Wavelet Denoising Research Articles

An Investigation of Signal Preprocessing for Photoacoustic Tomography.

Photoacoustic tomography (PAT) is increasingly being used for high-resolution biological imaging at depth. Signal-to-noise ratios and resolution are the main factors that determine image quality. Various reconstruction algorithms have been proposed and applied to reduce noise and enhance resolution, but the efficacy of signal preprocessing methods which also affect image quality, are seldom discussed. We, therefore, compared common preprocessing techniques, namely bandpass filters, wavelet denoising, empirical mode decomposition, and singular value decomposition. Each was compared with and without accounting for sensor directivity. The denoising performance was evaluated with the contrast-to-noise ratio (CNR), and the resolution was calculated as the full width at half maximum (FWHM) in both the lateral and axial directions. In the phantom experiment, counting in directivity was found to significantly reduce noise, outperforming other methods. Irrespective of directivity, the best performing methods for denoising were bandpass, unfiltered, SVD, wavelet, and EMD, in that order. Only bandpass filtering consistently yielded improvements. Significant improvements in the lateral resolution were observed using directivity in two out of three acquisitions. This study investigated the advantages and disadvantages of different preprocessing methods and may help to determine better practices in PAT reconstruction.

Gamma-Minimax Wavelet Shrinkage for Signals with Low SNR

In this paper, we propose a method for wavelet denoising of signals contaminated with Gaussian noise when prior information about the ${L^{2}}$-energy of the signal is available. Assuming the independence model, according to which the wavelet coefficients are treated individually, we propose simple, level-dependent shrinkage rules that turn out to be Γ-minimax for a suitable class of priors. The proposed methodology is particularly well suited in denoising tasks when the signal-to-noise ratio is low, which is illustrated by simulations on a battery of some standard test functions. Comparison to some commonly used wavelet shrinkage methods is provided.

A Hybrid Fault Diagnosis Method Using Translation Invariant Wavelet Denoising, Hierarchical Entropy, and Support Vector Machine with PSO Algorithm

The rolling element bearing is used in various machinery and produces vibration due to imperfections, surface irregularities during manufacture, damaged bearings, and inaccuracies in the allied element. Also, the rolling element bearing vibration generally shows non-linear dynamic characteristics and is masked with heavy background noise. This noble investigation advances a hybrid technique for removing background noise from the vibration signal and detecting bearing defects. Translation invariant wavelet denoising is the initial stage in this hybrid method for noise removal from the signal. The second phase uses Hierarchical Entropy (HE) for defect feature frequency extraction. Hierarchical entropy at scale four and SampEns of eight hierarchical decomposition nodes was utilized to determine the defect feature vector. In particular, low-frequency components are investigated through multi-scale entropy (MSE), but hierarchical entropy (HE) incorporates low-frequency and high-frequency components and can extract more defective information. Implemented a multi-class support vector machine (SVM) for extracting Hierarchical entropy as feature vectors. These feature vectors are trained by utilizing particle swarm optimization (PSO). To accomplish a prediction model, examine the optimal SVM parameters and then various bearing conditions with the variation of type, size, speed, and load severity identified by SVM. The investigation results show that hierarchical entropy can adequately and more precisely express the features of bearing vibration signals. It is beyond MSE, and the proposed Nobel hybrid Translation invariant wavelet denoising and Hierarchical entropy-based method will effectively remove the noisy background signal. Also, it distinguishes different bearings successfully, indicates the bearing conditions correctly, and is more prominent than those found on MSE.

VOLATILITY FORECASTING AFTER REMOVING THE NOISE: DOES IT REALLY PAY OFF?

