Wavelet Shrinkage Method Research Articles

Efficient resolution and basis functions selection in wavelet regression

In this paper we propose an efficient method to determine a primary resolution and wavelet basis functions in wavelet regression. Most wavelet shrinkage methods focus on thresholding the wavelet coefficients, given a primary resolution which is usually determined by the sample size. However, both a primary resolution and the basis functions are affected by the shape of an unknown function rather than the sample size. Unlike existing methods, our method takes the shape of the unknown function into account because a proper resolution can be much affected by the shape of it rather than the sample size. Our approach to determine a primary resolution and wavelet basis functions is developed under Bayesian framework using the posterior model probability. We demonstrate the advantage of our approach using a simulation study and a real data application.

NEW SELECTION APPROACH FOR RESOLUTION AND BASIS FUNCTIONS IN WAVELET REGRESSION

In this paper we propose a new approach to the variable selection problem for a primary resolution and wavelet basis functions in wavelet regression. Most wavelet shrinkage methods focus on thresholding the wavelet coefficients, given a primary resolution which is usually determined by the sample size. However, both a primary resolution and the basis functions are affected by the shape of an unknown function rather than the sample size. Unlike existing methods, our method does not depend on the sample size and also takes into account the shape of the unknown function.

Adaptive wavelet shrinkage for noise robust speaker recognition

Speaker recognition faces many practical difficulties, among which signal inconsistency due to environmental and acquisition channel factors is most challenging. The noise imposed to the voice signal varies greatly and a priori noise model is usually unavailable. In this article, we propose a robust speaker recognition method that employs a novel adaptive wavelet shrinkage method for noise suppression. In our method, wavelet subband coefficient thresholds are automatically computed, which are proportional to the noise contamination. In the application of wavelet shrinkage for noise removal, a dual-threshold strategy is developed to suppress noise, preserve signal coefficients and minimize the introduction of artifacts. The recognition is achieved using modification of Mel-frequency cepstral coefficient of overlapped voice signal segments. The efficacy of our method is evaluated with voice signals from two public available speech signal databases and is compared with state-of-the-art methods. It is demonstrated that our proposed method exhibits great robustness in various noise conditions. The improvement is significant especially when noise dominates the underlying speech.

Sonar target enhancement by shrinkage of incoherent wavelet coefficients

Background reverberation can obscure useful features of the target echo response in broadband low-frequency sonar images, adversely affecting detection and classification performance. This paper describes a resolution and phase-preserving means of separating the target response from the background reverberation noise using a coherence-based wavelet shrinkage method proposed recently for de-noising magnetic resonance images. The algorithm weights the image wavelet coefficients in proportion to their coherence between different looks under the assumption that the target response is more coherent than the background. The algorithm is demonstrated successfully on experimental synthetic aperture sonar data from a broadband low-frequency sonar developed for buried object detection.

Speckle reduction of retinal optical coherence tomography based on contourlet shrinkage

Speckle reduction of retinal optical coherence tomography (OCT) images helps the diagnosis of ocular diseases. In this Letter, we present a speckle reduction method based on shrinkage in the contourlet domain for retinal OCT images. The algorithm overcomes the disadvantages of the wavelet shrinkage method, which lacks directionality and anisotropy. The trade-off between speckle reduction and edge preservation is controlled by a single adjustable parameter, which determines the threshold in the contourlet domain. Results show substantial reduction of speckle noise and enhanced visualization of layer structures as demonstrated in the image of the central fovea region of the human retina. It is expected to be utilized in a wide range of biomedical imaging applications.

Noise Reduction in White Light Lidar Signal Using a One-Dim and Two-Dim Daubechies Wavelet Shrinkage Method

A 1-D and 2-D Daubechies 5 (db5) discrete wavelet shrinkage methods using a 10 level decomposition was applied to white light lidar data particularly at 350 nm and 550 nm backscattered signal. At 350 nm, the backscattered signal is very weak as compared to 550 nm backscattered signal because of the spectral intensity distribution of the generated white light. The 1-D and 2-D wavelet shrinkage method gave a much better result as compared with the moving average method. However, the 2-D wavelet shrinkage method produced a much better denoised lidar signal compared with the 1-D wavelet shrinkage method. This is indicated by the 142% increase in correlation coefficient between the 2-D denoised lidar signal and the 800 nm original lidar signal as compared with only 12% increase in correlation coefficient for the 1-D denoised lidar signal. The 2-D wavelet shrinkage method also gave a much higher SNR value of 65.9 compared to 1-D which is 38.8.

