Adaptive Wavelet Thresholding Research Articles

A Combined Fractal and Wavelet Angiography Image Compression Approach

In this paper, a combined Fractal and Wavelet (CFW) compression algorithm targeting x-ray angiogram images is proposed. Initially, the image is decomposed using wavelet transform. The smoothness of the low frequency part of the image appears as an approximation image with higher self similarities, therefore, it is coded using a fractal coding technique. However, the rest of the image is coded using an adaptive wavelet thresholding technique. This model is implemented and its performance is compared with best performances of the available published algorithms. A data set containing 1000 x-ray angiograms is used to study the performance of the algorithm. A minimum compression ratio of 30 with a peak signal to noise ratio (PSNR) of 36 dB and percent diameter stenosis deviation of (<0.2%) was achieved. Results demonstrate the effectiveness of the proposed technique in obtaining a diagnostic quality of reconstructed images at very low bit rates.

Locally Adaptive Wavelet Thresholding for Speech Enhancement

There are strong dependencies between wavelet coefficients of speech signal,in this article,based on that,a new corresponding nonlinear threshold function derived in Bayesian framework is proposed to decrease the effect of the ambient noise.Analysis of the data shows the effectiveness of the proposed method that it removes white noise more effectually and gets better edge preservation.

Fault diagnosis of diesel engine based on adaptive wavelet packets and EEMD-fractal dimension

In this paper a novel method for de-noising nonstationary vibration signal and diagnosing diesel engine faults is presented. The method is based on the adaptive wavelet threshold (AWT) de-noising, ensemble empirical mode decomposition (EEMD) and correlation dimension (CD). A new adaptive wavelet packet (WP) thresholding function for vibration signal de-noising is used in this paper. To alleviate the mode mixing problem occurring in EMD, ensemble empirical mode decomposition (EEMD) is presented. With EEMD, the components with truly physical meaning can be extracted from the signal. Utilizing the advantage of EEMD, this paper proposes a new AWT–EEMD-based method for fault diagnosis of diesel engine. A study of correlation dimension in engine condition monitoring is reported also. Some important influencing factors relating directly to the computational precision of correlation dimension are discussed. Industrial engine normal and fault vibration signals measured from different operating conditions are analyzed using the above method.These techniques have integrated with our proposed adaptive wavelet threshold de-noising to form a new AWT–EEMD–CD method. The advantage of combining of EEMD and fractal dimension is that it does not require the classifiers to recognize the diesel engine fault types, also the method can solve the difficulty of recognizing fault states when two or more fractal dimensions are close to each other. To verify the effectiveness of the EEMD–CD in detecting the faults, their induced vibrations are collected from a series of generators under normal and faulty engine conditions after de-noising. The results show that this method is capable of extracting the impact signal features induced by vibrations and is able to determine their types of fault accurately even when the impacts have been overwhelmed by other unrelated vibration signals.

Density estimation for compound Poisson processes from discrete data

In this article we investigate the nonparametric estimation of the jump density of a compound Poisson process from the discrete observation of one trajectory over [0,T]. We consider the case where the sampling rate Δ=ΔT→0 as T→∞. We propose an adaptive wavelet threshold density estimator and study its performance for Lp losses, p≥1, over Besov spaces. The main novelty is that we achieve minimax rates of convergence for sampling rates ΔT that vanish slowly. The estimation procedure is based on the explicit inversion of the operator giving the law of the increments as a nonlinear transformation of the jump density.

Application of Adaptive Wavelet Thresholding to Ultrasonic Signal Compression of Aluminum Alloy Forgings

In this paper, for the purpose of ultrasonic signal compression and the coherent noise depressing in nondestructive test of aluminum alloy forging, the mathematical model of defect echoes is discussed and confirmed. And then the wavelet kernel is also confirmed according the waveform of the defect echoes. As the algorithms of standard hard thresholding and soft thresholding of wavelet transform can not bring out effective compression and depression to the coherent noise, an adaptive wavelet thresholding algorithm is introduced. Experimental results indicate that the adaptive wavelet thresholding algorithm can offer effective signal compression and depression to the coherent noise.

Nonparametric estimation of a renewal reward process from discrete data

We study the nonparametric estimation of the jump density of a renewal reward process from one discretely observed sample path over [0,T]. We consider regimes where the sampling rate goes to 0 as T tends to infinity. We propose an adaptive wavelet threshold density estimator and study its performance for the Lp loss, over Besov spaces. We achieve minimax rates of convergence for sampling rates that vanish with T at arbitrary polynomial rate. In the same spirit as Buchmann and Grubel (2003) the estimation procedure is based on the inversion of the compounding operator. The inverse has no closed form expression and is approached with a fixed point technique.

