First-order optimality condition of basis pursuit denoise problem

A new first-order optimality condition for the basis pursuit denoise(BPDN)problem is derived. This condition provides a new approach to choose the penalty parameters adaptively for a fixed point iteration algorithm. Meanwhile, the result is extended to matrix completion which is a new field on the heel of the compressed sensing. The numerical experiments of sparse vector recovery and low-rank matrix completion show validity of the theoretic results.

基于EEMD、相关系数、排列熵和小波阈值去噪的新型水下声学信号去噪方法

The complexities of the marine environment and the unique characteristics of underwater channels pose challenges in obtaining reliable signals underwater,necessitating the filtration of underwater acoustic noise.Herein,an underwater acoustic signal denoising method based on ensemble empirical mode decomposition(EEMD),correlation coefficient(CC),permutation entropy(PE),and wavelet threshold denoising(WTD)is proposed.Furthermore,simulation experiments are conducted using simulated and real underwater acoustic data.The experimental results reveal that the proposed denoising method outperforms other previous methods in terms of signal-to-noise ratio,root mean square error,and CC.The proposed method eliminates noise and retains valuable information in the signal.

Attention-Based Residual Dense Shrinkage Network for ECG Denoising

Electrocardiogram(ECG)signal is one of the noninvasive physiological measurement techniques commonly usedin cardiac diagnosis.However,in real scenarios,the ECGsignal is susceptible to various noise erosion,which affectsthe subsequent pathological analysis.Therefore,the effective removal of the noise from ECG signals has becomea top priority in cardiac diagnostic research.Aiming at the problem of incomplete signal shape retention andlow signal-to-noise ratio(SNR)after denoising,a novel ECG denoising network,named attention-based residualdense shrinkage network(ARDSN),is proposed in this paper.Firstly,the shallow ECG characteristics are extractedby a shallow feature extraction network(SFEN).Then,the residual dense shrinkage attention block(RDSAB)isused for adaptive noise suppression.Finally,feature fusion representation(FFR)is performed on the hierarchicalfeatures extracted by a series of RDSABs to reconstruct the de-noised ECG signal.Experiments on the MIT-BIHarrhythmia database and MIT-BIH noise stress test database indicate that the proposed scheme can effectively resistthe interference of different sources of noise on the ECG signal.

Prediction of high-embankment settlement combining joint denoising technique and enhanced GWO-v-SVR method

Reliable long-term settlement prediction of a high embankment relates to mountain infrastructure safety.This study developed a novel hybrid model(NHM)that combines a joint denoising technique with an enhanced gray wolf optimizer(EGWO)-n-support vector regression(n-SVR)method.High-embankment field measurements were preprocessed using the joint denoising technique,which in-cludes complete ensemble empirical mode decomposition,singular value decomposition,and wavelet packet transform.Furthermore,high-embankment settlements were predicted using the EGWO-n-SVR method.In this method,the standard gray wolf optimizer(GWO)was improved to obtain the EGWO to better tune the n-SVR model hyperparameters.The proposed NHM was then tested in two case studies.Finally,the influences of the data division ratio and kernel function on the EGWO-n-SVR forecasting performance and prediction efficiency were investigated.The results indicate that the NHM suppresses noise and restores details in high-embankment field measurements.Simultaneously,the NHM out-performs other alternative prediction methods in prediction accuracy and robustness.This demonstrates that the proposed NHM is effective in predicting high-embankment settlements with noisy field mea-surements.Moreover,the appropriate data division ratio and kernel function for EGWO-n-SVR are 7:3 and radial basis function,respectively.

Vein visualization enhancement by dual-wavelength phase-locked denoising technology

Visual near-infrared imaging equipment has broad applications in various fields such as venipuncture,facial injections,and safety verification due to its noncontact,compact,and portable design.Currently,most studies utilize near-infrared single-wavelength for image acquisition of veins.However,many substances in the skin,including water,protein,and melanin can create significant background noise,which hinders accurate detection.In this paper,we developed a dual-wavelength imaging system with phase-locked denoising technology to acquire vein image.The signals in the effective region are compared by using the absorption valley and peak of hemoglobin at 700nm and 940nm,respectively.The phase-locked denoising algorithm is applied to decrease the noise and interference of complex surroundings from the images.The imaging results of the vein are successfully extracted in complex noise environment.It is demonstrated that the denoising effect on hand veins imaging can be improved with 57.3%by using our dual-wavelength phase-locked denoising technology.Consequently,this work proposes a novel approach for venous imaging with dual-wavelengths and phase-locked denoising algorithm to extract venous imaging results in complex noisy environment better.