The analysis in this paper represents the first attempt to examine whether the forecasting performance of one of the GARCH models can be improved after removing the noise from the stock market returns. Doing the analysis on eight developed stock markets helps in providing reliable results that can be generalized to more stock markets. This paper then examines the ability of GARCH models to forecast stock return volatility under a range of statistical forecasts. We specifically employ the multiscale-based approach, namely the maximum overlap discrete wavelet transformation, to remove the noisy data from the return series. Based on related theoretical literature, we assume that noise trading makes the forecasting performance more misleading, especially at the short-term horizon. Our particular interest then is whether wavelet de-noising of the data before estimation affects the ability of the models to provide accurate forecasts at a short investment horizon. To de-noise the data, we use soft thresholding and Stein’s Unbiased Risk Estimator to obtain the decomposition level-based threshold limit. Our key results demonstrate that de-noising returns improves the accuracy of volatility forecasts regardless of whether we used statistical metrics or tests of equal predictive accuracy. Moreover, in terms of a particular volatility model, the asymmetric GARCH approach tends to be preferred although this result is not universal. Indeed, the central result from our analysis is that the process of de-noising is more important than the specific model.

Diagnosis of arrhythmias with few abnormal ECG samples using metric-based meta learning

A major challenge in artificial intelligence based ECG diagnosis lies that it is difficult to obtain sufficient annotated training samples for each rhythm type, especially for rare diseases, which makes many approaches fail to achieve the desired performance with limited ECG records. In this paper, we propose a Meta Siamese Network (MSN) based on metric learning to achieve high accuracy for automatic ECG arrhythmias diagnosis with limited ECG records. First, the ECG signals from three different ECG datasets are preprocessed through resampling, wavelet denoising, R-wave localization, heartbeat segmentation and Z-score normalization. Then, an ECG dataset with limited records is constructed to verify the performance of the proposed model and explore variation of model performance with the sample size. Second, a metric-based meta-learning framework is proposed to address the challenge of few-shot learning for automatic ECG diagnosis of cardiac arrhythmia, and siamese network is employed to achieve arrhythmia diagnosis based on similarity metric. Finally, the N-way K-shot meta-testing strategy is proposed based on the siamese network with double inputs, and the experimental results demonstrate that the proposed strategy can effectively improve the robustness of the proposed model.

A synthetic denoising algorithm for full-waveform induced polarization based on deep learning

Induced polarization (IP) is a widely used geophysical exploration technique. Continuous random noise is one of the most prevalent interferences that can seriously contaminate the IP signal and distort the apparent electrical characteristics. We develop a noise separation algorithm based on deep learning to overcome this issue. The standard IP signals are first produced by combining the Cole-Cole model and Fourier series decomposition, and then the mathematical simulation is used to generate various types of random noise interferences, which are subsequently added to the IP signals. Then, a denoising autoencoder deep neural network structure is built and trained by using noisy signals as input samples and pure signals as output samples. The resulting optimum network is capable of automatically reconstructing a clean IP signal from the noisy input. This network is tested using synthetic data sets. The trained neural network can perform the noise reduction of thousands of survey points in a matter of seconds and reduce signal distortion from approximately 25% to less than 5%. Deep learning-based denoising provides superior computation speed and precision compared with the wavelet denoising and smoothing filtering approach. The data for high-quality signals do not vary considerably before and after noise reduction. The noise interferences are successfully suppressed for low-quality signals. Based on the findings, the denoising autoencoder deep neural network has a promising future for suppressing random noise interferences, which can aid in improving the quality of IP data with high efficiency and precision.

Single-channel electroencephalogram signal used for sleep state recognition based on one-dimensional width kernel convolutional neural networks and long-short-term memory networks

Aiming at the problem that the unbalanced distribution of data in sleep electroencephalogram(EEG) signals and poor comfort in the process of polysomnography information collection will reduce the model's classification ability, this paper proposed a sleep state recognition method using single-channel EEG signals (WKCNN-LSTM) based on one-dimensional width kernel convolutional neural networks(WKCNN) and long-short-term memory networks (LSTM). Firstly, the wavelet denoising and synthetic minority over-sampling technique-Tomek link (SMOTE-Tomek) algorithm were used to preprocess the original sleep EEG signals. Secondly, one-dimensional sleep EEG signals were used as the input of the model, and WKCNN was used to extract frequency-domain features and suppress high-frequency noise. Then, the LSTM layer was used to learn the time-domain features. Finally, normalized exponential function was used on the full connection layer to realize sleep state. The experimental results showed that the classification accuracy of the one-dimensional WKCNN-LSTM model was 91.80% in this paper, which was better than that of similar studies in recent years, and the model had good generalization ability. This study improved classification accuracy of single-channel sleep EEG signals that can be easily utilized in portable sleep monitoring devices.