A new evaluation method for image noise reduction and usefulness of the spatially adaptive wavelet thresholding method for CT images

We have proposed a direct evaluation method concerning preservation of noise-free components for image noise reduction. This evaluation method is to graphically estimate how well a noise-reduction method will preserve noise-free image components by using the normal probability plot of the image pixel value difference between an original image and its noise-reduced image; this difference is equivalent to the "method noise" which was defined by Buades etal. Further, by comparing the linearity of a normal probability plot for two different noise reduction methods, one can graphically assess which method will be more able to preserve the noise-free component than the other. As an illustrative example of this evaluation method, we have evaluated the effectiveness of the spatially-adaptive BayesShrink noise-reduced method devised by Chang etal., when applied to chest phantom CT images. The evaluation results of our proposed method were consistent with the visual impressions for the CT images processed in this study. The results of this study also indicate that the spatially-adaptive BayesShrink algorithm devised by Chang etal. will work well on the chest phantom CT images, although the assumption for this method is often violated in CT images, and the assumption postulated for the spatially-adaptive BayesShrink method is expected to have sufficient robustness for CT images.

Asymptotic normality of adaptive wavelet thresholding risk estimation

Asymptotic normality of adaptive wavelet thresholding risk estimation

Blurred Star Image Processing for Star Sensors under Dynamic Conditions

The precision of star point location is significant to identify the star map and to acquire the aircraft attitude for star sensors. Under dynamic conditions, star images are not only corrupted by various noises, but also blurred due to the angular rate of the star sensor. According to different angular rates under dynamic conditions, a novel method is proposed in this article, which includes a denoising method based on adaptive wavelet threshold and a restoration method based on the large angular rate. The adaptive threshold is adopted for denoising the star image when the angular rate is in the dynamic range. Then, the mathematical model of motion blur is deduced so as to restore the blurred star map due to large angular rate. Simulation results validate the effectiveness of the proposed method, which is suitable for blurred star image processing and practical for attitude determination of satellites under dynamic conditions.

EOG artifact removal using a wavelet neural network

In this paper, we developed a wavelet neural network (WNN) algorithm for electroencephalogram (EEG) artifact. The algorithm combines the universal approximation characteristics of neural networks and the time/frequency property of wavelet transform, where the neural network was trained on a simulated dataset with known ground truths. The contribution of this paper is two-fold. First, many EEG artifact removal algorithms, including regression based methods, require reference EOG signals, which are not always available. The WNN algorithm tries to learn the characteristics of EOG from training data and once trained, the algorithm does not need EOG recordings for artifact removal. Second, the proposed method is computationally efficient, making it a reliable real time algorithm. We compared the proposed algorithm to the independent component analysis (ICA) technique and an adaptive wavelet thresholding method on both simulated and real EEG datasets. Experimental results show that the WNN algorithm can remove EEG artifacts effectively without diminishing useful EEG information even for very noisy datasets.

MEMS Gyro Signal De-Noising Based on Adaptive Stationary Wavelet Threshold

Random drift is a significant index that can affect the precision of MEMS gyroscope. It is one of the important techniques to decrease the random drift error in improving the precision of MEMS gyro. According to analyzing the principle of traditional Wavelet Transform and Stationary Wavelet Transform, Stationary Wavelet Transform (SWT) is adopted to de-noise the signal of MEMS gyro. Due to SWT’s time-invariant, the Gibbs phenomenon is decreased. SWT with adaptive threshold is adopted to analyze the actual dynamic MEMS gyroscope data. The experimental results show that this presented method is better than traditional wavelet threshold de-noising methods. It can effectively restrain the noise in high frequency and improve the drift error of MEMS gyro.

Denoising algorithm based on wavelet adaptive threshold

the main idea of denoising algorithm based on wavelet adaptive threshold is that speech signals should be packet transformed to get the wavelet coefficients used in optimal wavelet. Since the signal and the noise have different relevance, there will be different attenuations in wavelet decomposition process. Based on above characteristics, the appropriate threshold can be calculated by a new threshold function and the minimum mean square algorithm, even if the noise coefficients can be removed and the signal coefficients can be saved. Finally, the retained coefficients can be reconstructed to restore the original signal for the purpose of de-noising.

