Discrete Wavelet Packet Transform Research Articles

A Proposed Turbo Coded Wavelet Packet Modulation based MC-CDMA

A turbo coded Discrete Wavelet Packet Transform DWPT based Multicarrier CDMA system has been proposed to enhance the bit error rate and complexity of the conventional MC-CDMA which based on Fast Fourier Transform FFT over different channel models. The decoding algorithm used maxlog-MAP algorithm. The computer simulation tests show that the BER of the coded DWPT based MC-CDMA has been improved by 4 dB compared with the coded FFT based MCCDMA over Additive White Gaussian Noise AWGN and 4.5 dB over the multipath fading channel at of BER=10.

패킷화 이산 웨이블릿 변환을 이용한 영상의 효율적인 암호화 기법

본 논문에서는 이산 웨이블릿 패킷 변환을 이용하여 디지털 시네마와 같은 영상의 중요 성분을 추적하고 암호화하는 새로운 방법을 제안한다. 공간과 주파수 영역에서 영상의 특성을 분석하여 영상을 다루는데 필요한 정보를 얻는다. 얻어진 정보들을 종합하여 웨이블릿 변환과 부대역의 패킷화를 이용한 암호화 방법을 제안한다. 웨이블릿 변환의 레벨과 에너지 값을 선택함으로써 다양한 강도로 암호화가 가능하다. 암호화 효과를 수치 및 시각적으로 분석하여 최적의 파라미터를 제시한다. 따라서 별도의 분석과정 없이 본 논문에서 제시된 파라미터를 이용하여 효율적으로 암호화를 수행할 수 있다. 실험결과를 살펴보면 전체 데이터 중에서 단지 0.18%의 데이터만을 암호화하더라도 객체를 분간할 수 없다. 부대역의 패킷화 정보와 암호화 시 이용한 키를 전체 암호키로 이용할 수 있다. In this paper, we propose a new method which estimates and encrypts significant component of digital image such as digital cinema using discrete wavelet packet transform (DWPT). After analyzing the characteristics of images in spatial and frequency domain, the required information for ciphering an image was extracted. Based on this information an ciphering method was proposed with wavelet transform and packetization of subbands. The proposed algorithm can encrypt images in various robust from selecting transform-level and energy threshold. From analyzing the encryption effect numerically and visually, the optimized parameter for encryption is presented. Without additional analyzing process, one can encrypt efficiently digital image using the proposed parameter. Although only 0.18% among total data is encrypted, the reconstructed image dose not identified. The paketization information of subbands and the cipher key can be used for the entire secret key.

Wavelet based denoising technique for liquid level system

The purpose of this paper is to employ wavelet based noise removal technique to remove measurement noise from differential pressure transmitter (DPT) output indicating the level of a process tank. The liquid level system (LLS) is approximated as a first order plant with time delay. When connected in closed loop, the LLS is ideally associated with a PI controller, an actuator, a final control element and a level sensor (DP transmitter in present system). There are enough chances of contaminating the output of LLS by the high frequency measurement noise. In this work, an attempt has been made to judge the performance of discrete wavelet transform (DWT) and discrete wavelet packet transform (DWPT) based noise removal technique when applied to LLS. The available denoised response using wavelet based filtering is compared with that of conventional Butterworth filtering method. Applying hard thresholding that typically retains a very small number of coefficients, the results are often smoothed at the cost of loosing information. By retaining larger number of coefficients and shrinking them, the soft thresholding methods usually give more useful results to denoise the signal. Threshold value has been calculated by Visu Shrink method and Minimax method in different cases.

Wavelet Packet Transform Based Driver Distraction Level Classification Using EEG

We classify the driver distraction level (neutral, low, medium, and high) based on different wavelets and classifiers using wireless electroencephalogram (EEG) signals. 50 subjects were used for data collection using 14 electrodes. We considered for this research 4 distraction stimuli such as Global Position Systems (GPS), music player, short message service (SMS), and mental tasks. Deriving the amplitude spectrum of three different frequency bands theta, alpha, and beta of EEG signals was based on fusion of discrete wavelet packet transform (DWPT) and FFT. Comparing the results of three different classifiers (subtractive fuzzy clustering probabilistic neural network, -nearest neighbor) was based on spectral centroid, and power spectral features extracted by different wavelets (db4, db8, sym8, and coif5). The results of this study indicate that the best average accuracy achieved by subtractive fuzzy inference system classifier is 79.21% based on power spectral density feature extracted by sym8 wavelet which gave a good class discrimination under ANOVA test.

