Levels Of Additive White Gaussian Noise Research Articles

Echo State Property upon Noisy Driving Input

The echo state property (ESP) is a key concept for understanding the working principle of the most widely used reservoir computing model, the echo state network (ESN). The ESP is achieved most of the operation time under general conditions, yet the property is lost when a combination of driving input signals and intrinsic reservoir dynamics causes unfavorable conditions for forgetting the initial transient state. A widely used treatment, setting the spectral radius of the weight matrix below the unity, is not sufficient as it may not properly account for the nature of driving inputs. Here, we characterize how noisy driving inputs affect the dynamical properties of an ESN and the empirical evaluation of the ESP. The standard ESN with a hyperbolic tangent activation function is tested using the MNIST handwritten digit datasets at different additive white Gaussian noise levels. The correlations among the neurons, input mapping, and memory capacity of the reservoir nonlinearly decrease with the noise level. These trends agree with the deterioration of the MNIST classification accuracy against noise. In addition, the ESP index for noisy driving input is developed as a tool to help easily assess ESPs in practical applications. Bifurcation analysis explicates how the noise destroys an asymptotical convergence in an ESN and confirms that the proposed index successfully captures the ESP against noise. These results pave the way for developing noise-robust reservoir computing systems, which may promote the validity and utility of reservoir computing for real-world machine learning applications.

Synergy between Semantic Segmentation and Image Denoising via Alternate Boosting

The capability of image semantic segmentation may be deteriorated due to the noisy input image, where image denoising prior to segmentation may help. Both image denoising and semantic segmentation have been developed significantly with the advance of deep learning. In this work, we are interested in the synergy between these two tasks by using a holistic deep model. We observe that not only denoising helps combat the drop of segmentation accuracy due to the noisy input, but also pixel-wise semantic information boosts the capability of denoising. We then propose a boosting network to perform denoising and segmentation alternately. The proposed network is composed of multiple segmentation and denoising blocks (SDBs), each of which estimates a semantic map and then uses the map to regularize denoising. Experimental results show that the denoised image quality is improved substantially and the segmentation accuracy is improved to close to that on clean images, and segmentation and denoising are both boosted as the number of SDBs increases. On the Cityscapes dataset, using three SDBs improves the denoising quality to 34.42 dB in PSNR, and the segmentation accuracy to 66.5 in mIoU, when the additive white Gaussian noise level is 50.

Field programmable gate arrays implementation of different standard deviation estimation techniques

Additive white Gaussian noise level estimation has found its application in many fields such as biomedical signal processing, communication system, and image processing. Many methods have been proposed with different output accuracy, system complexity, power consumption, and speed. In this paper, three of the most well-known and largely used algorithms (median based, root mean square (RMS) based, and P84 based methods) have been implemented and investigated in a full comparison between them to find their advantage and disadvantage, and the suitability of each method for a specific application. The three designs are created using Xilinx system generator (XSG) and implemented on Xilinx field programmable gate arrays (FPGA) development board with Zynq series "XC7Z020-1CLG484", to evaluate the design's performance and the results are discussed in the paper.

A novel complex-valued convolutional neural network for medical image denoising

Several applications of complex-valued networks have been reported for computer vision tasks like image processing and classification. However, complex-valued convolutional neural networks are yet to be explored for medical image denoising. In this paper, a novel complex-valued convolutional neural network-based model, termed as CVMIDNet, is investigated for medical image denoising. Unlike traditional approaches, which learn clean images from noisy images, the proposed model utilizes residual learning, which learns noise from noisy images and then subtracts it from noisy images so as to obtain clean images. To assess the denoising performance of CVMIDNet, standard image quality metrics, namely, peak signal to noise ratio and the structural similarity index, have been used for five different additive white Gaussian noise levels in chest X-ray images. Chest X-ray denoising performance of CVMIDNet was compared with four recent state-of-the-art models, namely, Block-Matching and 3D (BM3D) filtering, DnCNN, Feature-guided Denoising Convolutional Neural Network (FDCNN), and deep CNN with residual learning. Additionally, it is also benchmarked against its real-valued counterpart, termed RVMIDNet. In all the reported performance investigations, CVMIDNet was found to be superior. For instance, for a Gaussian noise level of σ = 15, peak signal to noise ratio and structural similarity index values achieved by the CVMIDNet are 37.2010 and 0.9227, respectively, against the 36.2292 and 0.9086, 36.3203 and 0.9139, 35.0995 and 0.9005, 36.1830 and 0.8968, 34.2436 and 0.8874 achieved by BM3D filtering, DnCNN, RVMIDNet, FDCNN, and deep CNN with residual learning, respectively. Therefore, based on the presented investigations, it is concluded that CVMIDNet is a potential deep learning model for medical image denoising.

