Wavelet-based Denoising Methods Research Articles

An efficient method for image denoising based on a new nonlinear wavelet thresholding function

Image noise is random variation of brightness or color information in images, and is usually an aspect of electronic noise. It can be produced by the image sensor and circuitry of a scanner or digital camera. In fact, there are different kinds of noise functions such as Gaussian noise, salt and pepper noise and speckle noise. Hence, image denoising is the process of removing noise from an image using one of the denoising methods such as spatial or transform techniques. The main aim of an image denoising technique is to achieve both noise reduction and feature preservation. In this context, the wavelet denoising method works in the transform domain, where the noise is uniformly spread throughout coefficients while most of the image information is concentrated in a few large ones.Therefore, the first wavelet-based denoising methods were based on thresholding of detail subband coefficients. However, most of the wavelet thresholding methods suffer from the drawback that the chosen threshold may not match the specific distribution of the image and noise components. Another thing: Studies have proven that the thresholding function has an effective role in obtaining better quality of the denoised image. To address these disadvantages, in this paper, we propose an efficient method for image denoising in wavelets domain. This method is based on a new nonlinear wavelet thresholding function, that is characterized by main mathematical properties and a shape parameter. The theoretical study of this new method proves that we can overcome the drawbacks of classical thresholding methods and by freely adjusting the shape parameter, we achieve a compromise between Hard and Soft thresholding. The experimental results show that our proposed method provides better performance compared to classical thresholding methods in terms of the visual quality of the denoised image.

Enhancing Low-Light Medical Imaging through Deep Learning-Based Noise Reduction Techniques

Background/ Objectives: Low-light medical imaging is highly challenging in clinical diagnostics due to increased noise levels that mask or obscure important anatomical details. In this respect, conventional noise reduction methods such as Gaussian filtering and median filtering usually lead to a trade-off between noise suppression and the preservation of important features in an image, thus resulting in poor-quality images. More advanced wavelet-based denoising and Non-Local Means methods exhibit superior noise reduction but remain computationally intensive and introduce artifacts. These challenges come with a need to develop more effective and efficient noise-reduction techniques. Methods: This study proposes an end-to-end deep learning framework for low-light medical image enhancement. We present a comprehensive deep-learning framework to enhance low-light medical images by integrating Convolutional Neural Networks with denoising autoencoders to build a robust noise reduction model. The CNN extracts the feature from the noisy input images, while the autoencoder does so for the reconstruction of clean images through the encoding of a noisy input in a lower-dimensional representation for the reduction of noise while retaining critical information. Findings: This study validates the proposed model through rigorous quantitative metrics such as peak signal-to-noise ratio and structural similarity index. These metrics are designed to provide a full assessment of image quality concerning noise reduction capability and preservation of details related to structure. Our model improves traditional methods in PSNR by about 5 dB on average and SSIM by 0.15, which means better noise reduction and preservation of image details. A comparative analysis of traditional techniques for noise reduction has been included, pointing out the advantages of deep learning approaches. Experimental results depict significant improvements over previous approaches. For instance, the proposed model reduces the noise level by up to 40% and facilitates clear and sharp images by up to 30%. In terms of quantification, these improvements manifest in a PSNR value of 35 dB and an SSIM score of 0.85 compared to 30 dB and 0.70 using traditional techniques. Furthermore, the study illustrates the training dynamics, feature maps, and evolution of images to present the model's incremental learning process. Novelty: This study's findings validate the proposed model's efficacy in enhancing diagnosis accuracy and improving patient outcomes in medical imaging. Keywords: Low-light medical imaging, Noise reduction, Convolutional Neural Networks, Denoising autoencoders, Medical diagnostics

WGLFNets: Wavelet-based global–local filtering networks for image denoising with structure preservation

Efficiency and denoising performance are two important indexes to objectively evaluate an image denoising method. Traditional model-based denoising methods usually pursue pleasing performance at the cost of highly computational complexity, while the popular deep learning-based methods perform well on efficiency improvement but still fail in rich structure preservation. To cope with these problems, this paper proposed a novel wavelet-based deep denoising methods, called as wavelet-based global–local filtering networks (WGLFNets). The WGLFNets includes the following three key points: First, an noisy image is decomposed into a base image and three-directional detail images by employing discrete wavelet transform (DWT). Second, the base component is denoised by a global denoising network while the detail components are recovered by a local detail restoration network. Finally, all processed components are utilized to construct the high-quality image by the inverse DWT (IDWT). Experimental results demonstrate that the WGLFNets is effective and is superior to the state-of-the-arts.