Research and application of composite stochastic resonance in enhancement detection

Aiming at the problem that the intermediate potential part of the traditional bistable stochastic resonance model cannot be adjusted independently, a new composite stochastic resonance(NCSR) model is proposed by combining the Woods–Saxon(WS) model and the improved piecewise bistable model. The model retains the characteristics of the independent parameters of WS model and the improved piecewise model has no output saturation, all the parameters in the new model have no coupling characteristics. Under α stable noise environment, the new model is used to detect periodic signal and aperiodic signal, the detection results indicate that the new model has higher noise utilization and better detection effect.Finally, the new model is applied to image denoising, the results showed that under the same conditions, the output peak signal-to-noise ratio(PSNR) and the correlation number of NCSR method is higher than that of other commonly used linear denoising methods and improved piecewise SR methods, the effectiveness of the new model is verified.

Automatic modulation recognition of radio fuzes using a DR2D-based adaptive denoising method and textural feature extraction

The identification of intercepted radio fuze modulation types is a prerequisite for decision-making in interference systems.However,the electromagnetic environment of modern battlefields is complex,and the signal-to-noise ratio(SNR)of such environments is usually low,which makes it difficult to implement accurate recognition of radio fuzes.To solve the above problem,a radio fuze automatic modulation recognition(AMR)method for low-SNR environments is proposed.First,an adaptive denoising algorithm based on data rearrangement and the two-dimensional(2D)fast Fourier transform(FFT)(DR2D)is used to reduce the noise of the intercepted radio fuze intermediate frequency(IF)signal.Then,the textural features of the denoised IF signal rearranged data matrix are extracted from the statistical indicator vectors of gray-level cooccurrence matrices(GLCMs),and support vector machines(SVMs)are used for classification.The DR2D-based adaptive denoising algorithm achieves an average correlation coefficient of more than 0.76 for ten fuze types under SNRs of-10 d B and above,which is higher than that of other typical algorithms.The trained SVM classification model achieves an average recognition accuracy of more than 96%on seven modulation types and recognition accuracies of more than 94%on each modulation type under SNRs of-12 d B and above,which represents a good AMR performance of radio fuzes under low SNRs.

Image Processing for Denoising Using Composite Adaptive Filtering Methods Based on RMSE

As one of the carriers for human communication and interaction, images are prone to contamination by noise during transmission and reception, which is often uncontrollable and unknown. Therefore, how to denoise images contaminated by unknown noise has gradually become one of the research focuses. In order to achieve blind denoising and separation to restore images, this paper proposes a method for image processing based on Root Mean Square Error (RMSE) by integrating multiple filtering methods for denoising. This method includes Wavelet Filtering, Gaussian Filtering, Median Filtering, Mean Filtering, Bilateral Filtering, Adaptive Bandpass Filtering, Non-local Means Filtering and Regularization Denoising suitable for different types of noise. We can apply this method to denoise images contaminated by blind noise sources and evaluate the denoising effects using RMSE. The smaller the RMSE, the better the denoising effect. The optimal denoising result is selected through comprehensively comparing the RMSE values of all methods. Experimental results demonstrate that the proposed method effectively denoises and restores images contaminated by blind noise sources.

BeFOI: A Novel Method Based on Conditional Diffusion Model for Medical Image Denoising

The progress in medical imaging technology highlights the importance of image quality for effective diagnosis and treatment.Yet,noise during capture and transmission can compromise image accuracy and reliability,complicating clinical decisions.The rising interest in diffusion models has led to their exploration of denoising images.We present Be-FOI(Better Fluoro Images),a weakly supervised model that uses cine images to denoise fluoroscopic images,both DR types.Trained through precise noise estimation and simulation,BeFOI employs Markov chains to denoise using only the fluoroscopic image as guidance.Our tests show that BeFOI outperforms other methods,reducing noise and enhancing clar-ity and diagnostic utility,making it an effective post-processing tool for medical images.

DFD-Net:lung cancer detection from denoised CT scan image using deep learning

The availability of pulmonary nodules in CT scan image of lung does not completely specify cancer.The noise in an image and morphology of nodules,like shape and size has an implicit and complex association with cancer,and thus,a careful analysis should be mandatory on every suspected nodules and the combination of information of every nodule.In this paper,we introduce a“denoising first”two-path convolutional neural network(DFD-Net)to address this complexity.The introduced model is composed of denoising and detection part in an end to end manner.First,a residual learning denoising model(DR-Net)is employed to remove noise during the preprocessing stage.Then,a two-path convolutional neural network which takes the denoised image by DR-Net as an input to detect lung cancer is employed.The two paths focus on the joint integration of local and global features.To this end,each path employs different receptive field size which aids to model local and global dependencies.To further polish our model performance,in different way from the conventional feature concatenation approaches which directly concatenate two sets of features from different CNN layers,we introduce discriminant correlation analysis to concatenate more representative features.Finally,we also propose a retraining technique that allows us to overcome difficulties associated to the image labels imbalance.We found that this type of model easily first reduce noise in an image,balances the receptive field size effect,affords more representative features,and easily adaptable to the inconsistency among nodule shape and size.Our intensive experimental results achieved competitive results.