Application of Artificial Neural Network for Image Noise Level Estimation in the SVD domain

The blind additive white Gaussian noise level estimation is an important and a challenging area of digital image processing with numerous applications including image denoising and image segmentation. In this paper, a novel block-based noise level estimation algorithm is proposed. The algorithm relies on the artificial neural network to perform a complex image patch analysis in the singular value decomposition (SVD) domain and to evaluate noise level estimates. The algorithm exhibits the capacity to adjust the effective singular value tail length with respect to the observed noise levels. The results of comparative analysis show that the proposed ANN-based algorithm outperforms the alternative single stage block-based noise level estimating algorithm in the SVD domain in terms of mean square error (MSE) and average error for all considered choices of block size. The most significant improvements in MSE levels are obtained at low noise levels. For some test images, such as “Car” and “Girlface”, at σ = 1 , these improvements can be as high as 99% and 98.5%, respectively. In addition, the proposed algorithm eliminates the error-prone manual parameter fine-tuning and automates the entire noise level estimation process.

Adaptive Block-Based Approach to Image Noise Level Estimation in the SVD Domain

Estimation of additive white Gaussian noise levels in images has a variety of image processing applications including image enhancement, segmentation and feature extraction. Designing an algorithm with a consistent performance across a range of noise levels and image contents is a challenging problem; without any prior information, it is difficult to differentiate the noise signal from the underlying image signal. In this paper, an adaptive block-based noise level estimation algorithm in the singular value decomposition domain is proposed. The algorithm has the ability to change the singular value tail length according to the observed noise levels. A number of different choices of block size are considered and, for each choice, a mathematical model is proposed to describe how to adjust the singular value tail length as a function of the initial noise level estimates. In comparison with a seminal fixed singular value tail length algorithm, the proposed algorithm significantly improves the noise level estimation accuracy at low noise levels at the expense of a small increase in computational time; for example, for the block size of 64 × 64 and AWGN level σ = 1 , the MSE is reduced by 65%, whilst the computational time is increased by less than 1.3%.

Adaptive SVD Domain-Based White Gaussian Noise Level Estimation in Images

Noise level estimation is a challenging area of digital image processing with a variety of applications, including image enhancement, image segmentation, and feature extraction. In this paper, an adaptive estimation of additive white Gaussian noise level based on the singular value decomposition (SVD) of images is proposed. The proposed algorithm aims to improve the performance of noise level estimation in the SVD domain at low noise levels. An initial noise level estimate is used to adjust the parameters of the algorithm in order to increase the accuracy of noise level estimation. The proposed algorithm exhibits the ability to adapt the number of considered singular values and to accordingly adjust the slope of a linear function that describes how the average value of the singular value tail varies with noise levels. Although, for each image, the proposed algorithm performs the noise level estimation twice in two distinct stages, the singular value decompositions are only performed in the first stage of the algorithm. The experimental results demonstrate that the proposed algorithm improves the noise level estimation at low noise levels without a significant increase in computational complexity. At noise level $\sigma = 15$ , the improvements in the mean square level are about 39% at the expense of slightly higher additional computational time.

Signal Denoising Using Double Density Discrete Wavelet Transform

Reality signals do not exist without noise. Wavelet transform based denoising seem to be a powerful tool for suppressing noise in signals. In this paper, we investigate the using of double density discrete wavelet transform “DD-DWT” which based on one scaling function and two wavelet functions, for signal denoising and comparing its performance with the traditional DWT. Three groups of additive White Gaussian Noise levels (5 dB, 3 dB, 2 dB) are added to some standard test signals with both hard and soft threshold function to evaluate the performance of each method in term of Root Mean Square Error (RMSE) and Signal to Noise Ratio (SNR). Experiment results show that DD-DWT performs better than traditional DWT in both RMSE and SNR especially at low SNR.

Block Based SVD approach for Additive White Gaussian Noise level Estimation in Satellite Images

In this digital era, estimation of noise and de-noising of digital image is one of the chart-topping fields. In real time, noise may happen at any stage starting from capturing to reception. Noise estimation is ever challenging field even till now! Additive White Gaussian Noise is the basic type, when dealing with images on statistical way of studying. So, this paper as a first step proposed an effective technique for the estimation of noise in an image by using Block based SVD domain approach. This paper addresses the following issues 1) Noise estimation by trail method of singular values 2) Corrupting the image by known noise and study the change 3) Divide the whole image into blocks and add the known noise to the image and finally retrieve the effect on original image. It is one of best techniques for estimating AWGN.

Image noise level estimation based on higher-order statistics

Noise level estimation is a required step for many preprocessing algorithms in computer vision such as image denoising. In this paper, a model-based technique for additive white Gaussian noise level estimation is proposed via matching moments of eligible transform coefficients of a single image. We assume that noise and image signals are independent and seek to use an image transform that preserves distribution characteristics of noise. This transform should also result in coefficients with a generalized Gaussian distribution for the image itself. We use block-based discrete cosine transform (DCT) and discrete wavelet transform (DWT) which are shown to satisfy these requirements. The proposed method fits the histogram of AC coefficients of all DCT blocks or histogram of all high frequency wavelet coefficients with a generalized Gaussian distribution and attempts to estimate the noise variance through matching the estimated and true values of moments. Since the modeled distributions are symmetric and hence all odd moments are zero, our approach involves solving a nonlinear system of equations based on the method of moments using only even moments. The performance of the proposed method is compared to those of the best prevalent algorithms proposed for noise level estimation using patch-based and model-based techniques. The results on three different image databases show that the proposed scheme outperforms previous techniques in general.