Dyadic Discrete Wavelet Transform Research Articles

Random noise attenuation using the novel Estimated Noise Pattern Denoising Algorithm

This paper introduces the estimated pattern denoising (EPD) wavelet transform for random noise attenuation in geophysical data. The proposed approach combines the capability of the Gaussian filter and dual-tree rational dilation wavelet transform (DT-RADWT) in random noise detection and suppression; we called this method Estimated Pattern Denoising (EPD). The EPD is an innovative approach in terms of estimation of the location and amplitude of the noise pattern, directly from the data. The employed approach produces a higher quality factor (Q-factor) than the conventional dyadic discrete wavelet transform (DWT) and separates the noise from the signal with higher accuracy. The EPD provides a data-driven scheme that resolves the complexity of the random noise model in noise suppression, using an auxiliary Gaussian filter. This approach does not require prior information about the noise source, statistical distribution, or frequency range. We show successful suppression of random noise using the proposed approach on synthetic and real field data.

Complex-Pan-Tompkins-Wavelets: Cross-channel ECG beat detection and delineation

The Electro Cardiogram (ECG) provides insight into the different phases of a heart beat and various kinds of disorders which may affect them. For the identification and treatment of these conditions it is crucial to properly detect each heartbeat and delineate P-, QRS and T-waves. The presented Complex-Pan-Tompkins-Wavelets (CPTW) algorithm aims at detecting and delineating heart beats in real-time across any number of channels between one and 64 sampled between 256 Hz and 4.8 kHz. It merges three well established single channel algorithms, the complex-lead by Christov, the Pan-Tompkins and the discrete dyadic wavelet-transform, such that the shortcomings of one algorithm are compensated by the strength of the other. A first study testing the CPTW algorithm was conducted using 75 records of 30 min duration provided by the INCART database. An initial implementation in Python 3 allows to localize and detect QRS complexes with an average sensitivity of 99.57% and a precision of 99.58% could be achieved. The average time required to process a single data set thereby was 12 min. In a second test which included 3 recordings of 3 min duration the scalability of the algorithm with respect to number of channels and sampling rates was accessed. Incrementing the number of channels by a factor of 5.2–62 channels resulted in an 3.1 fold increment in run-time. Raising the sampling rate from 256 Hz to 4.8 kHz elongated the run-time by a factor of just 3.2.

Integrated approach based on flexible analytical wavelet transform and permutation entropy for fault detection in rotary machines

This paper presents an integrated approach for the detection and classification of the faults of rolling bearing in rotary machines. Permutation entropy (PE) is integrated with a flexible analytical wavelet transform (FAWT). The signals from healthy and faulty bearing systems with different operating conditions are decomposed by FAWT. To compare effectiveness of the proposed methodology, dyadic discrete wavelet transform (DWT) is also used in integration with PE. PE values of decomposed signals are calculated and are then fed as feature vectors to support vector machine (SVM) classifier for the classification of different types and fault sizes. The classification results of both approaches are compared. The results demonstrate the effectiveness and robustness of FAWT-integrated-PE over the DWT integrated with PE, for detection of bearing faults and their classification.

Wheeze type classification using non-dyadic wavelet transform based optimal energy ratio technique

Background and objectiveWheezes in pulmonary sounds are anomalies which are often associated with obstructive type of lung diseases. The previous works on wheeze-type classification focused mainly on using fixed time-frequency/scale resolution based on Fourier and wavelet transforms. The main contribution of the proposed method, in which the time-scale resolution can be tuned according to the signal of interest, is to discriminate monophonic and polyphonic wheezes with higher accuracy than previously suggested time and time-frequency/scale based methods. MethodsAn optimal Rational Dilation Wavelet Transform (RADWT) based peak energy ratio (PER) parameter selection method is proposed to discriminate wheeze types. Previously suggested Quartile Frequency Ratios, Mean Crossing Irregularity, Multiple Signal Classification, Mel-frequency Cepstrum and Dyadic Discrete Wavelet Transform approaches are also applied and the superiority of the proposed method is demonstrated in leave-one-out (LOO) and leave-one-subject-out (LOSO) cross validation schemes with support vector machine (SVM), k nearest neighbor (k-NN) and extreme learning machine (ELM) classifiers. ResultsThe results show that the proposed RADWT based method outperforms the state-of-the-art time, frequency, time-frequency and time-scale domain approaches for all classifiers in both LOO and LOSO cross validation settings. The highest accuracy values are obtained as 86% and 82.9% in LOO and LOSO respectively when the proposed PER features are fed into SVM. ConclusionsIt is concluded that time and frequency domain characteristics of wheezes are not steady and hence, tunable time-scale representations are more successful in discriminating polyphonic and monophonic wheezes when compared with conventional fixed resolution representations.

