Denoising of an Image Using Discrete Stationary Wavelet Transform and Various Thresholding Techniques

Image denoising has remained a fundamental problem in the field of image processing. With Wavelet transforms, various algorithms for denoising in wavelet domain were introduced. Wavelets gave a superior performance in image denoising due to its properties such as multi-resolution. The problem of estimating an image that is corrupted by Additive White Gaussian Noise has been of interest for practical and theoretical reasons. Non-linear methods especially those based on wavelets have become popular due to its advantages over linear methods. Here I applied non-linear thresholding techniques in wavelet domain such as hard and soft thresholding, wavelet shrinkages such as Visu-shrink (non-adaptive) and SURE, Bayes and Normal Shrink (adaptive), using Discrete Stationary Wavelet Transform (DSWT) for different wavelets, at different levels, to denoise an image and determine the best one out of them. Performance of denoising algorithm is measured using quantitative performance measures such as Signal-to-Noise Ratio (SNR) and Mean Square Error (MSE) for various thresholding techniques.

Coupling denoising algorithm based on discrete wavelet transform and modified median filter for medical image

In order to overcome the phenomenon of image blur and edge loss in the process of collecting and transmitting medical image,a denoising method of medical image based on discrete wavelet transform(DWT)and modified median filter for medical image coupling denoising is proposed.The method is composed of four modules:image acquisition,image storage,image processing and image reconstruction.Image acquisition gets the medical image that contains Gaussian noise and impulse noise.Image storage includes the preservation of data and parameters of the original image and processed image.In the third module,the medical image is decomposed as four sub bands(LL,HL,LH,HH)by wavelet decomposition,where LL is low frequency,LH,HL,HH are respective for horizontal,vertical and in the diagonal line high frequency component.Using improved wavelet threshold to process high frequency coefficients and retain low frequency coefficients,the modified median filtering is performed on three high frequency sub bands after wavelet threshold processing.The last module is image reconstruction,which means getting the image after denoising by wavelet reconstruction.The advantage of this method is combining the advantages of median filter and wavelet to make the denoising effect better,not a simple combination of the two previous methods.With DWT and improved median filter coefficients coupling denoising,it is highly practical for high-precision medical images containing complex noises.The experimental results of proposed algorithm are compared with the results of median filter,wavelet transform,contourlet and DT-CWT,etc.According to visual evaluation index PSNR and SNR and Canny edge detection,in low noise images,PSNR and SNR increase by 10%–15%;in high noise images,PSNR and SNR increase by 2%–6%.The experimental results of the proposed algorithm achieved better acceptable results compared with other methods,which provides an important method for the diagnosis of medical condition.

The Second-generation Wavelet Transform and its Application in Denoising of Seismic Data

This paper discusses the principle and procedures of the second-generation wavelet transform and its application to the denoising of seismic data. Based on lifting steps, it is a flexible wavelet construction method using linear and nonlinear spatial prediction and operators to implement the wavelet transform and to make it reversible. The lifting scheme transform -includes three steps： split, predict, and update. Deslauriers-Dubuc （4, 2） wavelet transforms are used to process both synthetic and real data in our second-generation wavelet transform. The processing results show that random noise is effectively suppressed and the signal to noise ratio improves remarkably. The lifting wavelet transform is an efficient algorithm.

Study on Denoising Based on the Wavelet Transform

The wavelet transform has remarkable advantages and wide applications in denoising because of its characteristic of good time-frequency. Based on the analysis of traditional wavelet denoising methods, which are based on Fourier transform, an improved method is proposed. It overcomes the shortcomings of the traditional Fourier denoising method. In this paper, the denoising procedures are introduced respectively based on the wavelet transform and the method of connecting the wavelet threshold with the wavelet basis is adopted. Through Matlab simulation and concrete data, it arrives at the conclusion that the method of signal denoising based on the wavelet transform is obviously more effective and better than the traditional method based on Fourier transform.

Image denoising algorithm of refuge chamber by combining wavelet transform and bilateral filtering

In order to preferably identify infrared image of refuge chamber, reduce image noises of refuge chamber and retain more image details, we propose the method of combining two-dimensional discrete wavelet transform and bilateral denoising. First, the wavelet transform is adopted to decompose the image of refuge chamber, of which low frequency component remains unchanged. Then, three high-frequency components are treated by bilateral filtering, and the image is reconstructed. The result shows that the combination of bilateral filtering and wavelet transform for image denoising can better retain the details which are included in the image, while providing better visual effect. This is superior to using either bilateral filtering or wavelet transform alone. It is useful for perfecting emergency refuge system of coal mines.