A De-Noising Method for Medical Ultrasonic Image Based on ROF Decomposition and Adaptive Wavelet Threshold

There are always lots of speckle noises in medical ultrasonic images because of the imaging mechanism of it. These speckle noises significantly reduce the clarity of the image and as a result, cause great difficulties in ultrasound diagnosis. To solve this problem, this paper presents a new de-noising method for medical ultrasonic image based on ROF model and adaptive wavelet threshold de-noising method. In addition to inhibiting the speckle noises in the medical ultrasonic image, this method can retain and even enhance the image detail information as much as possible.

Method of Adaptive Wavelet Thresholding Used in Image Denoising

According to multi-resolution analysis of wavelet threshold denoising principle, this paper presented two improved algorithms of continuity and adaptive threshold based on hard thresholding. The soft thresholding (hyperbolic thresholding) was used in the intervals after setting two thresholds, and the isolated points were removed according to the adjacent correlation coefficient during the processing. As a result, the hard thresholding’s shortcomings were reduced. The simulation results show that improved algorithms have both better visual effect and PSNR than the traditional approaches.

Statistical inference across time scales

This thesis studies the problem of statistical inference across time scales for a stochastic process. More particularly we study how the choice of the sampling parameter affects statistical procedures. We narrow down to the inference of jump processes from the discrete observation of one trajectory over [0,T]. As the length of the observation interval T tends to infinity, the sampling rate either goes to 0 (microscopic scale) or to some positive constant (intermediate scale) or grows to infinity (macroscopic scale). We set in a case where there are infinitely many observations. First we specialise in a toy model: a compound Poisson process of unknown intensity with symmetric Bernoulli jumps. Chapter 2 highlights the concept of statistical estimation in the three regimes defined above and the phenomena at stake. We study the properties of the statistical experiments in each regime, we show that the Local Asymptotic Normality property holds in every regimes (microscopic, intermediate and macroscopic). We also provide the formula of the associated Fisher information in each regime. Then we study how a statistical procedure which is optimal (of minimal variance) at a given scale is affected when we use it on data coming from another scale. We focus on the empirical quadratic variation estimator, it is an optimal procedure at macroscopic scales. We apply it on data coming from intermediate and microscopic regimes. Although the estimator remains efficient at microscopic scales, it shows a substantial loss of information when used on data coming from an intermediate regime. That loss can be explicitly related to the sampling rate. We provide an unified procedure, efficient in all regimes. Chapters 3 and 4 focus on microscopic regimes, when the sampling rate decreases to 0. The nonparametric estimation of the jump density of a renewal reward process is studied. We propose an adaptive wavelet threshold density estimator. It achieves minimax rates of convergence for sampling rates that vanish polynomially with T, namely in T^{-alpha} for alpha>0. The estimation procedure is based on the inversion of the compounding operator in the same spirit as Buchmann and Grubel (2003), which specialiase in the study of discrete compound laws. The inverse operator is explicit in the case of a compound Poisson process (see Chapter 3), but has no closed form expression for renewal reward processes (see Chapter 4). In that latter case the inverse operator is approached with a fixed point technique. Finally Chapter 5 studies at which rate identifiability is lost in macroscopic regimes. Indeed when a jump process is observed at an arbitrarily large sampling rate, limit approximations, like Gaussian approximations, become valid and the specificities of the jumps may be lost, as long as the structure of the process is more complex than the one introduced in Chapter 2. First we study a toy model depending on a 2-dimensional parameter. We distinguish two different regimes: fast (macroscopic) regimes where all information on the parameter is lost and slow regimes where the parameter remains identifiable but where optimal estimators converge with slower rates than the expected usual parametric ones. From this toy model lower bounds are derived, they ensure that consistent estimation of Levy processes or renewal reward processes is not possible when the sampling rate grows faster than the square root of T. Finally we identify regimes where an experiment consisting in increments of a compound Poisson process is asymptotically equivalent to an experiment consisting in Gaussian random variables. We also give regimes where there is no consistent estimator for compound Poisson processes depending on too many parameters

