the Gaussian noise or impulse noise. The basic strategy is to combine the spatial just noticeable distortion (JND) with local image characteristics for spatial filtering and utilize the motion compensation for temporal filtering. For spatial filtering, an adaptive scheme composed of the harmonic mean filter, weighted arithmetic mean filter, alpha-trimmed mean filter, median filter and thresholding filter is dedicated to reducing noises on an image. Then, a motion-compensation based temporal filter is focused on refining the spatial-filtered image frame with the previous and following frames. Experimental results show that the proposed noise-reduction method is better than four previous methods with a PSNR improvement rate of 8.85% on Gaussian noise, 11.69% on fixed-value impulse noise and 11.64% on random-value impulse noise over the average of these four methods.

Image noise is defined as the random variation of color information or intensity in images. It is recognized as a type of electronic noise. Impulse noise is a “high level-low level” noise that affects an image abruptly. A filtering technique defined as an improved switching vector median filter (ISVMF) is proposed for removing impulse noise from color images in this manuscript. The performance analysis has been done for varied noise densities. Though performance has been shown in terms of Lena images, it delivers improved results irrespective of variation of images. The performance comparison has been done on the basis of standard metrics like peak signal to noise ratio (PSNR) and structural similarity index (SSIM), etc. It is observed that the proposed improved switching vector median filter (ISVMF) provides better results both visually and statistically as compared to the other conventional filtering techniques. This better performance may be due to the fact that the threshold has been localized rather than generalized in the filter resulting in better homogeneity across the various sections of the image.

The Wigner distribution (WD) produces highly concentrated time-frequency (TF) representation of nonstationary signals. It may be used as an efficient signal analysis tool, including the cases of frequency modulated signals corrupted with the Gaussian noise. In some applications, a significant amount of impulse noise is present. Then, the WD fails to produce satisfactory results. The robust periodogram has been introduced for spectral estimation of this kind of noisy signals. It can produce good concentration for pure harmonic signals. However, it is not so efficient in the cases of signals with rapidly varying frequency. This is the motivation for introducing the robust WD. It is a reliable TF representation tool for wide class of nonstationary signals corrupted with impulse noise. This distribution produces good accuracy of the instantaneous frequency (IF) estimation. Using the Huber (1981) loss function, a generalization of the WD is presented. It includes both the standard and the robust WD as special cases. This distribution can be used for TF analysis of signals corrupted with a mixture of impulse and Gaussian noise. The presented theory is illustrated on examples, including applications on the IF estimation and time-varying filtering of signals corrupted with a mixture of the Gaussian and impulse noise. The case study analysis of the IF estimators' accuracy, based on the standard and the robust WD forms, is performed. In order to improve the IF estimation, a median filter is applied on the obtained IF estimate.

Image De-noising is a problem of prime importance in the field of Image Processing ranging from Medical Imaging to Satellite imaging. The main purpose of an Image de-noising algorithm is to reduce the noise level to improve both the interpretability and visual aspect of the images. This paper propose to indicate the suitability of different Multi-resolution transforms, viz Wavelets, Ridgelets and Curvelets in de-noising various imaging modalities corrupted by Random noise, Gaussian noise, Speckle Noise, Salt and Pepper Noise and Poisson noise. Though the comparative study is based on various imaging modalities, due relevance is given to medical images like Computed Tomography (CT), Magnetic resonance Imaging (MRI) and X-ray images. Experiments are conducted on various image data sets namely Natural, Satellite and Medical Images with the Multi-resolution transforms using two existing thresholding strategies, namely Soft and Hard Thresholding. A comprehensive evaluation of three different types of Multiresolution transforms corrupted with different types of noise is provided and the quality of de-noising is measured in terms of Peak Signal to Noise ratio (PSNR). Experimental results indicate that the Curvelets reveal superior performance over wavelets and Ridgelets in terms of PSNR value and perceptible quality.

Recently, compressed sensing (CS) has been an effective data compression technique for telemonitoring of multichannel electroencephalogram (EEG) signals through wireless body-area networks. Most of the existing multichannel EEG CS methods ignore the noise or only consider the Gaussian noise. However, there are also some other types of noise, such as heavy-tailed impulsive noise. In this paper, to overcome the above mentioned problems, we propose a novel multichannel EEG CS method based on sparse and low rank representation in the presence of mixed noise (SLRMN), which can take both Gaussian noise and impulsive noise into consideration. Moreover, we develop the alternative direction method of multipliers (ADMM) to solve the proposed SLRMN. The experimental results demonstrate the advantage of the proposed SLRMN over state-of-the-art multichannel EEG CS methods in the presence of mixed noise.

The wide-field electromagnetic (WFEM) method is widely used in resource exploration in complex geological environments due to its effectiveness in deep detection, interference resistance, and adaptability to various surface conditions. Noise interference remains a significant challenge in areas with high human activity, such as mining regions and urban environments. In these regions, electromagnetic noise is often complex, non-periodic, and pseudo-random, severely degrading the signal-to-noise ratio (SNR) and complicating subsurface interpretation. Traditional denoising methods struggle to effectively handle such complex, non-periodic noise. We propose a novel denoising approach that combines Particle Swarm Optimization (PSO) and Grey Wolf Optimization (GWO) to optimize a Convolutional Neural Network (CNN). This hybrid algorithm enhances CNN’s ability to extract nonlinear features and effectively separate multiple noise types, such as Gaussian white noise, impulse noise, and attenuation noise. The method was tested on WFEM data from the Sichuan Changning Block and the Shanxi Xinyuan Coal Mine area. Simulation results demonstrate that the PSO-GWO-optimized CNN effectively handles complex, non-periodic noise, improving signal clarity and successfully reducing noise interference, thereby enhancing data quality and enabling more accurate geological interpretations. The integration of CNN with PSO-GWO optimization not only improves the SNR but also enhances interpretative accuracy in resource exploration. The successful application of this method in regions with strong electromagnetic interference highlights its broader applicability and practicality.

We consider the design of near-capacity-achieving error-correcting codes for a discrete multitone (DMT) system in the presence of both additive white Gaussian noise and impulse noise. Impulse noise is one of the main channel impairments for digital subscriber lines (DSL). One way to combat impulse noise is to detect the presence of the impulses and to declare an erasure when an impulse occurs. In this paper, we propose a coding system based on low-density parity-check (LDPC) codes and bit-interleaved coded modulation that is capable of taking advantage of the knowledge of erasures. We show that by carefully choosing the degree distribution of an irregular LDPC code, both the additive noise and the erasures can be handled by a single code, thus eliminating the need for an outer code. Such a system can perform close to the capacity of the channel and for the same redundancy is significantly more immune to the impulse noise than existing methods based on an outer Reed-Solomon (RS) code. The proposed method has a lower implementation complexity than the concatenated coding approach.