Implementation and Optimization of Image Processing on the Map of SABRE i.MX_6

Vision relieves humans to understand the environmental deviations over a period. These deviations are seen by capturing the images. The digital image plays a dynamic role in everyday life. One of the processes of optimizing the details of an image whilst removing the random noise is image denoising. It is a well-explored research topic in the field of image processing. In the past, the progress made in image denoising has advanced from the improved modeling of digital images. Hence, the major challenges of the image process denoising algorithm is to advance the visual appearance whilst preserving the other details of the real image. Significant research today focuses on wavelet-based denoising methods. This research paper presents a new approach to understand the Sobel imaging process algorithm on the Linux platform and develop an effective algorithm by using different optimization techniques on SABRE i.MX_6. Our work concentrated more on the image process algorithm optimization. By using the OpenCV environment, this paper is intended to simulate a Salt and Pepper noisy phenomenon and remove the noisy pixels by using Median Filter Algorithm. The Sobel convolution method included and used in the design of a Sobel Filter and then process the image following the median filter, to achieve an effective edge detection result. Finally, this paper optimizes the algorithm on SABRE i.MX_6 Linux environment. By using algorithmic optimization (lower complexity algorithm in the mathematical sense, using appropriate data structures), optimization for RISC (loop unrolling) processors, including optimization for efficient use of hardware resources (access to data, cache management and multi-thread), this paper analyzed the different response parameters of the system with varied inputs, different compiler options (O1, O2, or O3), and different doping degrees. The proposed denoising algorithm shows the meaningful addition of the visual quality of the images and the algorithmic optimization assessment.

GA-based multi-objective optimization technique for medical image denoising in wavelet domain

Medical images that are acquired with reduced radiation exposure or following the administration of imaging agents with a low dose, are often known to experience problems by the noise stemming from acquisition hardware as well as psychological sources. This noise can adversely affect the quality of diagnosis, but also prevent practitioners from computing quantitative functional information. With a view to overcoming these challenges, the current paper puts forward optimization of multi-objective for denoising medical images within the wavelet domain. This proposed technique entails the use of genetic algorithm (GA) to get the threshold optimized within the denoising framework of wavelets. Two purposes are associated with this technique: First, its ability to adapt with different noise types of noise in the image without requiring prior information about the imaging process per se. In addition, it balances relevant diagnostic details’ preservation against the reduction of noise by considering the optimization of the error factor of Liu and SNR as the foundation of objective function. According to the implementation of this method on magnetic resonance (MR) and ultrasound (US) images of the brain, a better performance has been observed as compared to the existing wavelet-based denoising methods with regard to quantitative and qualitative metrics.

A wavelet denoising approach based on unsupervised learning model

Image denoising plays an important role in image processing, which aims to separate clean images from noisy images. A number of methods have been presented to deal with this practical problem over the past several years. The best currently available wavelet-based denoising methods take advantage of the merits of the wavelet transform. Most of these methods, however, still have difficulties in defining the threshold parameter which can limit their capability. In this paper, we propose a novel wavelet denoising approach based on unsupervised learning model. The approach taken aims at exploiting the merits of the wavelet transform: sparsity, multi-resolution structure, and similarity with the human visual system, to adapt an unsupervised dictionary learning algorithm for creating a dictionary devoted to noise reduction. Using the K-Singular Value Decomposition (K-SVD) algorithm, we obtain an adaptive dictionary by learning over the wavelet decomposition of the noisy image. Experimental results on benchmark test images show that our proposed method achieves very competitive denoising performance and outperforms state-of-the-art denoising methods, especially in the peak signal to noise ratio (PSNR), the structural similarity (SSIM) index, and visual effects with different noise levels.

Data pre-processing effect on ANN-based prediction intervals construction of the evaporation process at different climate regions in Iran