Regularization by Multiple Dual Frames for Compressed Sensing Magnetic Resonance Imaging With Convergence Analysis

Plug-and-play priors are popular for solving illposed imaging inverse problems. Recent efforts indicate that the convergence guarantee of the imaging algorithms using plug-andplay priors relies on the assumption of bounded denoisers. However, the bounded properties of existing plugged Gaussian denoisers have not been proven explicitly. To bridge this gap, we detail a novel provable bounded denoiser termed as BMDual,which combines a trainable denoiser using dual tight frames and the well-known block-matching and 3D filtering(BM3D)denoiser. We incorporate multiple dual frames utilized by BMDual into a novel regularization model induced by a solver. The proposed regularization model is utilized for compressed sensing magnetic resonance imaging(CSMRI). We theoretically show the bound of the BMDual denoiser, the bounded gradient of the CSMRI data-fidelity function, and further demonstrate that the proposed CSMRI algorithm converges. Experimental results also demonstrate that the proposed algorithm has a good convergence behavior, and show the effectiveness of the proposed algorithm.

A robust deformed convolutional neural network(CNN)for image denoising

Due to strong learning ability,convolutional neural networks(CNNs)have been developed in image denoising.However,convolutional operations may change original distributions of noise in corrupted images,which may increase training difficulty in image denoising.Using relations of surrounding pixels can effectively resolve this problem.Inspired by that,we propose a robust deformed denoising CNN(RDDCNN)in this paper.The proposed RDDCNN contains three blocks:a deformable block(DB),an enhanced block(EB)and a residual block(RB).The DB can extract more representative noise features via a deformable learnable kernel and stacked convolutional architecture,according to relations of surrounding pixels.The EB can facilitate contextual interaction through a dilated convolution and a novel combination of convolutional layers,batch normalisation(BN)and ReLU,which can enhance the learning ability of the proposed RDDCNN.To address long-term dependency problem,the RB is used to enhance the memory ability of shallow layer on deep layers and construct a clean image.Besides,we implement a blind denoising model.Experimental results demonstrate that our denoising model outperforms popular denoising methods in terms of qualitative and quantitative analysis.Codes can be obtained at https://github.com/hellloxiaotian/RDDCNN.

Denoising Fault-Aware Wavelet Network:A Signal Processing Informed Neural Network for Fault Diagnosis

Deep learning(DL) is progressively popular as a viable alternative to traditional signal processing(SP) based methods for fault diagnosis. However, the lack of explainability makes DL-based fault diagnosis methods difficult to be trusted and understood by industrial users. In addition, the extraction of weak fault features from signals with heavy noise is imperative in industrial applications. To address these limitations, inspired by the Filterbank-Feature-Decision methodology, we propose a new Signal Processing Informed Neural Network(SPINN) framework by embedding SP knowledge into the DL model. As one of the practical implementations for SPINN, a denoising fault-aware wavelet network(DFAWNet) is developed, which consists of fused wavelet convolution(FWConv), dynamic hard thresholding(DHT),index-based soft filtering(ISF), and a classifier. Taking advantage of wavelet transform, FWConv extracts multiscale features while learning wavelet scales and selecting important wavelet bases automatically;DHT dynamically eliminates noise-related components via point-wise hard thresholding;inspired by index-based filtering, ISF optimizes and selects optimal filters for diagnostic feature extraction. It’s worth noting that SPINN may be readily applied to different deep learning networks by simply adding filterbank and feature modules in front. Experiments results demonstrate a significant diagnostic performance improvement over other explainable or denoising deep learning networks. The corresponding code is available at https://github. com/alber tszg/DFAWn et.

Hformer:highly efficient vision transformer for low-dose CT denoising

In this paper,we propose Hformer,a novel supervised learning model for low-dose computer tomography(LDCT)denoising.Hformer combines the strengths of convolutional neural networks for local feature extraction and transformer models for global feature capture.The performance of Hformer was verified and evaluated based on the AAPM-Mayo Clinic LDCT Grand Challenge Dataset.Compared with the former representative state-of-the-art(SOTA)model designs under different architectures,Hformer achieved optimal metrics without requiring a large number of learning parameters,with metrics of33.4405 PSNR,8.6956 RMSE,and 0.9163 SSIM.The experiments demonstrated designed Hformer is a SOTA model for noise suppression,structure preservation,and lesion detection.