Explicit Coherence Enhancing Filter With Spatial Adaptive Elliptical Kernel

The goal of this letter is to provide an elliptical filter to improve image coherence for the task of image smoothing and inpainting. The kernel of this filter is adaptively weighted and its shape is determined by local coherence estimation. The long axis of its ellipse is the same as the coherence direction and we put more weight there to enhance coherence. Compared with the related anisotropic partial differential equations (PDEs) or wavelet shrinkage methods, the proposed filter is extremely simple, instinctive and easy to code. Numerical examples and comparisons illustrate clearly the good performance of the proposed filter.

Doppler Signal Denoising Based on Feature Adaptive Wavelet Shrinkage Method

The envelope extraction of Doppler signal spectrum is very important in ultrasonic blood flow detection, due to the fact that it can provide the diagnosis information of blood circulatory system. Doppler signals are often polluted by noises, which will affect the performance of the envelope extraction. Therefore, it is necessary to remove the noises before extracting the spectrum envelope. In this paper, a Doppler denoising method based on the Feature Adaptive Wavelet Shrinkage is proposed. The advantage of this method is that the threshold of each coefficient is set by using the coefficient at the current location and its two neighbor coefficients. Simulation results demonstrate that the proposed method can remove the noises of Doppler signals more effectively compared to the traditional wavelet threshold method.

PEMILIHAN PARAMETER THRESHOLD OPTIMAL DALAM ESTIMATOR REGRESI WAVELET THRESHOLDING DENGAN PROSEDUR FALSE DISCOVERY RATE (FDR)

If X is predictor variable and Y is response variable of following model Y = f (X) +e with function f is regression which not yet been known and e is independent random variable with mean 0 and variant , hence function of f can estimate with parametric and nonparametric approach. At this paper estimate f with nonparametric approach. Nonparametric approach that used is wavelet shrinkage or wavelet thresholding method. At function estimation with method of wavelet thresholding, what most dominant determine level of smoothing estimator is value of threshold. The small threshold give function estimation very no smoothly, while the big value of threshold give function estimation very smoothly. Therefore require to be selected value of optimal threshold to determine optimal function estimation. One of the method to determine the value of optimal threshold is with procedure of False Discovery Rate ( FDR). In procedure of FDR, the optimal threshold determined by selection of level of significance. Smaller mount used significance progressively smoothly its . Keywords : Nonparametric regression, wavelet thresholding estimator, procedure of False Discovery Rate

Development of AE Monitoring System with Noise Reduction Function by Spectral Subtraction

In order to monitor acoustic emission (AE) in a noisy environment, an AE monitoring system with a real-time noise reduction function using spectral subtraction (SS) was developed. First, the improvement in the S/N ratio and distortion of the waveform after the process were compare to those in ¾-filter and wavelet shrinkage methods. The improvement in the S/N ratio of the waveform processed by SS constantly increased and was observed to be independent of the S/N ratio of the wave before processing. The distortion of the waveform processed by SS was less than the distortions of the waves processed using ¾-filter and by wavelet shrinkage. Next, the effect of two parameters in the SS process ®frame number (fn) and over-subtraction factor (i) ®on the noise reduction performance was studied. The S/N ratio of the signals processed by the SS technique improved with decreasing fn and with increasing i. However, the processed waveform was distorted when i was large. It is necessary to set the value of fn to 16 or less and i to 5 or less so that SS showed an advantage to reduce noise with low waveform distortion. Cylindrical wave AE signals produced by the Hsu-Nielsen source (pencil lead breaking) were monitored with the developed system in an environment with artificial noise. The developed system was able to acquire AE signals with a sampling frequency of up to 25MHz. The noise was reduced and AE signals with S/N ratio of 0dB before the process could be detected. The S/N ratio of the AE signal was improved by approximately 10dB using the SS technique. [doi:10.2320/matertrans.I-M2011855]