디지털 홀로그램의 보안을 위한 고성능 암호화기의 하드웨어 구조

In this paper, we implement a new hardware for finding the significant coefficients of a digital hologram and ciphering them using discrete wavelet packet transform (DWPT). Discrete wavelet transform (DWT) and packetization of subbands is used, and the adopted ciphering technique can encrypt the subbands with various robustness based on the level of the wavelet transform and the threshold of subband energy. The hologram encryption consists of two parts; the first is to process DWPT, and the second is to encrypt the coefficients. We propose a lifting based hardware architecture for fast DWPT and block ciphering system with multi-mode for the various types of encryption. The unit cell which calculates the repeated arithmetic with the same structure is proposed and then it is expanded to the lifting kernel hardware. The block ciphering system is configured with three block cipher, AES, SEED and 3DES and encrypt and decrypt data with minimal latency time(minimum 128 clocks, maximum 256 clock) in real time. The information of a digital hologram can be hided by encrypting 0.032% data of all. The implemented hardware used about 200K gates in 0.25μm CMOS library and was stably operated with 165MHz clock frequency in timing simulation.

A subscriber classification approach for mobile cellular networks

The classification of subscriber types in mobile cellular networks is valuable for network service providers since it provides a mechanism to plan network services by better understanding subscriber behaviour in a network. Mobile networks contain vast repositories of data that store valuable information regarding subscriber behaviour. In this paper, a new approach for subscriber classification in mobile cellular networks is proposed. The proposed approach considers network traffic generated from a mobile cellular network operator in South Africa. The proposed approach makes use of a difference histogram approach for feature extraction and a fuzzy c-means clustering algorithm to classify traffic data into subscriber classes. To validate the proposed approach, a comparative analysis of two different multi-resolution feature extraction approaches, the empirical mode decomposition (EMD) approach and the discrete wavelet packet transform (DWPT) are compared with results obtained with the difference histogram (DH) approach. It is shown that the difference histogram provides better clustering results when compared to the two multi-resolution approaches demonstrating the potential of the difference histogram approach.

Classification of power quality disturbances using wavelet packet energy and multiclass support vector machine

PurposeThe purpose of this paper is to develop a new method for classification of power quality (PQ) disturbances such as the sag, interruption, swell, harmonic, notch, oscillatory transient and impulsive transient.Design/methodology/approachA PQ disturbances classification system based on wavelet packet energy and multiclass support vector machines (MSVM) is proposed to discriminate seven types of PQ disturbances. The PQ disturbance signals are first decomposed into components in different subbands using discrete wavelet packet transform (DWPT). Statistical features of the decomposed signals are required to characterize the PQ disturbances. A MSVM classifier follows to classify the PQ disturbances.FindingsThe proposed method could effectively detect information from disturbance waveforms using DWPT and MSVM techniques, which is verified on over 700 samples.Research limitations/implicationsThe classification stage of the proposed method does not differentiate the disturbances occurred simultaneously.Practical implicationsThe proposed method possesses high recognition rate, so it is suitable for the PQ monitoring system for detection and classification of disturbances.Originality/valueThe paper describes a new and efficient way of classification of PQ disturbances. In this paper, an attempt has been made to extract efficient features of the PQ disturbances using DWPT. It is observed that these features can help correctly classify the PQ disturbances, even under noisy conditions. The MSVM is compared with artificial neural network (ANN) and it is found that the MSVM classifier gives the better result.