Underwater acoustic signal denoising model based on secondary variational mode decomposition

Due to the complexity of marine environment,underwater acoustic signal will be affected by complex background noise during transmission.Underwater acoustic signal denoising is always a difficult problem in underwater acoustic signal processing.To obtain a better denoising effect,a new denoising method of underwater acoustic signal based on optimized variational mode decomposition by black widow optimization algorithm(BVMD),fluctuation-based dispersion entropy threshold improved by Otsu method(OFDE),cosine similarity stationary threshold(CSST),BVMD,fluctuation-based dispersion entropy(FDE),named BVMD-OFDE-CSST-BVMD-FDE,is proposed.In the first place,decompose the original signal into a series of intrinsic mode functions(IMFs)by BVMD.Afterwards,distinguish pure IMFs,mixed IMFs and noise IMFs by OFDE and CSST,and reconstruct pure IMFs and mixed IMFs to obtain primary denoised signal.In the end,decompose primary denoising signal into IMFs by BVMD again,use the FDE value to distinguish noise IMFs and pure IMFs,and reconstruct pure IMFs to obtain the final denoised signal.The proposed mothod has three advantages:(i)BVMD can adaptively select the decomposition layer and penalty factor of VMD.(ii)FDE and CS are used as double criteria to distinguish noise IMFs from useful IMFs,and Otsu algorithm and CSST algorithm can effectively avoid the error caused by manually selecting thresholds.(iii)Secondary decomposition can make up for the deficiency of primary decomposition and further remove a small amount of noise.The chaotic signal and real ship signal are denoised.The experiment result shows that the proposed method can effectively denoise.It improves the denoising effect after primary decomposition,and has good practical value.

Noise reduction and periodic signal extraction for GNSS height data in the study of vertical deformation

Global navigation satellite system(GNSS)technique has irreplaceable advantages in the continuous monitoring of surface deformation.Reducing noise to improve the signal-to-noise ratio(SNR)and extract the concerned signals is of great significance.As an improved algorithm of empirical mode decomposition(EMD),complete ensemble empirical mode decomposition with adaptive noise(CEEMDAN)algorithm has better signal processing ability.Using the CEEMDAN algorithm,the height time series of 29GNSS stations in Chinese mainland were analyzed,and good denoising effects and extraction from periodic signals were achieved.The numerical results showed that the annual signal obtained with the CEEMDAN algorithm was significantly based on Lomb_Scargle spectrum analysis,and large differences in the long-term signals were found between the stations at different locations in Chinese mainland.With respect to data denoising,compared with the EMD and wavelet denoising algorithms,the CEEMDAN algorithm respectively improved the SNR by 29.35% and 36.54%,increased the correlation coefficient by 8.67% and 11.96%,and reduced root mean square error(RMSE)by 44.68% and 43.48%,indicating that the CEEMDAN algorithm had better denoising behavior than the other two algorithms.In addition,the results demonstrated that different denoising methods had little influence on estimating the annual vertical deformation velocity.The extraction of periodic signals showed that more components were retained by using the CEEMDAN algorithm than the EMD algorithm,which indicated that the CEEMDAN algorithm had advantages over frequency aliasing.In conclusion,the CEEMDAN algorithm was recommended for processing the GNSS height time series to analyze the vertical deformation due to its excellent features of denoising and the extraction of periodic signals.

Adaptive Noise Detector and Partition Filter for Image Restoration

The random-value impulse noise(RVIN)detection approach in image denoising,which is dependent on manually defined detection thresholds or local window information,does not have strong generalization performance and cannot successfully cope with damaged pictures with high noise levels.The fusion of the K-means clustering approach in the noise detection stage is reviewed in this research,and the internal relationship between the flat region and the detail area of the damaged picture is thoroughly explored to suggest an unique two-stage method for gray image denoising.Based on the concept of pixel clustering and grouping,all pixels in the damaged picture are separated into various groups based on gray distance similarity features,and the best detection threshold of each group is solved to identify the noise.In the noise reduction step,a partition decision filter based on the gray value characteristics of pixels in the flat and detail areas is given.For the noise pixels in flat and detail areas,local consensus index(LCI)weighted filter and edge direction filter are designed respectively to recover the pixels damaged by the RVIN.The experimental results show that the accuracy of the proposed noise detection method is more than 90%,and is superior to most mainstream methods.At the same time,the proposed filtering method not only has good noise reduction and generalization performance for natural images and medical images with medium and high noise but also is superior to other advanced filtering technologies in visual effect and objective quality evaluation.