Multi-level denoising and enhancement method based on wavelet transform for mine monitoring

Based on low illumination and a large number of mixed noises contained in coal mine, denoising with one method usually cannot achieve good results, so a multi-level image denoising method based on wavelet correlation relevant inter-scale is presented. Firstly, we used directional median filter to effectively reduce impulse noise in the spatial domain, which is the main cause of noise in mine. Secondly, we used a Wiener filtration method to mainly reduce the Gaussian noise, and then finally used a multi-wavelet transform to minimize the remaining noise of low-light images in the transform domain. This multi-level image noise reduction method combines spatial and transform domain denoising to enhance benefits, and effectively reduce impulse noise and Gaussian noise in a coal mine, while retaining good detailed image characteristics of the underground for improving quality of images with mixing noise and effective low-light environment.

Implementation of Adaptive Wavelet Thresholding Denoising Algorithm Based on DSP

By utilizing the capability of high-speed computing,powerful real-time processing of TMS320F2812 DSP,wavelet thresholding denoising algorithm is realized based on Digital Signal Processors.Based on the multi-resolution analysis of wavelet transformation,this paper proposes a new thresholding function,to some extent,to overcome the shortcomings of discontinuity in hard-thresholding function and bias in soft-thresholding function.The threshold value can be abtained adaptively according to the characteristics of wavelet coefficients of each layer by adopting adaptive threshold algorithm and then the noise is removed.The simulation results show that the improved thresholding function and the adaptive threshold algorithm have a good effect on denoising and meet the criteria of smoothness and similarity between the original signal and denoising signal.

An Improved Image Denoising Method Based on Wavelet Thresholding

VisuShrink, ModineighShrink and NeighShrink are efficient image denoising algorithms based on the discrete wavelet transform (DWT). These methods have disadvantage of using a suboptimal universal threshold and identical neighbouring window size in all wavelet subbands. In this paper, an improved method is proposed, that determines a threshold as well as neighbouring window size for every subband using its lengths. Our experimental results illustrate that the proposed approach is better than the existing ones, i.e., NeighShrink, ModineighShrink and VisuShrink in terms of peak signal-to-noise ratio (PSNR) i.e. visual quality of the image.

A Dual Tree Complex Discrete Cosine Harmonic Wavelet Transform (ADCHWT) and Its Application to Signal/Image Denoising

A new simple and efficient dual tree analytic wavelet transform based on Discrete Cosine Harmonic Wavelet Transform DCHWT (ADCHWT) has been proposed and is applied for signal and image denoising. The analytic DCHWT has been realized by applying DCHWT to the original signal and its Hilbert transform. The shift invariance and the envelope extraction properties of the ADCHWT have been found to be very effective in denoising speech and image signals, compared to that of DCHWT.

Denoising of X-ray pulsar observed profile using biorthogonal lifting wavelet transform

In X-ray pulsar-based navigation, strong X-ray background noise leads to a low signal-to-noise ratio（SNR） of the observed profile, which consequently makes it very difficult to obtain an accurate pulse phase that directly determines the navigation precision. This signifies the necessity of denoising of the observed profile. Considering that the ultimate goal of denoising is to enhance the pulse phase estimation, a profile denoising algorithm is proposed by fusing the biorthogonal lifting wavelet transform of the linear phase characteristic with the thresholding technique. The statistical properties of X-ray background noise after epoch folding are studied. Then a wavelet-scale dependent threshold is introduced to overcome correlations between wavelet coefficients. Moreover, a modified hyperbola shrinking function is presented to remove the impulsive oscillations of the observed profile. The results of numerical simulations and real data experiments indicate that the proposed method can effectively improve SNR of the observed profile and pulse phase estimation accuracy, especially in short observation durations. And it also outperforms the Donoho thresholding strategy normally used in combination with the orthogonal discrete wavelet transform.