The point predictions of stochastic processes, such as evaporation, by data-driven methods such as Artificial Neural Network (ANN), are associated with uncertainties. Furthermore, the performance of data-driven models, as well as their uncertainty, are dependent on the quality and quantity of the used data. The main aim of this research was the Uncertainty Quantifying (UQ) of the ANN-based evaporation predictions by Prediction Intervals (PIs) analysis using the data from three stations in Iran (i.e. Tabriz, Urmia, and Ardabil). In this way, data pre-processing methods i.e. Wavelet-based De-noising (WD), training with Jitted Data (JD) and also their combination i.e. Hybrid Wavelet De-noising and Jitted Data (HWDJD) were applied to examine their effects on the estimated values of PIs. The Lower-Upper-Bound Estimation (LUBE) method as the direct NN-based PI construction was utilized for estimating the PI values. Since the efficiency of any ANN model and consequently, the robustness of the uncertainty analysis is sensitive to the correct selection of input variables, the first order Partial Derivation (PaD) sensitivity analysis method was also used to select dominant inputs among all potential input variables. The results indicated that the LUBE technique could provide acceptable results in estimating the uncertainty bounds, whereas the uncertainty quantity would be affected by the used data pre-processing methods. The reduction of uncertainty effect via data pre-processing methods was significant in modeling Urmia and Ardabil stations. Results showed that the reduction of PI bandwidths via HWDJD, WD, and JD methods were up to 30%, 21%, and 9%, respectively. It means that to reduce the ANN-based modeling uncertainty due to the uncertainty involved in the input data set, at first, the contaminant noise of the available data should be eliminated from the time series, then artificially generated time series (JD) that mimic the smoothed time series pattern can be generated and used in the training process.

Acquisition of weak GPS signals using wavelet-based de-noising methods

Various factors cause GPS signals to be weakened in their path from satellites to receiver. This phenomenon leads to some problems in the normal stages of the positioning process, including acquisition stage. The wavelet transform is one of the tools that have been employed in several methods to improve receiver’s sensitivity in confronting weak GPS signals. Choosing an appropriate threshold plays a key role in the performance of this de-noising method. This study presents two methods for selecting an appropriate threshold. In the first method, the threshold is determined based on the statistical information extracted from the signal. On the other hand, the threshold in the second method is determined by type II fuzzy sets. The results show that employment of these two methods increases SNR gain as well as the range of acquirable SNR which makes signals acquisition with minimum post-correlation SNR of in a GPS receiver possible.

Single Image Super Resolution Technique: An Extension to True Color Images

The super-resolution (SR) technique reconstructs a high-resolution image from single or multiple low-resolution images. SR has gained much attention over the past decade, as it has significant applications in our daily life. This paper provides a new technique of a single image super-resolution on true colored images. The key idea is to obtain the super-resolved image from observed low-resolution images. A proposed technique is based on both the wavelet and spatial domain-based algorithms by exploiting the advantages of both of the algorithms. A back projection with an iterative method is implemented to minimize the reconstruction error and for noise removal wavelet-based de-noising method is used. Previously, this technique has been followed for the grayscale images. In this proposed algorithm, the colored images are taken into account for super-resolution. The results of the proposed method have been examined both subjectively by observation of the results visually and objectively by considering the peak signal-to-noise ratio (PSNR) and mean squared error (MSE), which gives significant results and visually better in quality from the bi-cubic interpolation technique.

Pre‐processing approach for de‐noising on‐line oil chromatography data based on self‐adapting wavelet analysis

Due to the influence of the external environment and the performance of measuring equipment, the on-line oil chromatography data contains obvious noise which makes the signal to oscillate. The monitoring data is difficult to be directly applied to the equipment state analysis. A novel wavelet-based de-noising method is proposed for pre-processing the on-line oil chromatography data. By analysing the characteristics of on-line oil chromatography data, the method of determining the decomposition layer number based on the probability distribution of wavelet coefficients and the method of determining the threshold value based on outliers conservation are proposed. The improved wavelet de-noising method is applied to analysing the on-line oil chromatography data of a defective ultra-high voltage (UHV) reactor. The results show that the proposed method is feasible and effective.

Despeckling of medical ultrasound images by wavelet threshold optimisation

Speckle noise is the primary factor that limits the contrast resolution of diagnostic ultrasound images, thereby limiting the detection of small low-contrast lesions and making the ultrasound images generally difficult for a nonspecialist to interpret. Therefore, speckle is more often considered as a dominant source of noise in ultrasound imaging and should be filtered out by a robust despeckling technique. In this paper, we compare two despeckling techniques, based on wavelet thresholding. Bayes shrinkage and genetic-algorithm-based wavelet denoising despeckling technique are implemented. Wavelet functions were studied in detail and the two algorithms were implemented using the Haar wavelet as a wavelet function. The application of this new filter on ultrasound images has shown a superior performance over the state-of-the-art wavelet-based denoising methods in terms of visual quality and structural similarity index map.