Asymmetric Loss Based on Image Properties for Deep Learning-Based Image Restoration

Deep learning techniques have significantly improved image restoration tasks in recent years.As a crucial compo-nent of deep learning,the loss function plays a key role in network optimization and performance enhancement.However,the currently prevalent loss functions assign equal weight to each pixel point during loss calculation,which hampers the ability to reflect the roles of different pixel points and fails to exploit the image’s characteristics fully.To address this issue,this study proposes an asymmetric loss function based on the image and data characteristics of the image recovery task.This novel loss function can adjust the weight of the reconstruction loss based on the grey value of different pixel points,thereby effectively optimizing the network training by differentially utilizing the grey information from the original image.Specifically,we calculate a weight factor for each pixel point based on its grey value and combine it with the reconstruction loss to create a new loss function.This ensures that pixel points with smaller grey values receive greater attention,improving network recovery.In order to verify the effectiveness of the proposed asymmetric loss function,we conducted experimental tests in the image super-resolution task.The experimental results show that the model with the introduction of asymmetric loss weights improves all the indexes of the processing results without increasing the training time.In the typical super-resolution network SRCNN,by introducing asymmetric weights,it is possible to improve the peak signal-to-noise ratio(PSNR)by up to about 0.5%,the structural similarity index(SSIM)by up to about 0.3%,and reduce the root-mean-square error(RMSE)by up to about 1.7%with essentially no increase in training time.In addition,we also further tested the performance of the proposed method in the denoising task to verify the potential applicability of the method in the image restoration task.

Simultaneous denoising and resolution enhancement of seismic data based on elastic convolution dictionary learning

Enhancing seismic resolution is a key component in seismic data processing, which plays a valuable role in raising the prospecting accuracy of oil reservoirs. However, in noisy situations, existing resolution enhancement methods are difficult to yield satisfactory processing outcomes for reservoir characterization. To solve this problem, we develop a new approach for simultaneous denoising and resolution enhancement of seismic data based on convolution dictionary learning. First, an elastic convolution dictionary learning algorithm is presented to efficiently learn a convolution dictionary with stronger representation capability from the noisy data to be processed. Specifically, the algorithm introduces the elastic L1/2 norm as a sparsity constraint and employs a steepest gradient descent strategy to efficiently solve the frequency-domain linear system with substantial computational cost in a half-quadratic splitting framework. Then, based on the learned convolution dictionary, a weighted convolutional sparse representation paradigm is designed to encode the noisy data to acquire an optimal sparse approximation of the effective signal. Subsequently, a high-resolution dictionary with a broadband spectrum is constructed by the proposed parameter scaling strategy and matched filtering technique on the basis of atomic spectrum modeling. Finally, the optimal sparse approximation of the effective signal and the constructed high-resolution dictionary are used for data reconstruction to obtain the seismic signal with high resolution and high signal-to-noise ratio. Synthetic and field dataset examples are executed to check the effectiveness and reliability of the developed method. The results indicate that this method has a more competitive performance in seismic applications compared with the conventional deconvolution and spectral whitening methods.

An Intelligent Secure Adversarial Examples Detection Scheme in Heterogeneous Complex Environments

Image-denoising techniques are widely used to defend against Adversarial Examples(AEs).However,denoising alone cannot completely eliminate adversarial perturbations.The remaining perturbations tend to amplify as they propagate through deeper layers of the network,leading to misclassifications.Moreover,image denoising compromises the classification accuracy of original examples.To address these challenges in AE defense through image denoising,this paper proposes a novel AE detection technique.The proposed technique combines multiple traditional image-denoising algorithms and Convolutional Neural Network(CNN)network structures.The used detector model integrates the classification results of different models as the input to the detector and calculates the final output of the detector based on a machine-learning voting algorithm.By analyzing the discrepancy between predictions made by the model on original examples and denoised examples,AEs are detected effectively.This technique reduces computational overhead without modifying the model structure or parameters,effectively avoiding the error amplification caused by denoising.The proposed approach demonstrates excellent detection performance against mainstream AE attacks.Experimental results show outstanding detection performance in well-known AE attacks,including Fast Gradient Sign Method(FGSM),Basic Iteration Method(BIM),DeepFool,and Carlini&Wagner(C&W),achieving a 94%success rate in FGSM detection,while only reducing the accuracy of clean examples by 4%.