Exploring an optimal wavelet-based filter for cryo-ET imaging

Cryo-electron tomography (cryo-ET) is one of the most advanced technologies for the in situ visualization of molecular machines by producing three-dimensional (3D) biological structures. However, cryo-ET imaging has two serious disadvantages—low dose and low image contrast—which result in high-resolution information being obscured by noise and image quality being degraded, and this causes errors in biological interpretation. The purpose of this research is to explore an optimal wavelet denoising technique to reduce noise in cryo-ET images. We perform tests using simulation data and design a filter using the optimum selected wavelet parameters (three-level decomposition, level-1 zeroed out, subband-dependent threshold, a soft-thresholding and spline-based discrete dyadic wavelet transform (DDWT)), which we call a modified wavelet shrinkage filter; this filter is suitable for noisy cryo-ET data. When testing using real cryo-ET experiment data, higher quality images and more accurate measures of a biological structure can be obtained with the modified wavelet shrinkage filter processing compared with conventional processing. Because the proposed method provides an inherent advantage when dealing with cryo-ET images, it can therefore extend the current state-of-the-art technology in assisting all aspects of cryo-ET studies: visualization, reconstruction, structural analysis, and interpretation.

Wavelet Approach to Damage Detection of Mechanical Systems and Structures

The damage detection methods of mechanical and civil structures have been drawing much interest from various fields. Many techniques to detect damage are based on the examination of the system response signals. Crack-like damages may contribute to the response signal the edges (also called slopes), i.e. the localized sharp transitions of signal values. A powerful tool to characterize such local feature signals is the continuous wavelet transform (CWT). Despite its name, the CWT can be calculated on discrete data and requires enormous computational cost. However, in many cases, the crack-like changes in the signal can be detected and localized using the discrete dyadic wavelet transform (DDWT) that has a fast transform algorithm. This paper presents application of the DDWT to detect and localize the response signal features (slopes) due to cracks in mechanical and civil structures. The wavelets used to calculate the DDWT are cubic box splines. The numerical results for a response signal simulating cracks in structures are presented in this article.

Directional dual-tree rational-dilation complex wavelet transform.

Dyadic discrete wavelet transform (DWT) has been used successfully in processing signals having non-oscillatory transient behaviour. However, due to the low Q-factor property of their wavelet atoms, the dyadic DWT is less effective in processing oscillatory signals such as embolic signals (ESs). ESs are extracted from quadrature Doppler signals, which are the output of Doppler ultrasound systems. In order to process ESs, firstly, a pre-processing operation known as phase filtering for obtaining directional signals from quadrature Doppler signals must be employed. Only then, wavelet based methods can be applied to these directional signals for further analysis. In this study, a directional dual-tree rational-dilation complex wavelet transform, which can be applied directly to quadrature signals and has the ability of extracting directional information during analysis, is introduced.

A SURVEY ON EFFICIENT NO-REFERENCE BLUR ESTIMATION METHODS

Blur estimation in image processing has come to be of great importance in assessing the quality of ima ges. This work presents a survey of no-reference blur estimation methods. A n o-reference method is particularly useful, when the input image used for blur estimation does not have an available corresponding reference image. This paper provides a comparison of the methodologies of four no-reference blur estimation methods. The first met hod applies a scale adaptive technique of blur esti mation to get better accuracy in the results. The second blur metric involves findin g the energy using second order derivatives of an i mage using derivative pair of quadrature filters. The third blur metric is based on the kurtosis measurement in the discrete dyadic wavelet transform (DDWT) of the images. The fourth method of blur estimation is obt ained by finding the ratio of sum of the edge width s of all the detected edges to the total number of edges. The results provided are use ful in comparing the methods based on metrics like Spearman correlation coefficient. The results are obtained by evaluation on images from the Laboratory for Image and Video Engineering (LIVE) database. The various methods are evaluated on the images by adding varying content of noise. The performance is evaluated for 3 different categories namely Gaussian blur, motion blur and al so JPEG2000 compressed images. Blur estimation fin ds its application in quality assessment, image fusion and auto-focusing in image s. The sharpness of an image can also be found from the blur metric as sharpness is inversely proportional to blur. Sharpness metric s can also be combined with other metrics to measur e overall quality of the image.