TV white spaces exploitation for multimedia signal distribution

The new spectrum regulation policies for dynamic spectrum access, especially those concerning the use of the white spaces in the Digital Terrestrial Television (DTT) bands, arise the need for fast and reliable signal identification and classification methods. In this paper we present a two-stage identification method for signals in the white spaces, using combined energy detection and feature detection. The band of interest is divided by means of the Discrete Wavelet Packet Transformation (DWPT) in sub-bands where the signal power is calculated. Modulation classifiers taking into account the statistical parameters of the signal in the wavelet domain are used as features for identifying the modulation schemes, in this case specifically for the DVB-T broadcast standard. Finally, a signal transmission architecture based on Motion JPEG XR has been implemented in order to explore and evaluate a practical application of indoor signal distribution over white-spaces.

Discrete harmony search based expert model for epileptic seizure detection in electroencephalography

Seizure detection and classification using signal processing methods has been an important issue of research for the last two decades. In the present study, a novel scheme was presented to detect epileptic seizure activity with very fast and highest accuracy from background electro encephalogram (EEG) data recorded from epileptic and normal subjects. The proposed scheme is based on discrete wavelet packet transform (DWT) with energy, entropy, standard deviation, mean, kurtosis, skewness and entropy estimation at each node of the decomposition tree followed by application of probabilistic neural network (PNN). Normal as well as epileptic EEG epochs were decomposed into approximation and details coefficients till sixth-level using DWT packet. Discrete harmony search with modified differential operator was used to select the optimal features out of all above mentioned statistical and non-statistical parameters. In order to demonstrate the efficacy of the proposed algorithm for classification purpose using PNN, we have implemented 10-fold cross validation. Clinical EEG data recorded from normal as well as epileptic subjects are used to test the performance of this new scheme. It is found that the detection rate is 100% accurate with same level of sensitivity and specificity.

Generation of Self-Similar Gaussian Time Series by Means of the DWT and DWPT Variance Maps

Due to the several kinds of services that use the Internet and data networks infra-structures, the present networks are characterized by the diversity of types of traffic that have statistical properties as complex temporal correlation and nongaussian distribution. The networks complex temporal correlation may be characterized by the Short Range Dependence - (SRD) and the Long Range Dependence - (LRD). Models as the fGN (Fractional Gaussian Noise) may capture the LRD but not the SRD. This work presents two methods for traffic generation that synthesize approximate realizations of the self-similar fGN with SRD random process. The first one employs the IDWT (Inverse Discrete Wavelet Transform) and the second the IDWPT (Inverse Discrete Wavelet Packet Transform). It has been developed the variance map concept that allows to associate the LRD and SRD behaviors directly to the wavelet transform coefficients. The developed methods are extremely flexible and allow the generation of Gaussian time series with complex statistical behaviors.

Wavelet Packets-Based Blind Watermarking for Medical Image Management

The last decade has witnessed an explosive use of medical images and Electronics Patient Record (EPR) in the healthcare sector for facilitating the sharing of patient information and exchange between networked hospitals and healthcare centers. To guarantee the security, authenticity and management of medical images and information through storage and distribution, the watermarking techniques are growing to protect the medical healthcare information. This paper presents a technique for embedding the EPR information in the medical image to save storage space and transmission overheads and to guarantee security of the shared data. In this paper a new method for protecting the patient information in which the information is embedded as a watermark in the discrete wavelet packet transform (DWPT) of the medical image using the hospital logo as a reference image. The patient information is coded by an error correcting code (ECC), BCH code, to enhance the robustness of the proposed method. The scheme is blind so that the EPR can be extracted from the medical image without the need of the original image. Therefore, this proposed technique is useful in telemedicine applications. Performance of the proposed method was tested using four modalities of medical images; MRA, MRI, Radiological, and CT. Experimental results showed no visible difference between the watermarked and the original image. Moreover, the proposed watermarking method is robust against a wide range of attacks such as JPEG coding, Gaussian noise addition, histogram equalization, gamma correction, contrast adjustment, and sharpen filter and rotation.