High-Spatial-Resolution OFDR Distributed Temperature Sensor Based on Step-by-Step and Image Wavelet Denoising Methods.

A high-spatial-resolution OFDR distributed temperature sensor based on Au-SMF was experimentally demonstrated by using step-by-step and image wavelet denoising methods (IWDM). The measured temperature between 50 and 600 °C could be successfully demodulated by using SM-IWDM at a spatial resolution of 3.2 mm. The temperature sensitivity coefficient of the Au-SMF was 3.18 GHz/°C. The accuracy of the demodulated temperature was approximately 0.24 °C. Such a method has great potential to expand the temperature measurement range, which is very useful for high-temperature applications.

Long Distance Distributed Strain Sensing in OFDR by BM3D-SAPCA Image Denoising

We present a long distance distributed strain sensing in optical frequency domain reflectometry (OFDR) by shape-adaptive principal component analysis Block-Matching three-dimensional filter (BM3D-SAPCA) image denoising, which uses correlated patterns and high degree redundancy of sensing data for enhancing the performance of distributed sensing by image processing for removing noise and increasing the signal-to-noise ratio (SNR) of noisy measurements. Compared with 2D image denoising methods, BM3D-SAPCA method searches similar 2D image blocks and stacks them together in 3D arrays, which takes full advantage of the high level of similitude and redundancy contained on the multidimensional information to denoise. We find that the BM3D-SAPCA method can effectively suppresses noise aggravation along with an increasing of the sensing distance. Without modifying the hardware system of OFDR, we achieve a distributed strain sensing with a 5 cm spatial resolution, a 2 μϵ strain resolution on a 200 m all grating fiber. We compare the performance of distributed strain sensing by BM3D-SAPCA with Gaussian filter, wavelet denoising (WD) and non-local mean filter (NLM) using the same data. The mean maximal strain measurement error at loaded strain areas is reduced from 2.3791 μϵ to 0.6545 μϵ by BM3D-SAPCA. These mean errors by Gaussian filter, NLM and WD are 1.1177 μϵ, 1.6668 μϵ and 1.9721 μϵ, respectively. The mean standard deviations of strain measurement in eight repeat experiments is reduced from 1.5221 μϵ to 0.3134 μϵ after noise reduction by BM3D-SAPCA, which is 79.37% lower than the raw data. The mean standard deviations after noise reduction by Gaussian filter, NLM and WD are decreased by 68.85%, 64.24% and 14.41% respectively.

Nondestructive Evaluation of Thermal Barrier Coatings Thickness Using Terahertz Time-Domain Spectroscopy Combined with Hybrid Machine Learning Approaches

To ensure the thermal stability of aero-engine blades under high temperature and harsh service environments, it is necessary to quickly and accurately evaluate the thickness of thermal barrier coatings (TBCs). In this work, it was proposed to use the terahertz nondestructive testing (NDT) technique combined with the hybrid machine learning algorithm to measure the thickness of TBCs. The finite difference time-domain (FDTD) method was used to model the optical propagation characteristics of TBC samples with different thicknesses (101–300 μm) in the frequency band. To make the terahertz time-domain signal obtained simulation more realistic, uniform white noise was added to the simulation data and wavelet denoising was conducted to mimic the real testing environment. Principal components analysis (PCA) algorithm and whale optimization algorithm (WOA) combined with an optimized Elman neural network algorithm was employed to set up the hybrid machine learning model. Finally, the hybrid thickness regression prediction model shows low error, high accuracy, and an exceptional coefficient of determination R2 of 0.999. It was demonstrated that the proposed hybrid algorithm could meet the thickness evaluation requirements. Meanwhile, a novel, efficient, safe, and accurate terahertz nondestructive testing method has shown great potential in the evaluation of structural integrity of thermal barrier coatings in the near future.