Vegetation field spectrum denoising via lifting wavelet transform

Field spectrum pretreatment experiments were carried out, and denoising numerical experiment via lifting wavelet transform （LWT） was designed, and several famous test signals including blocks, bumps, heavy sine and doppler were processed via Lw＇r in these experiment. And the field spectrum was processed via Lw＇r. Experiments proved that SNRG-tO-SNRN curves have similar feature and they all have a peak. And SNRG of almost all employed wavelets have higher value with SNRN between 0 and 20 dB. When signal is at high SNR, the SNRG is very little, and the MSED of denoised signal became little by little. LWT is more suite to denoise the low SNR or heavy noise contaminated signals. Bior4.4 have wider SNRN interval for denoising comparing with other five wavelets, includ- ing haar, db6, sym6, bior2.2 and bior3.3. Original field spectrum is processed by 3 stage liftings based on bior4.4 to denoise the trivial noise-contaminated regions. On processing the water band signal, logarithm transform is firstly taken. And then the spectrum is denoised via LWT based on bior4.4. The results show that an excellent denoised spectrum can be get, especially between 350 nm and 1 800 nm, and between 1 960 nm to 2 500 nm. While there is still a bump around 1 900 nm, this maybe due to the spectrum machine＇s limited precision.

Comparison of Wavelet Types and Thresholding Methods on Wavelet Based Denoising of Heart Sounds

This paper focuses on the denoising of phonocardiogram (PCG) signals by means of discrete wavelet transform (DWT) using different wavelets and noise level estimation methods. The signal obtained by denoising from PCG signal contaminated white noise and the original PCG signal is compared to determine the appropriate parameters for denoising. The comparison is evaluated in terms of signal to noise ratio (SNR) before and after denoising. The results showed that the decomposition level is the most important parameter determining the denoising quality.

A New Image Denoising Scheme Using Soft-Thresholding

The VisuShrink is one of the important image denoising methods. It however does not provide good quality of image due to removing too many coefficients especially using soft-thresholding technique. This paper proposes a new image denoising scheme using wavelet transformation. In this paper, we modify the coefficients using soft-thresholding method to enhance the visual quality of noisy image. The experimental results show that our proposed scheme has better performance than the VisuShrink in terms of peak signal-to-noise ratio (PSNR) i.e., visual quality of the image.

AMicroseismic Signal Denoising Algorithm Combining VMD and Wavelet Threshold Denoising Optimized by BWOA

The denoising of microseismic signals is a prerequisite for subsequent analysis and research.In this research,a new microseismic signal denoising algorithm called the Black Widow Optimization Algorithm(BWOA)optimized VariationalMode Decomposition(VMD)jointWavelet Threshold Denoising(WTD)algorithm(BVW)is proposed.The BVW algorithm integrates VMD and WTD,both of which are optimized by BWOA.Specifically,this algorithm utilizes VMD to decompose the microseismic signal to be denoised into several Band-Limited IntrinsicMode Functions(BLIMFs).Subsequently,these BLIMFs whose correlation coefficients with the microseismic signal to be denoised are higher than a threshold are selected as the effective mode functions,and the effective mode functions are denoised using WTD to filter out the residual low-and intermediate-frequency noise.Finally,the denoised microseismic signal is obtained through reconstruction.The ideal values of VMD parameters and WTD parameters are acquired by searching with BWOA to achieve the best VMD decomposition performance and solve the problem of relying on experience and requiring a large workload in the application of the WTD algorithm.The outcomes of simulated experiments indicate that this algorithm is capable of achieving good denoising performance under noise of different intensities,and the denoising performance is significantly better than the commonly used VMD and Empirical Mode Decomposition(EMD)algorithms.The BVW algorithm is more efficient in filtering noise,the waveform after denoising is smoother,the amplitude of the waveform is the closest to the original signal,and the signal-to-noise ratio(SNR)and the root mean square error after denoising are more satisfying.The case based on Fankou Lead-Zinc Mine shows that for microseismic signals with different intensities of noise monitored on-site,compared with VMD and EMD,the BVW algorithm ismore efficient in filtering noise,and the SNR after denoising is higher.

A Robust Denoising Algorithm for Sounds of Musical Instruments Using Wavelet Packet Transform

In this paper, a robust DWPT based adaptive bock algorithm with modified threshold for denoising the sounds of musical instruments shehnai, dafli and flute is proposed. The signal is first segmented into multiple blocks depending upon the minimum mean square criteria in each block, and then thresholding methods are used for each block. All the blocks obtained after denoising the individual block are concatenated to get the final denoised signal. The discrete wavelet packet transform provides more coefficients than the conventional discrete wavelet transform (DWT), representing additional subtle detail of the signal but decision of optimal decomposition level is very important. When the sound signal corrupted with additive white Gaussian noise is passed through this algorithm, the obtained peak signal to noise ratio (PSNR) depends upon the level of decomposition along with shape of the wavelet. Hence, the optimal wavelet and level of decomposition may be different for each signal. The obtained denoised signal with this algorithm is close to the original signal.