Noise Elimination of Vibration Signal of Distributed Optical Fiber-Sensing System Based on Wavelet Analysis

To the noise in the vibration information of long-distance distributed optical fiber-sensing system, discrete wavelet transform was adopted to eliminate. On the basis of analyzing noise eliminating theory, wavelet shrinkage method was proposed and a few kinds of threshold selection rules were discussed. The processing results of different noise eliminating techniques to vibration signal and its energy distribution in frequency domain were simulated and analyzed. The results show that discrete wavelet transform has the same excellent performance with stationary wavelet transform in noise eliminating to vibration signal.

Curve denoising by multiscale singularity detection and geometric shrinkage

We propose a method for denoising piecewise smooth curves, given a number of noisy sample points. Using geometric variants of wavelet shrinkage methods, our algorithm preserves corners while enforcing that the smoothed arcs lie in an L 2 Sobolev space H α of order α chosen by the operator. The reconstruction is scale-invariant when using the Sobolev space H 3 / 2 , adapts to the local noise level, and is essentially free of tuning parameters. In particular, our noise-adaptivity ensures that there is no arbitrarily-chosen “diffusion time” parameter in the denoising. Further, in cases where the distinction between signal and noise is unclear, we show how statistics gathered from the curve can be used to identify a finite number of “good” choices for the denoising.

Non-linear Wavelet Shrinkage Based Method for Defect Detection in Ultrasonic Signal

In the weld tested ultrasonic signal,noise is the leading factors that interfering defect detection.In order to suppress ultrasonic noise and recognize defect signal effectively,an improved non-linear wavelet shrinkage(NWS) method is proposed on the basis of the cross-correlation of sub-waves.The proposed method inherits the merit of multi-resolution of wavelet,and takes cross-correlation between defects waves in the two adjacent signals into account at the same time.By employing the conventional and improved NWS methods,both computer simulated data and weldment tested ultrasonic signal are de-noising processed.The effects of mother wavelets and threshold estimation methods on the noise suppression are researched.Compared with conventional NWS,the improved method is robust to mother wavelets and threshold estimation methods,and shows wide adaptability to noise of complicated frequency.The proposed method has the technical advantage of both noise suppression and defect wave reconstruction,and can effectively identify and quantitatively detect of defects in ultrasonic tested signal.

Scale dependent wavelet selection for de-noising of partial discharge detection

Wavelet shrinkage methods are effective for de-noising of partial discharge (PD) detection. Base wavelets are related to distortion of PD signals de-noised by wavelet shrinkage methods. This paper presents a scale dependent wavelet selection scheme for de-noising of PD detection. The scale dependent wavelet selection scheme is called the energy based wavelet selection (EBWS) because an energy criterion is proposed for the scheme. In the proposed energy criterion, a base wavelet is selected as an optimal base wavelet if it can generate an approximation with the largest energy among all base wavelets for selection at each scale. PD high-frequency signals are simulated and PD ultra-high-frequency signals are obtained by experiments in laboratory for de-noising experiments and analysis. In comparison with the correlation-based wavelet selection (CBWS) scheme, the wavelet shrinkage, based on the EBWS, generates significantly smaller waveform distortion and magnitude errors of de-noised PD signals.

Ultrasonic Signal Denoising for Robust Measurement of Solid-Propellant Burning Rates

Recently, an effective approach (namely, an ultrasonic full-waveform analysis method) has been proposed for the ultrasonic measurement of solid-propellant burning rate as a function of pressure in a single test. In this study, highfrequency ultrasonic transducers are adopted for the acquisition of ultrasonic full waveforms in order to increase the spatial resolution of the measurement. Unfortunately, however, these transducers are susceptible to random noise. This paper addresses an effective approach for reducing high-frequency random noise to the ultrasonic full waveforms using the wavelet-shrinkage method. Furthermore, this paper presents the results of the noise reduction at ultrasonic full waveforms captured from solid-propellant samples together with the improvement in the measurement accuracy of solid-propellant burning rates obtained by adopting the proposed approach.