Portfolio Selection Based on EMD Denoising with Correlation Coefficient Test Criterion.

Noise is an important factor affecting portfolio performance, how to construct an effective denoising strategy is becoming increasingly important for investors. In this study, we theoretically explain the impact of noise on portfolio and argue the necessity of denoising. Next, the empirical mode decomposition (EMD) denoising strategy based on the correlation coefficient test criterion is proposed to improve portfolio performance. In detail, EMD is used to decompose the noisy price, then, a series of correlation coefficient tests are performed to determine which intrinsic mode functions (IMFs) are noise. In the empirical analysis, we apply the proposed method to denoise the SSE 50 index's constituents, and further test the out-of-sample performance under the mean-variance framework. The empirical results show that the proposed denoising method outperforms four common EMD, Ensemble EMD (EEMD) and wavelet denoising methods in return-risk ratio. The proposed method is the optimal denoising strategy, which can help investors improve portfolio performance to the greatest extent.

Design, calibration, and testing of a mobile sensor system for air pollution and built environment data collection: The urban scanner platform

This paper describes a mobile air pollution sampling system, the Urban Scanner, which aims at gathering dense spatiotemporal air quality data to support urban air quality and exposure science. Urban Scanner comprises custom vehicle-mounted sensors for air pollution, meteorology, and built environment data collection (low-cost sensors, wind anemometer, 360 deg camera, LIDAR, GPS) as well as a server to store, process, and map all gathered geo-referenced sensory information. Two levels of sensor calibration were implemented, both in a chamber and in the field, against reference instrumentation. Chamber tests and a set of mathematical tools were developed to correct for sensor noise (wavelet denoising), misalignment (linear and nonlinear), and hysteresis removal. Models based on chamber testing were further refined based on field co-location. While field co-location captures natural changes in air pollution and meteorology, chamber tests allow for simulating fast transitions in these variables, like the transitions experienced by a mobile sensor in an urban environment. The best suite of models achieved an R2 higher than 0.9 between sensor output and reference station observations and an RMSE of 2.88 ppb for nitrogen dioxide and 4.03 ppb for ozone. A mobile sampling campaign was conducted in the city of Toronto, Canada, to further test Urban Scanner. We observe that the platform adequately captures spatial and temporal variability in urban air pollution, leading to the development of land-use regression models with high explanatory power.

Frequency Identification and Damage Detection of Bridges Using Virtual Contact-Point Responses of Railway Vehicle

This paper proposed an indirect bridge frequency identification and damage detection method based on the virtual contact-point (CP) responses of railway vehicles moving over the bridge. The virtual CP response is acquired to reduce the inverse effects of the track irregularity and vehicle dynamic components on the indirect bridge monitoring of the vehicle–bridge interaction (VBI) system. By combining the virtual CP responses of multiple connected vehicles, the first three bridge frequencies can be identified when vehicles run at high speed. The synchrosqueezing transform (SST) is then adopted to extract bridge-related dynamic components from the virtual CP response for bridge modal identification. The time-frequency (TF) representation of the virtual CP response using SST is further analyzed for bridge damage detection. The spectral entropy (SE) of the TF representation is introduced to quantify TF changes and serves as a damage index for bridge damage localization. Numerical studies are conducted to investigate the effects of measurement noise, damage conditions, and track irregularity on the effectiveness of the proposed method. The results demonstrate that SE is a good indicator for damage detection, and that the proposed method combined with wavelet denoising has good anti-noise performance and can well locate bridge damage using virtual CP response.