Spatially Adaptive Image Denoising using Undecimated Directionlet Transform

paper a novel de-noising method based on directionlet transform and on sub band adaptive Bayesian threshold is presented. The denoising scheme used in wavelet domain has been extended to the directionlet domain to make the image features to concentrate on fewer coefficients so that more effective thresholding is possible. Here the directionality of the spatially segmented image is first computed using a parameter called directional variance for selecting the optimum direction for decomposing the image using undecimated directionlet transform. The decomposed images with directional energy are used for threshold computation using Bayes scheme. This threshold is then applied to the sub- bands except the LLL subband. The threshold corrected sub- bands with the unprocessed first sub-band are given as input to the inverse directionlet algorithm for getting the de-noised image. Experimental results show that the proposed method outperforms the standard wavelet-based denoising methods in terms of perceptual and numerical estimates.

A review of applying second-generation wavelets for noise removal from remote sensing data

The processing of remotely sensed data includes compression, noise reduction, classification, feature extraction, change detection and any improvement associated with the problems at hand. In the literature, wavelet methods have been widely used for analysing remote sensing images and signals. The second-generation of wavelets, which is designed based on a method called the lifting scheme, is almost a new version of wavelets, and its application in the remote sensing field is fresh. Although first-generation wavelets have been proven to offer effective techniques for processing remotely sensed data, second-generation wavelets are more efficient in some respects, as will be discussed later. The aim of this review paper is to examine all existing studies in the literature related to applying second-generation wavelets for denoising remote sensing data. However, to make a better understanding of the application of wavelet-based denoising methods for remote sensing data, some studies that apply first-generation wavelets are also presented. In the part of hyperspectral data, there is a focus on noise removal from vegetation spectrum.

Experimental study of infrasonic signal generation during rock fracture under uniaxial compression

The low frequency infrasonic signals generated during micro fracture process of six types of rocks (including granite, mudstone, sandstone, phyllite, limestone and red sandstone) under uniaxial compression were detected. A specialized data collection system was developed for infrasonic signals sensing and analog-to-digital conversion. The wavelet-based de-noising method, Short-Time Fourier Transform (STFT) time-frequency analysis and accumulative ring-down count (ARC) of events were used to process and analyze digital infrasonic signals in order to investigate the characteristics of infrasonic emission (IE) event during rock micro fracture process. The experimental results indicate obvious infrasonic emission events before rock failure. The characteristic frequency typically ranges from about 2.0 to 8.0Hz for the six kinds of rocks and it has no necessary relationship with structure or lithology. According to the ARC estimate, hard rocks (such as granite, limestone) can generate much more infrasonic emission events than soft ones (mudstone, phyllite), in other words, the brittle fracture is more prone to generate infrasonic signals. In addition, infrasound is an inaudible and low-attenuate signal that cannot be absorbed easily by water or air, and can propagate avoiding huge obstacles due to its long wavelength. The research results and the advantages of the infrasound will provide a beneficial supplement for our further studies on rock instability or rocky landslide in field combined with other advanced methods.

Image Denoising Using Sure-Based Adaptive Thresholding in Directionlet Domain

The standard separable two dimensional wavelet transform has achieved a great success in image denoising applications due to its sparse representation of images. However it fails to capture efficiently the anisotropic geometric structures like edges and contours in images as they intersect too many wavelet basis functions and lead to a non-sparse representation. In this paper a novel de-noising scheme based on multi directional and anisotropic wavelet transform called directionlet is presented. The image denoising in wavelet domain has been extended to the directionlet domain to make the image features to concentrate on fewer coefficients so that more effective thresholding is possible. The image is first segmented and the dominant direction of each segment is identified to make a directional map. Then according to the directional map, the directionlet transform is taken along the dominant direction of the selected segment. The decomposed images with directional energy are used for scale dependent subband adaptive optimal threshold computation based on SURE risk. This threshold is then applied to the sub-bands except the LLL subband. The threshold corrected sub-bands with the unprocessed first sub-band (LLL) are given as input to the inverse directionlet algorithm for getting the de-noised image. Experimental results show that the proposed method outperforms the standard wavelet-based denoising methods in terms of numeric and visual quality.