A penalised data-driven block shrinkage approach to empirical Bayes wavelet estimation

In this paper we propose a simple Bayesian block wavelet shrinkage method for estimating an unknown function in the presence of Gaussian noise. A data-driven procedure which can adaptively choose the block size and the shrinkage level at each resolution level is provided. The asymptotic property of the proposed method, BBN (Bayesian BlockNorm shrinkage), is investigated in the Besov sequence space. The numerical performance and comparisons with some of existing wavelet denoising methods show that the new method can achieve good performance but with the least computational time.

Alternating Minimization Method for Total Variation Based Wavelet Shrinkage Model

In this paper, we introduce a novel hybrid variational model which gen- eralizes the classical total variation method and the wavelet shrinkage method. An alternating minimization direction algorithm is then employed. We also prove that it converges strongly to the minimizer of the proposed hybrid model. Finally, some nu- merical examples illustrate clearly that the new model outperforms the standard total variation method and wavelet shrinkage method as it recovers better image details and avoids the Gibbs oscillations. AMS subject classifications: 90C25, 52A41, 28E99, 62P35

IMAGE DENOISING BASED ON WAVELET SHRINKAGE USING NEIGHBOR AND LEVEL DEPENDENCY

Since Donoho et al. proposed the wavelet thresholding method for signal denoising, many different denoising approaches have been suggested. In this paper, we present three different wavelet shrinkage methods, namely NeighShrink, NeighSure and NeighLevel. NeighShrink thresholds the wavelet coefficients based on Donoho's universal threshold and the sum of the squares of all the wavelet coefficients within a neighborhood window. NeighSure adopts Stein's unbiased risk estimator (SURE) instead of the universal threshold of NeighShrink so as to obtain the optimal threshold with minimum risk for each subband. NeighLevel uses parent coefficients in a coarser level as well as neighbors in the same subband. We also apply a multiplying factor for the optimal universal threshold in order to get better denoising results. We found that the value of the constant is about the same for different kinds and sizes of images. Experimental results show that our methods give comparatively higher peak signal to noise ratio (PSNR), are much more efficient and have less visual artifacts compared to other methods.

Method of Selection of Poisson-Based Wavelet Shrinkage Sites

When effective programs to improve roadway safety are being developed, one of the primary tasks is to select sites for data collection. Selecting sites by ranking them simply by crash counts or crash rates is a common practice of transportation agencies because only crash data are required. Although the empirical Bayes (EB) method is a better option for site selection than this simple ranking method, the EB method requires additional data that might not be readily available or up to date, such as on annual average daily traffic and roadway characteristics, and this requirement could subsequently hinder the implementation of any EB method. This research, sponsored by the Georgia Department of Transportation, is motivated by the need to develop a more effective site selection method. The contributions of this paper include ( a) proposing a Poisson distribution–based wavelet shrinkage site selection (WASSS) method that can incorporate various wavelet shrinkage methods; ( b) obtaining a superior wavelet shrinkage method, the Bayesian Multiscale method (BMSM), for WASSS by evaluating various wavelet shrinkage methods; and ( c) comparing the EB method and this proposed WASSS method. It is found that the proposed BMSM-based WASSS method, as compared with the EB method, produces slightly better (or at least the same) level of performance (i.e., in terms of rates of false negatives and false positives); in addition this proposed method does not require additional data (as does the EB method). This study demonstrates that the proposed WASSS method is a promising site selection alternative that requires only crash data and that performs acceptably.

A Signal Denoising Method Based on the Improved ICI Rule

In this letter, we have proposed a signal denoising method based on a modification of the intersection of confidence intervals (ICI) rule. The ICI rule is complemented by the relative intersection of confidence intervals length which is used as an additional criterion for adaptive filter support selection. It is shown that the proposed method outperforms the original ICI method equipped with the local polynomial approximation (LPA), as well as various conventional wavelet shrinkage methods.