Performance improvement of on-chip mid-infrared waveguide methane sensor using wavelet denoising and Savitzky-Golay filtering

Due to mode interference and reflection, waveguide gas sensor is prone to generate noise, which affects gas detection performance. In order to improve the performance of waveguide methane (CH4) sensor, wavelet denoising (WD) and Savitzky-Golay (SG) filtering were combined to process the noisy signal. With the fabricated silicon-on-insulator (SOI) ridge waveguide, a waveguide CH4 sensing system was built, and the absorbance signal was processed by denoising schemes. Experimental results show that compared with the traditional WD scheme, the WD-SG scheme has obvious advantages in suppressing low-frequency random noise and interference noise. Using WD-SG scheme, the signal-to-noise ratio (SNR) of the absorbance signal is increased by 4.95 times. According to the Allan deviation analysis, the 1σ limit of detection (LoD) of the sensor is reduced from 2929 parts per million (ppm) to 397 ppm when the WD-SG scheme is adopted. The sensor shows a fast response time of less than 2.5 s. Our work shows that the WD-SG scheme can effectively improve the SNR and reduce the influence of noise on the waveguide sensor system on the basis of real-time monitoring.

Spatiotemporal singular value decomposition for denoising in photoacoustic imaging with a low-energy excitation light source.

Photoacoustic (PA) imaging is an emerging hybrid imaging modality that combines rich optical spectroscopic contrast and high ultrasonic resolution, and thus holds tremendous promise for a wide range of pre-clinical and clinical applications. Compact and affordable light sources such as light-emitting diodes (LEDs) and laser diodes (LDs) are promising alternatives to bulky and expensive solid-state laser systems that are commonly used as PA light sources. These could accelerate the clinical translation of PA technology. However, PA signals generated with these light sources are readily degraded by noise due to the low optical fluence, leading to decreased signal-to-noise ratio (SNR) in PA images. In this work, a spatiotemporal singular value decomposition (SVD) based PA denoising method was investigated for these light sources that usually have low fluence and high repetition rates. The proposed method leverages both spatial and temporal correlations between radiofrequency (RF) data frames. Validation was performed on simulations and in vivo PA data acquired from human fingers (2D) and forearm (3D) using a LED-based system. Spatiotemporal SVD greatly enhanced the PA signals of blood vessels corrupted by noise while preserving a high temporal resolution to slow motions, improving the SNR of in vivo PA images by 90.3%, 56.0%, and 187.4% compared to single frame-based wavelet denoising, averaging across 200 frames, and single frame without denoising, respectively. With a fast processing time of SVD (∼50 µs per frame), the proposed method is well suited to PA imaging systems with low-energy excitation light sources for real-time in vivo applications.

Paper Defect Detection Algorithm Based on the Mathematical Morphology and Computer Vision

A method for detecting paper’s surface defects is proposed, which is based on mathematical morphology algorithm and computer vision technique. Firstly, the mean filtering and wavelet denoising in image pre-processing are used to eliminate the image noise, and wavelet analysis can achieve image enhancement and increase the contrast between the target area and the background. And then, an improved threshold Canny operator is used to segment the image to extract the complete scratch line and other defect edges. Finally, the target region features are coloured by mathematical morphology processing. The method’s stimulating result is verified in the Matlab software, from which we can conclude that the method’s detecting effect is very effective.

Application of Hyperspectral Technology Combined with Genetic Algorithm to Optimize Convolution Long- and Short-Memory Hybrid Neural Network Model in Soil Moisture and Organic Matter

