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.

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.

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.

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.

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.

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.

Vegetation field spectrum denoising via lifting wavelet transform

Field spectrum pretreatment experiments were carried out,and denoising nu- merical experiment via lifting wavelet transform (LWT) was designed,and several famous test signals including blocks,bumps,heavy sine and doppler were processed via LWT in these experiment.And the field spectrum was processed via LWT.Experiments proved that SNRG'tO-SNRN curves have similar feature and they all have a peak.And SNRG of al- most all employed wavelets have higher value with SNRN between 0 and 20 dB.When sig- nal 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 de- noised 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.

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.

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.

An Efficient Framework for Indian Sign Language Recognition Using Wavelet Transform

Hand gesture recognition system is considered as a way for more intuitive and proficient human computer interaction tool. The range of applications includes virtual prototyping, sign language analysis and medical training. In this paper, an efficient Indian Sign Language Recognition System (ISLR) is proposed for deaf and dump people using hand gesture images. The proposed ISLR system is considered as a pattern recognition technique that has two important modules: feature extraction and classification. The joint use of Discrete Wavelet Transform (DWT) based feature extraction and nearest neighbour classifier is used to recognize the sign language. The experimental results show that the proposed hand gesture recognition system achieves maximum 99.23% classification accuracy while using cosine distance classifier.

Wavelet-Based Hybrid Thresholding Method for Ultrasonic Liver Image Denoising

This paper presents a wavelet-based hybrid threshold method according to the soft- and hard-threshold functions proposed by Donoho. The wavelet-based hybrid threshold method may help doctors to know more details on the liver disease through denoising the ultrasound image of the liver. First of all, an analytical expression for the hybrid threshold function is discussed. The wavelet-based hybrid threshold method is then investigated for ultrasound image of the liver. Finally, we test the influence of this parameter on the proposed method with the real ultrasound image corrupted by speckle noise with different variances. Moreover, we compare the proposed method under the varying parameters with the soft-threshold function and the hard-threshold function. Three metrics, which are correlation coefficient, edge preservation index and structural similarity index, are measured to quantify the denoised results of ultrasound liver image. Experimental results demonstrate the potential of the proposed method for ultrasound liver image denosing.

Adaptive Dual-Threshold Edge Detection Based on Wavelet Transform

In order to solve the problems of local maximum modulus extraction and threshold selection in the edge detection of finite resolution digital images, a new wavelet transform based adaptive dual threshold edge detection algorithm is proposed. The local maximum modulus is extracted by linear interpolation in wavelet domain. With the analysis on histogram, the image is filtered with an adaptive dual threshold method, which effectively detects the contours of small structures as well as the boundaries of large objects. A wavelet domain's propagation function is used to further select weak edges. Experimental results have shown the self adaptivity of the threshold to images having the same kind of histogram, and the efficiency even in noise tampered images.

WAVELET TRANSFORM THRESHOLD NOISE REDUCTION METHODS IN THE OIL PIPELINE LEAKAGE MONITORING AND POSITIONING SYSTEM

This letter investigates the wavelet transform, as well as the principle and the method of the noise reduction based on wavelet transform, it chooses the threshold noise reduction, and discusses in detail the principles, features and design steps of the threshold method. Rigrsure, heursure, sqtwolog and minimization four kinds of threshold selection method are compared qualitatively, and quantitatively. The wavelet analysis toolbox of MATLAB helps to realize the computer simulation of the signal noise reduction. The graphics and calculated standard deviation of the various threshold noise reductions show that, when dealing with the actual pressure signal of the oil pipeline leakage, sqtwolog threshold selection method can effectively remove the noise. Aiming to the pressure signal of the oil pipeline leakage, the best choice is the wavelet threshold noise reduction with sqtwolog threshold. The leakage point is close to the actual position, with the relative error of less than 1%.

Optical and SAR image registration based on improved nonsubsampled wavelet transform for sea islands

Homologous feature point extraction is a key problem in the optical and synthetic aperture radar （SAR） image registration for islands. A new feature point extraction method using a threshold shrink operator and non-subsampled wavelet transform （TSO-NSWT） for optical and SAR image registration was proposed. Moreover, the matching for this proposed feature was different from the traditional feature matching strategies and was performed using a similarity measure computed from neighborhood circles in low-frequency bands. Then, a number of reliably matched couples with even distributions were obtained, which assured the accuracy of the registration. Application of the proposed algorithm to SPOT-5 （multi-spectral） and YG-1 （SAR） images showed that a large number of accurately matched couples could be identified. Additionally, both of the root mean square error （RMSE） patterns of the registration parameters computed based on the TSO-NSWT algorithm and traditional NSWT algorithm were analyzed and compared, which further demonstrated the effectiveness of the proposed algorithm. The algorithm can supply the crucial step for island image registration and island recognition.

New Wavelet Threshold Denoising Method in Noisy Blind Source Separation

In general conditions, most blind source separation algorithms are established on noisy-free model and ignore the noise that affects the quality of separated sources. Firstly, this paper introduces an improved natural gradient algorithm based on bias removal technology to estimate the demixing matrix under noisy environment. Then the discrete wavelet transform technology is applied to the separated signals to further remove noise. In order to improve the separation effect, this paper analyzes the deficiency of hard threshold and soft threshold, and proposes a new wavelet threshold function based on the wavelet decomposition and reconfiguration. The simulations have verified that this method improves the signal noise ratio （SNR） of the separation results and the separation precision.