Dyadic wavelet for image coding implementation on a Xilinx MicroBlaze processor: Application to neutron radiography

In this work, we present a mixed software/hardware implementation of 2-D signals encoder/decoder using dyadic discrete wavelet transform (DWT) based on quadrature mirror filters (QMF); using fast wavelet Mallat's algorithm. This work is designed and compiled on the embedded development kit EDK6.3i, and the synthesis software, ISE6.3i, which is available with Xilinx Virtex-IIV2MB1000 FPGA. Huffman coding scheme is used to encode the wavelet coefficients so that they can be transmitted progressively through an Ethernet TCP/IP based connection. The possible reconfiguration can be exploited to attain higher performance. The design will be integrated with the neutron radiography system that is used with the Es-Salem research reactor.

Feature Extraction on Brain Computer Interfaces using Discrete Dyadic Wavelet Transform: Preliminary Results

The purpose of this work is to evaluate different feature extraction alternatives to detect the event related evoked potential signal on brain computer interfaces, trying to minimize the time employed and the classification error, in terms of sensibility and specificity of the method, looking for alternatives to coherent averaging. In this context the results obtained performing the feature extraction using discrete dyadic wavelet transform using different mother wavelets are presented. For the classification a single layer perceptron was used. The results obtained with and without the wavelet decomposition were compared; showing an improvement on the classification rate, the specificity and the sensibility for the feature vectors obtained using some mother wavelets.

TWO-DIMENSIONAL STATIONARY DYADIC WAVELET TRANSFORM, DECIMATED DYADIC DISCRETE WAVELET TRANSFORM AND THE FACE RECOGNITION APPLICATION

Currently, two-dimensional dyadic wavelet transform (2D-DWT) is habitually considered as the one presented by Mallat, which is defined by an approximation component, two detail components in horizontal and vertical directions. This paper is to introduce a new type of two-dimensional dyadic wavelet transform and its application so that dyadic wavelet can be studied and used widely furthermore. (1) Two-dimensional stationary dyadic wavelet transform (2D-SDWT) is proposed, it is defined by approximation coefficients, detail coefficients in horizontal, vertical and diagonal directions, which is essentially the extension of two-dimensional stationary wavelet transform for orthogonal/biorthogonal wavelet filters. (2) ε-decimated dyadic discrete wavelet transform (DDWT) is introduced and its relation with 2D-SDWT is given, where ε is a sequence of 0's and 1's. (3) Mallat decomposition algorithm based on dyadic wavelet is introduced as a special case of ε-decimated DDWT, and so a face recognition algorithm based on dyadic wavelet is proposed, and experimental results are given to show its effectiveness.

SUBBAND VARIANCE COMPUTATION OF HOMOSCEDASTIC ADDITIVE NOISE IN DISCRETE DYADIC WAVELET TRANSFORM

The paper deals with noise power variation that occurs when Discrete Dyadic Wavelet Transform (DDWT) is applied to signals affected by Wide Sense Stationary (WSS) additive white noise owing to the use of a non orthonormal expansion. An exact relationship between the noise variance in the original signal and the noise variance in the wavelet coefficients at a generic level is derived. This relationship is crucial in the application of wavelet thresholding for signal denoising to properly select the threshold in each subband.

Efficient compression of borehole resistivity and acoustic imaging data using wavelets

This paper presents a new approach to borehole resistivity and acoustic imaging data compression. The method is based on the discrete wavelet transform (DWT) combined with the set partitioning in the hierarchical trees (SPIHT) coding method. The primary advantages of the DWT + SPIHT method are its superior compression performance, simple implementation, and constant compression and transmission rate control. This new approach generally performs better than the traditional discrete cosine transform (DCT) followed by Huffman coding methods such as JPEG, particularly for target compression ratios greater than 50:1. Image block size plays a key role in using this method. To achieve the best compression performance, the image block size needs to be selected appropriately. In general, large image block sizes and more DWT decomposition levels result in higher compression ratios and/or fewer reconstruction errors. Whenever possible, image block sizes that allow the maximum levels of dyadic DWT decomposition should be used. When insufficient data samples are available in either depth or azimuthal direction, a small number of extra data samples can be added without sacrificing the overall compression performance. The DWT + SPIHT method also shows good fidelity in representing major features in borehole images such as fractures and sinusoids.

WAVEWAT—Improved Solvent Suppression in NMR Spectra Employing Wavelet Transforms

WAVEWAT is a new processing algorithm to suppress the on-resonance water signal in NMR spectra. It is based on a multiresolution analysis (MRA) of the free induction decay (FID) using a dyadic discrete wavelet transform (DWT). The width of the suppressed signal can be adjusted so that signals close to water are recovered without distortion of the signal shape and intensity. Computational efficiency is comparable to that of convolution filters employing a Fourier transform.