FUSION OF SURVEILLANCE IMAGES IN INFRARED AND VISIBLE BAND USING CURVELET, WAVELET AND WAVELET PACKET TRANSFORM

This paper presents two methods for fusion of infrared (IR) and visible surveillance images. The first method combines Curvelet Transform (CT) with Discrete Wavelet Transform (DWT). As wavelets do not represent long edges well while curvelets are challenged with small features, our objective is to combine both to achieve better performance. The second approach uses Discrete Wavelet Packet Transform (DWPT), which provides multiresolution in high frequency band as well and hence helps in handling edges better. The performance of the proposed methods have been extensively tested for a number of multimodal surveillance images and compared with various existing transform domain fusion methods. Experimental results show that evaluation based on entropy, gradient, contrast etc., the criteria normally used, are not enough, as in some cases, these criteria are not consistent with the visual quality. It also demonstrates that the Petrovic and Xydeas image fusion metric is a more appropriate criterion for fusion of IR and visible images, as in all the tested fused images, visual quality agrees with the Petrovic and Xydeas metric evaluation. The analysis shows that there is significant increase in the quality of fused image, both visually and quantitatively. The major achievement of the proposed fusion methods is its reduced artifacts, one of the most desired feature for fusion used in surveillance applications.

AREA LEVEL FUSION OF MULTI-FOCUSED IMAGES USING DUAL TREE DISCRETE WAVELET PACKET TRANSFORM

The fast development of digital image processing leads to the growth of feature extraction of images which leads to the development of Image fusion. Image fusion is defined as the process of combining two or more different images into a new single image retaining important features from each image with extended information content. There are two approaches to image fusion, namely spatial fusion and multi scale transform fusion. In spatial fusion, the pixel values from the source images are directly summed up and taken average to form the pixel of the composite image at that location. Multi scale transform fusion uses transform for representing the source image at multi scale. The most common widely used transform for image fusion at multi scale is Discrete Wavelet Transform (DWT) since it minimizes structural distortions. But, wavelet transform suffers due to poor directionality and does not provide a geometrically oriented decomposition in multiple directions. One way to generalize the discrete wavelet transform so as to generate a structured dictionary of base is given by the Discrete Wavelet Packet Transform (DWPT). This benefit comes from the ability of the wavelet packets to better represent high frequency content and high frequency oscillating signals in particular. However, it is well known that both DWT and DWPT are shift varying. The Dual Tree Discrete Wavelet Transform (DTDWT) introduced by Kingsbury, is approximately shift -invariant and provides directional analysis. And there are three levels for image fusion namely pixel level, area level and region level. In this paper, it is proposed to implement area level fusion of multi focused images using Dual Tree Discrete Wavelet Packet Transform (DTDWPT), extending the DTDWT as the DWPT extends the DWT and the performance is measured in terms of various performance measures like root mean square error, peak signal to noise ratio, quality index and normalized weighted performance metric.

The wavelet packet transform: A technique for investigating temporal variation of river water solutes

Understanding factors influencing river water quality is of increasing importance. We are now able to intensively monitor water variables resulting in large time series which can be used to facilitate this understanding. These time series represent the aggregation of many complex processes driven by external factors and occurring at different temporal scales. The challenge is to use the time series to elucidate the dominant climatic, hydrological and biogeochemical processes occurring at each temporal scale (or frequency). The time series are typically non-stationary and so classical methods, such as Fourier analysis, are not suitable. In this paper we demonstrate that the Discrete wavelet packet transform (DWPT) and an adaptation of this (the Maximal Overlap DWPT—MODWPT) are appropriate tools for analysing these complex signals. We exemplify this by considering measurements of nitrate and chloride concentration, temperature and discharge from the Taw River, Devon, UK. The wavelet analysis is able to distinguish frequency specific behaviour as well as intermittent events that were not visually apparent in the original time series. We find supporting evidence for observations made on similar systems by other workers and make some additional observations. We conclude that the MODWPT is an important tool which can help hydrologists and biogeochemists gain insight into the complex behaviour of catchment systems.