A method of soil moisture and organic matter content detection based on hyperspectral technology is proposed. A total of 800 different soil samples and hyperspectral data were collected in the laboratory and from the field. A hyperspectral database was established. After wavelet denoising and principal component analysis (PCA) preprocessing, the convolutional neural network (CNN) module was first used to extract the wavelength features of the data. Then, the long- and short-memory neural network (LSTM) module was used to extract the feature bands and nearby hidden state vectors. At the same time, the genetic algorithm (GA) was used to optimize the hyperparametric weight and bias value of the LSTM training network. At the initial stage, the data were normalized, and all features were analyzed by grey correlation degree to extract important features and to reduce the computational complexity of the data. Then, the GA-optimized CNN-LSTM hybrid neural network (GA-CNN-LSTM) algorithm model proposed in this paper was used to predict soil moisture and organic matter. The prediction performance was compared with CNN, support vector regression (SVR), and CNN-LSTM hybrid neural network model without GA optimization. The GA-CNN-LSTM algorithm was superior to other models in all indicators. The highest accuracy rates of 94.5% and 92.9% were obtained for soil moisture and organic matter, respectively. This method can be applied to portable hyperspectrometers and unmanned aerial vehicles to realize large-scale monitoring of moisture and organic matter distribution and to provide a basis for rational irrigation and fertilization in the future.

An Early Warning Intelligent Algorithm System for Forest Resource Management and Monitoring.

The development of remote sensing technology has passed an effective means for forest resource management and monitoring, but remote sensing technology is limited by sensor hardware equipment, and the quality of remote sensing image data is low, which is difficult to meet the needs of forest resource change monitoring. This paper presents a remote sensing image classification method based on the combination of the SSIF algorithm and wavelet denoising. Forest information is extracted from PALSAR/PALSAR-2 radar remote sensing data. The forest distribution map is generated by pixel level fusion algorithm, and the accuracy of the forest distribution map is evaluated by a confusion matrix. The remote sensing image is spatio-temporal fused by the SSIF algorithm to capture more details of forest distribution. The simulation analysis shows that the overall accuracy of the forest classification results obtained by the fusion algorithm is 96% ± 1, and the kappa coefficient is 0.66. The accuracy of forest recognition meets the requirements.

Wavelet denoising approach in long-distance optical communications.

For free-space optical communication links, the light spot collected by the photodetector at the receiving terminal is not an ideal light spot that is affected by atmospheric turbulence. The light spot collected by the photodetector will also be accompanied by various noises. More importantly, the presence of all noise will bring errors to acquire the light spot's center. As a result, the tracking error can affect the stability of the optoelectronic tracking system. Therefore, it is necessary to remove noise from the collected images. The method of removing noise needs to be effective, but it cannot bring a large amount of calculation to affect the real-time performance. The calculation amount of wavelet transform is small, and the effect of noise removal is better, which can focus on local details with arbitrary expansion coefficients. An improved wavelet denoising method is proposed. The long-distance verification experiment (11.16 km) verified the effectiveness of this approach, compared with the traditional method. Furthermore, to the best of our knowledge, this new approach would be beneficial for the design of optical communication systems.

Research on adaptive combined wind speed prediction for each season based on improved gray relational analysis.

The stability of the power grid and the operational security of the power system depend on the precise prediction of wind speed. In consideration of the nonlinear and non-stationary characteristics of wind speed in different seasons, this paper employs the weight of wind resource index calculated by triangular fuzzy analytic hierarchy process (TF-AHP), criteria importance through inter-criteria correlation (CRITIC), and entropy weight method (EWM) to improve gray correlation analysis (GRA) and obtain the gray correlation degree of each season. In addition, a wind speed prediction model is provided that includes single-layer and two-layer weighting and is based on both deep and shallow machine learning models. At first, we establish each quarter's wind resource characteristics at typical monthly intervals of 10min, 30min, 60min, and 120min. The GRA's TF-AHP-CRITIC-EWM, enhanced with subjective and objective weights, is used to assess the available wind resources in each season and to compute the forecasted combination of wind speed for each season. As the final prediction results, the prediction values of each layer model are evaluated independently. For the intervals with considerable errors, we apply wavelet denoising and replacement combination. The simulation findings show that the proposed combined model surpasses earlier benchmark models in terms of goodness of fit, prediction accuracy, and generalizability.