Multichannel boxcar deconvolution with growing number of channels

We consider the problem of estimating the unknown response function in the multichannel deconvolution model with a boxcar-like kernel which is of particular interest in signal processing. It is known that, when the number of channels is finite, the precision of reconstruction of the response function increases as the number of channels M grow (even when the total number of observations n for all channels M remains constant) and this requires that the parameter of the channels form a Badly Approximable M-tuple. Recent advances in data collection and recording techniques made it of urgent interest to study the case when the number of channels M=Mn grow with the total number of observations n. However, in real-life situations, the number of channels M=Mn usually refers to the number of physical devices and, consequently, may grow to infinity only at a slow rate as n→∞. Unfortunately, existing theoretical results cannot be blindly applied to accommodate the case when M=Mn→∞ as n→∞. This is due to the fact that, to the best of our knowledge, so far no one have studied the construction of a Badly Approximable M-tuple of a growing length on a specified interval, of a non-asymptotic length, of the real line, as M is growing. Therefore, this generalization requires non-trivial results in number theory. When M=Mn grows slowly as n increases, we develop a procedure for the construction of a Badly Approximable M-tuple on a specified interval, of a non-asymptotic length, together with a lower bound associated with this M-tuple, which explicitly shows its dependence on M as M is growing. This result is further used for the evaluation of the L2-risk of the suggested adaptive wavelet thresholding estimator of the unknown response function and, furthermore, for the choice of the optimal number of channels M which minimizes the L2-risk.

Adaptive threshold speech de-noising based on Bark scale wavelet package

When input signal has low Signal-to-Noise Ratio (SNR), the commonly used speech de-noising algorithm will cause distortion for reconstructed signal because of unvoiced sounds weak information losses. In order to overcome this, this paper presented a new method for speech enhancement. Wavelet packet decomposition was used to fit speech critical band, and the voiced and unvoiced sounds were processed separately based on sub-band energy ratio. Then, eight scales of wavelet packet decomposition and four scales of wavelet packet decomposition were employed for the unvoiced and the voiced sounds. A new wavelet adaptive threshold algorithm was obtained based on Bark sub-band, in Bark frequency domain real-time tracking noise level and the adaptive adjustment of coefficient can increase the accuracy of threshold value judgment, and effectively reduces signal reconstruction distortion. The computer simulation results indicate that the new method compared to traditional algorithm has obvious advantages in improving output SNR and effectively reducing the speech distortion. When this new algorithm is combined with spectral subtraction, it can further improve the quality of speech de-noising.

Partial discharge signal denoising with spatially adaptive wavelet thresholding and support vector machines

In this paper an improved method to denoise partial discharge (PD) signals is presented. The method is based on the wavelet transform (WT) and support vector machines (SVM) and is distinct from other WT-based denoising strategies in the sense that it exploits the high spatial correlations presented by PD wavelet decompositions as a way to identify and select the relevant coefficients. PD spatial correlations are characterized by WT modulus maxima propagation along decomposition levels (scales), which are a strong indicative of the their time-of-occurrence. Denoising is performed by identification and separation of PD-related maxima lines by an SVM pattern classifier. The results obtained confirm that this method has superior denoising capabilities when compared to other WT-based methods found in the literature for the processing of Gaussian and discrete spectral interferences. Moreover, its greatest advantages become clear when the interference has a pulsating or localized shape, situation in which traditional methods usually fail.

Elimination Noise by Adaptive Wavelet Threshold

Elimination Noise by Adaptive Wavelet Threshold

Speckle Noise Reduction in Ultrasound Images Using Context-based Adaptive Wavelet Thresholding

In medical imaging, image denoising has become a very essential exercise all through the diagnosis. Compromise between the preservation of useful diagnostic information and noise suppression must be respected in medical images. One of the ultimate goals of an imaging modality is to provide the clinician with the best possible information needed to make an accurate diagnosis. Ultrasound images suffer from an intrinsic artifact called speckle. Speckle degrades spatial and contrast resolution and obscures the underlying anatomy. Thus, it seems sensible to reduce speckle artifacts before performing image analysis, provided the image that might distinguish one tissue from another is preserved. The main goal of this thesis was the development of novel methods for suppression of speckle in medical ultrasound images in the wavelet domain. We have adopted weighted variance for estimating the threshold and multiscale product scheme for thresholding the coefficients. To employ the wavelet interscale dependencies, the adjacent wavelet subbands are multiplied. Multiplying the adjacent wavelet scales would sharpen the important structures while reducing noise. In the multiscale products, edges can be efficiently discriminated from noise. Then, an adaptive threshold was calculated and imposed on the products, instead of on the wavelet coefficients, to identify important features. Fundamentally speckle noise is a signal-dependent one, and so weighted variance of each background pixel was taken into account while calculating threshold. Experiments show that the proposed scheme better suppresses noise and preserves edges than other wavelet-denoising methods. Experiments with synthetic and real ultrasound imagery show that the proposed method improves the signal-to-noise ratio and preserves edge clarity.