On the Dual-Tree Complex Wavelet Packet and $M$-Band Transforms

<para xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> The two-band discrete wavelet transform (DWT) provides an octave-band analysis in the frequency domain, but this might not be “optimal” for a given signal. The discrete wavelet packet transform (DWPT) provides a dictionary of bases over which one can search for an optimal representation (without constraining the analysis to an octave-band one) for the signal at hand. However, it is well known that both the DWT and the DWPT are shift-varying. Also, when these transforms are extended to 2-D and higher dimensions using tensor products, they do not provide a geometrically oriented analysis. The dual-tree complex wavelet transform <formula formulatype="inline"><tex>$({\hbox {DT}}{\hbox {-}}\BBC{\hbox {WT}})$</tex></formula>, introduced by Kingsbury, is approximately shift-invariant and provides directional analysis in 2-D and higher dimensions. In this paper, we propose a method to implement a dual-tree complex wavelet packet transform <formula formulatype="inline"><tex>$({\hbox {DT}}{\hbox {-}}\BBC{\hbox {WPT}})$</tex></formula>, extending the <formula formulatype="inline"><tex>${\hbox {DT}}{\hbox {-}}\BBC{\hbox {WT}}$</tex> </formula> as the DWPT extends the DWT. To find the best complex wavelet packet frame for a given signal, we adapt the basis selection algorithm by Coifman and Wickerhauser, providing a solution to the basis selection problem for the <formula formulatype="inline"><tex>${\hbox {DT}}{\hbox {-}}\BBC{\hbox {WPT}}$</tex></formula>. Lastly, we show how to extend the two-band <formula formulatype="inline"><tex>${\hbox {DT}}{\hbox {-}}\BBC{\hbox {WT}}$</tex> </formula> to an <formula formulatype="inline"><tex>$M$</tex></formula>-band <formula formulatype="inline"><tex>${\hbox {DT}}{\hbox {-}}\BBC{\hbox {WT}}$</tex> </formula> (provided that <formula formulatype="inline"><tex>$M=2^{b}$</tex> </formula>) using the same method. </para>

Compression of Biomedical Signals With Mother Wavelet Optimization and Best-Basis Wavelet Packet Selection

We propose a novel scheme for signal compression based on the discrete wavelet packet transform (DWPT) decompositon. The mother wavelet and the basis of wavelet packets were optimized and the wavelet coefficients were encoded with a modified version of the embedded zerotree algorithm. This signal dependant compression scheme was designed by a two-step process. The first (internal optimization) was the best basis selection that was performed for a given mother wavelet. For this purpose, three additive cost functions were applied and compared. The second (external optimization) was the selection of the mother wavelet based on the minimal distortion of the decoded signal given a fixed compression ratio. The mother wavelet was parameterized in the multiresolution analysis framework by the scaling filter, which is sufficient to define the entire decomposition in the orthogonal case. The method was tested on two sets of ten electromyographic (EMG) and ten electrocardiographic (ECG) signals that were compressed with compression ratios in the range of 50%-90%. For 90% compression ratio of EMG (ECG) signals, the percent residual difference after compression decreased from (mean +/- SD) 48.6 +/- 9.9% (21.5 +/- 8.4%) with discrete wavelet transform (DWT) using the wavelet leading to poorest performance to 28.4 +/- 3.0% (6.7 +/- 1.9%) with DWPT, with optimal basis selection and wavelet optimization. In conclusion, best basis selection and optimization of the mother wavelet through parameterization led to substantial improvement of performance in signal compression with respect to DWT and randon selection of the mother wavelet. The method provides an adaptive approach for optimal signal representation for compression and can thus be applied to any type of biomedical signal.

Comparison of Speech Features on the Speech Recognition Task

In the present work we overview some recently proposed discrete Fourier transform (DFT)- and discrete wavelet packet transform (DWPT)-based speech parameterization methods and evaluate their performance on the speech recognition task. Specifically, in order to assess the practical value of these less studied speech parameterization methods, we evaluate them in a common experimental setup and compare their performance against traditional techniques, such as the Mel-frequency cepstral coefficients (MFCC) and perceptual linear predictive (PLP) cepstral coefficients which presently dominate the speech recognition field. In particular, utilizing the well established TIMIT speech corpus and employing the Sphinx-III speech recognizer, we present comparative results of 8 different speech parameterization techniques.