Application of fast wavelet transformation in signal processing of MEMS gyroscope

Decomposition and reconstruction of Mallat fast wavelet transformation （WT） is described. A fast algorithm, which can greatly decrease the processing burden and can be very easy for hardware implementation in real-time, is analyzed. The algorithm will no longer have the processing of decimation and interpolation of usual WT. The formulae of the decomposition and the reconstruction are given. Simulation results of the MEMS （micro-electro mechanical systems） gyroscope drift signal show that the algorithm spends much less processing time to finish the de-noising process than the usual WT. And the de-noising effect is the same. The fast algorithm has been implemented in a TMS320C6713 digital signal processor. The standard variance of the gyroscope static drift signal decreases from 78. 435 5 （°）/h to 36. 763 5 （°）/h. It takes 0. 014 ms to process all input data and can meet the real-time analysis of signal.

IMAGE WAVELET DENOISING USING THE ROBUST LOCAL THRESHOLD

This paper suggests a scheme of image denoising based on two-dimensional discrete wavelet transform. The denoising algorithm is described with some operators. By thresholding the wavelet transform coefficients of noisy images, the original image can be reconstructed correctly. Different threshold selections and thresholding methods are discussed. A new robust local threshold scheme is proposed. Quantifying the performance of image denoising schemes by using the mean square error, the performance of the robust local threshold scheme is demonstrated and is compared with the universal threshold scheme. The experiment shows that image denoising using the robust local threshold performs better than that using the universal threshold.

Denoising of hyperspectral imagery by cubic smoothing spline in the wavelet domain

The acquired hyperspectral images （HSIs） are inherently attected by noise wlm Dano-varylng level, which cannot be removed easily by current approaches. In this study, a new denoising method is proposed for removing such kind of noise by smoothing spectral signals in the transformed multi- scale domain. Specifically, the proposed method includes three procedures： 1 ） applying a discrete wavelet transform （DWT） to each band; 2） performing cubic spline smoothing on each noisy coeffi- cient vector along the spectral axis; 3 ） reconstructing each band by an inverse DWT. In order to adapt to the band-varying noise statistics of HSIs, the noise covariance is estimated to control the smoothing degree at different spectra｜ positions. Generalized cross validation （GCV） is employed to choose the smoothing parameter during the optimization. The experimental results on simulated and real HSIs demonstrate that the proposed method can be well adapted to band-varying noise statistics of noisy HSIs and also can well preserve the spectral and spatial features.

NEW METHOD OF EXTRACTING WEAK FAILURE INFORMATION IN GEARBOX BY COMPLEX WAVELET DENOISING

Because the extract of the weak failure information is always the difficulty and focus of fault detection. Aiming for specific statistical properties of complex wavelet coefficients of gearbox vibration signals, a new signal-denoising method which uses local adaptive algorithm based on dual-tree complex wavelet transform （DT-CWT） is introduced to extract weak failure information in gear, especially to extract impulse components. By taking into account the non-Gaussian probability distribution and the statistical dependencies among wavelet coefficients of some signals, and by taking the advantage of near shift-invariance of DT-CWT, the higher signal-to-noise ratio （SNR） than common wavelet denoising methods can be obtained. Experiments of extracting periodic impulses in gearbox vibration signals indicate that the method can extract incipient fault feature and hidden information from heavy noise, and it has an excellent effect on identifying weak feature signals in gearbox vibration signals.

Image denoising using statistical model based on quaternion wavelet domain

Image denoising is the basic problem of image processing. Quaternion wavelet transform is a new kind of multiresolution analysis tools. Image via quaternion wavelet transform, wavelet coefficients both in intrascale and in interscale have certain correla- tions. First, according to the correlation of quaternion wavelet coefficients in interscale, non-Ganssian distribution model is used to model its correlations, and the coefficients are divided into important and unimportance coefficients. Then we use the non-Gaussian distribution model to model the important coefficients and its adjacent coefficients, and utilize the MAP method estimate original image wavelet coefficients from noisy coefficients, so as to achieve the purpose of denoising. Experimental results show that our al- gorithm outperforms the other classical algorithms in peak signal-to-noise ratio and visual quality.