Total variation versus wavelet‐based methods for image denoising in fluorescence lifetime imaging microscopy

We report the first application of wavelet-based denoising (noise removal) methods to time-domain box-car fluorescence lifetime imaging microscopy (FLIM) images and compare the results to novel total variation (TV) denoising methods. Methods were tested first on artificial images and then applied to low-light live-cell images. Relative to undenoised images, TV methods could improve lifetime precision up to 10-fold in artificial images, while preserving the overall accuracy of lifetime and amplitude values of a single-exponential decay model and improving local lifetime fitting in live-cell images. Wavelet-based methods were at least 4-fold faster than TV methods, but could introduce significant inaccuracies in recovered lifetime values. The denoising methods discussed can potentially enhance a variety of FLIM applications, including live-cell, in vivo animal, or endoscopic imaging studies, especially under challenging imaging conditions such as low-light or fast video-rate imaging.

Accelerated MR imaging using compressive sensing with no free parameters

We describe and evaluate a robust method for compressive sensing MRI reconstruction using an iterative soft thresholding framework that is data-driven, so that no tuning of free parameters is required. The approach described here combines a Nesterov type optimal gradient scheme for iterative update along with standard wavelet-based adaptive denoising methods, resulting in a leaner implementation compared with the nonlinear conjugate gradient method. Tests with T₂ weighted brain data and vascular 3D phase contrast data show that the image quality of reconstructions is comparable with those from an empirically tuned nonlinear conjugate gradient approach. Statistical analysis of image quality scores for multiple datasets indicates that the iterative soft thresholding approach as presented here may improve the robustness of the reconstruction and the image quality, when compared with nonlinear conjugate gradient that requires manual tuning for each dataset. A data-driven approach as illustrated in this article should improve future clinical applicability of compressive sensing image reconstruction.

Genetic Algorithm Assisted Wavelet Noise Reduction Scheme for Chaotic Signals

We present a Genetic Algorithm-based wavelet denoising method which incorporates a Genetic Algorithm within a wavelet framework for threshold optimization. The new method not only intelligently adapts itself to different types of noise without any prior knowledge of the noise, but also balances the preservation of dynamics against the degree of noise reduction by optimizing the Signal-to-Noise Ratio and the Liu’s error factor. The presented method performs better than the state-of-the-art wavelet-based denoising methods when applied to chaotic signals.

A Novel Method to Improve the Visual Quality of X-ray CR Images

The aim of this study is to improve the visual quality of x-ray CR images displayed at general displays. Firstly, we investigate a series of wavelet-based denoising methods for removing quantum noise remains in the original images. The denoised image is obtained by using the scheme of wavelet thresholding, where the best suitable wavelet and level are chosen based on theory analysis. Secondly, the image contrast is enhanced using Gamma correction. Thirdly, we improve unsharp masking method for enhancing some useful information and restraining other information selectively. Fourthly, we fuse the denoised image with the enhanced image. Fively, the used display is calibrated, so that it could offer full compliance with the Grayscale Standard Display Function (GSDF) defined in Digital Imaging and Communications in Medicine (DICOM) Part 14. Finally, we decide parameters of the image fusion, resulting in the diagnosis image. A number of experiments are performed over some x-ray CR images by using the proposed method. Experimental results show that this method can effectively reduce the quantum noise while enhancing the subtle details; the visual quality of X-ray CR images is highly improved.

Denoising methods for thermomechanical decomposition for quasi-equilibrium molecular dynamics simulations

In this work, we applied robust denoising methods well established in the signal processing field for the thermomechanical decomposition of velocity data obtained from molecular dynamics (MD) simulations. In the decomposition, the atomic velocity was assumed to be the sum of the mechanical velocity and the thermal velocity, which can be linked to the stress and temperature field at the continuum scale, respectively. For the quasi-equilibrium process, with the thermal velocity treated as the Gaussian distributed stationary noise with zero mean and a positive variance that is linearly proportional to temperature and mechanical velocity as the clean signal, the velocity decomposition can be recasted into a denoising problem, for which powerful denoising methods have been developed to estimate a clean signal from noisy data. We investigated the widely-used linear parametric real-domain, linear nonparametric Fourier-based, and nonlinear nonparametric wavelet-based denoising methods, first on their theoretical properties and then made comparsion among them for denosing some synthetic noisy 1-dimensional (1D) data generated from MD simulations. The nonlinear wavelet-based thresholding estimator possessed better optimality properties than the other estimators, and also outperformed the other estimators in the synthetic data test. A further test comparing the various denoising methods for an adiabatic shear crack nucleation and propagation process simulated using MD simulations showed better performance by the wavelet-based denoisng method. Results from this work reveal good potential of applying wavelet-based denoising method to the study of thermomechanical processes simulated using MD simulations.