Efficient VLSI Architecture for Lifting-Based Discrete Wavelet Packet Transform

This brief presents a novel very large-scale integration (VLSI) architecture for discrete wavelet packet transform (DWPT). By exploiting the in-place nature of the DWPT algorithm, this architecture has an efficient pipeline structure to implement high-throughput processing without any on-chip memory/first-in first out access. A folded architecture for lifting-based wavelet filters is proposed to compute the wavelet butterflies in different groups simultaneously at each decomposition level. According to the comparison results, the proposed VLSI architecture is more efficient than the previous proposed architectures in terms of memory access, hardware regularity and simplicity, and throughput. The folded architecture not only achieves a significant reduction in hardware cost but also maintains both the hardware utilization and high-throughput processing with comparison to the direct mapped tree-structured architecture

An investigation of the multi-scale temporal variability of beach profiles at Duck using wavelet packet transforms

In an earlier paper a particular discrete wavelet transform (DWT) was used to study the complex variation of beach profile changes. However, use of the DWT requires that the sequence of spatial and temporal resolution is fixed as a dyadic sequence, which means that the variability over longer intervals is not characterised well. Here we introduce the discrete wavelet packet transform (DWPT) that uses an adaptive scaling to partition the data variance, according to an entropy cost function. The advantages of this approach are demonstrated by its application to the study of temporal variability of a 22 year record of beach profile data from the Field Research Facility (FRF) at Duck, North Carolina, USA. Time series of beach elevations at three locations across a particular profile are investigated in detail. We conclude that the DWPT provides a superior analysis of non-stationary time series to that of the DWT, with improved resolution of the scale intervals of the variability. The beach elevation around the shoreline is shown to respond at both sub-annual and interannual scales, but variability at an annual scale is weak. Moving seaward into deeper water, the variance is partitioned into fewer and longer scales. It is confirmed that elevation changes around the inner bar at Duck exhibit a strong interannual variation consistent with Plant et al. (Plant, N.G., Holman, R.A. and Freilich, M.H., 1999. A simple model for interannual sandbar behaviour. Journal of Geophysical Research 104(C7), 15755–15776). Around 23% of the variance around the inner bar is explained at the temporal scale of 64–128 months, which is consistent with the bar behaviour of 6 years found by Ruessink et al. (Ruessink, B. G., Wijnberg, K. M., Holman, R. A., Kuriyama, Y. and Van Enckevort, I. M. J., 2003. Intersite comparison of interannual nearshore bar behaviour. Journal of Geophysical Research, 108 (C8): 1–12). A significant new finding is, however, that about 26% of the variance is attributable to temporal scales of 16–21.3 months. Reconstruction of the wavelet packet components for individual temporal scales is shown to provide a means for identifying the impact and scale of non-stationary events, such as storms, on the beach response. This provides further information that can be used to interpret the morphological changes in terms of the forcing processes and also serves to inform morphodynamic modelling.

The representation of complex soil variation on wavelet packet bases

SummaryThe discrete wavelet packet transform (DWPT) is an advanced wavelet technique that has distinct advantages over the discrete wavelet transform (DWT) previously used in soil science. Because the DWT divides the spatial frequencies of the data into non‐uniform intervals, it may fail to resolve features of the spatial variation that a simpler spectral analysis might identify under stationary conditions. However, the DWPT allows us to retain the advantages of the DWT (particularly the lack of stationarity assumptions) while achieving much better resolution in the spatial frequency domain. This is at the cost of poorer spatial resolution at the higher frequencies. However, by selecting a best wavelet packet basis from among the many possible, according to some appropriate criterion, we can find a compromise between frequency and spatial resolution that is best suited to the representation of our particular data set. In this paper, I describe a number of analyses based on the DWPT and apply them to two data sets on the soil. The advantages of the DWPT with best basis selection are clearly illustrated. In particular, non‐stationary behaviour of a significant periodic component of variation was identified that could not be effectively resolved by the DWT. Improved resolution in the frequency domain allowed aspects of the non‐stationary variation of soil to be resolved in a multiresolution analysis (MRA) adapted to the variation of the data.