Wavelet and wavelet packet compression of electrocardiograms

Wavelets and wavelet packets have recently emerged as powerful tools for signal compression. Wavelet and wavelet packet-based compression algorithms based on embedded zerotree wavelet (EZW) coding are developed for electrocardiogram (ECG) signals, and eight different wavelets are evaluated for their ability to compress Holter ECG data. Pilot data from a blind evaluation of compressed ECG's by cardiologists suggest that the clinically useful information present in original ECG signals is preserved by 8:1 compression, and in most cases 16:1 compressed ECG's are clinically useful     

Fast adaptive wavelet packet image compression

Wavelets are ill-suited to represent oscillatory patterns: rapid variations of intensity can only be described by the small scale wavelet coefficients, which are often quantized to zero, even at high bit rates. Our goal is to provide a fast numerical implementation of the best wavelet packet algorithm in order to demonstrate that an advantage can be gained by constructing a basis adapted to a target image. Emphasis is placed on developing algorithms that are computationally efficient. We developed a new fast two-dimensional (2-D) convolution decimation algorithm with factorized nonseparable 2-D filters. The algorithm is four times faster than a standard convolution-decimation. An extensive evaluation of the algorithm was performed on a large class of textured images. Because of its ability to reproduce textures so well, the wavelet packet coder significantly out performs one of the best wavelet coder on images such as Barbara and fingerprints, both visually and in term of PSNR.     

Wavelet packet division multiplexing and wavelet packet designunder timing error effects

Wavelet packet division multiplexing (WPDM) is a multiple signal transmission technique in which the message signals are waveform coded onto wavelet packet basis functions for transmission. The overlapping nature of such waveforms in time and frequency provides a capacity improvement over the commonly used frequency division multiplexing (FDM) and time division multiplexing (TDM) schemes while their orthogonality properties ensure that the overlapping message signals can be separated by a simple correlator receiver. The interference caused by timing offset in transmission is examined. A design procedure that exploits the inherent degrees of freedom in the WPDM structure to mitigate the effects of timing error is introduced, and a waveform that minimizes the energy of the timing error interference is designed. An expression for the probability of error due to the presence of Gaussian noise and timing error for the transmission of binary data is derived. The performance advantages of the designed waveform over standard wavelet packet basis functions are demonstrated by both analytical and simulation methods. The capacity improvement of WPDM, its simple implementation, and the possibility of having optimum waveform designs indicate that WPDM holds considerable promise as a multiple signal transmission technique     

Optimal wavelet denoising for phonocardiograms

Phonocardiograms (PCGs), recordings of heart sounds, have many advantages over traditional auscultation in that they may be replayed and analysed for spectral and frequency information. PCG is not a widely used diagnostic tool as it could be. One of the major problems with PCG is noise corruption. Many sources of noise may pollute a PCG including foetal breath sounds if the subject is pregnant, lung and breath sounds, environmental noise and noise from contact between the recording device and the skin. An electronic stethoscope is used to record heart sounds and the problem of extracting noise from the signal is addressed via the use of wavelets and averaging. Using the discrete wavelet transform, the signal is decomposed. Due to the efficient decomposition of heart signals, their wavelet coefficients tend to be much larger than those due to noise. Thus, coefficients below a certain level are regarded as noise and are thresholded out. The signal can then be reconstructed without significant loss of information in the signal content. The questions that this study attempts to answer are which wavelet families, levels of decomposition, and thresholding techniques best remove the noise in a PCG. The use of averaging in combination with wavelet denoising is also addressed. Possible applications of the Hilbert transform to heart sound analysis are discussed.     

Complexity-constrained best-basis wavelet packet algorithm forimage compression

The concept of adapted waveform analysis using a best-basis selection out of a predefined library of wavelet packet (WP) bases allows an efficient image representation for the purpose of compression. Image coding methods based on the best-basis WP representation have shown significant coding gains for some image classes compared with methods using a fixed dyadic structured wavelet basis, at the expense however, of considerably higher computational complexity. A modification of the best-basis method, the so-called complexity constrained best-basis algorithm (CCBB), is proposed which parameterises the complexity gap between the fast (standard) wavelet transform and the best wavelet packet basis of a maximal WP library. This new approach allows a `suboptimal' best basis to be found with respect to a given budget of computational complexity or, in other words, it offers an instrument to control the trade-off between compression speed and, coding efficiency. Experimental results are presented for image coding applications showing a highly nonlinear relationship between the rate-distortion performance and the computational complexity in such a way that a relatively small increase in complexity with respect to the standard wavelet basis results in a relatively high rate distortion gain     

Multi-domain speech compression based on wavelet packet transform

The authors present a multi-domain speech compression method based on a wavelet packet transform. The signals are compressed in domains with different time-frequency resolutions according to their energy distribution in these domains. It is shown that this method is simple to implement and is effective at compressing speech and audio signals, even at bit rates as low as 2 kbit/s     

小波包变换在指纹图像压缩中的应用实现

小波包是近年来的一个研究热点,在图像处理方面有着广泛的应用.数据压缩是伴随小波分析产生最早的应用领域.指纹自动识别系统因其本身的特殊性对指纹图像压缩提出了特殊的要求.为此,简要的介绍了小波包变换的基本原理,给出了基于小波包变换的指纹图像压缩方法.     

ECG compression method based on adaptive quantization of main wavelet packet subbands

In this study, a new compression algorithm for ECG signal is proposed based on selecting important subbands of wavelet packet transform (WPT) and applying subband-dependent quantization algorithm. To this end, first WPT was applied on ECG signal and then more important subbands are selected according to their Shannon entropy. In the next step, content-based quantization and denoising method are applied to the coefficients of the selected subbands. Finally, arithmetic coding is employed to produce compressed data. The performance of the proposed compression method is evaluated using compression rate (CR), percentage root-mean-square difference (PRD) as signal distortion, and wavelet energy-based diagnostic distortion (WEDD) as diagnostic distortion measures on MIT-BIH Arrhythmia database. The average CR of the proposed method is 29.1, its average PRD is <2.9 % and WEDD is <3.2 %. These results demonstrated that the proposed method has a good performance compared to the state-of-the-art compression algorithms.     

Synthetic aperture radar image compression using tree-structured edge-directed orthogonal wavelet packet transform

Currently, wavelet-based coding algorithms are popular for synthetic aperture radar (SAR) image compression, which is very important for reducing the cost of data storage and transmission in relatively slow channels. However, standard wavelet transform is limited by spatial isotropy of its basis functions that is not completely adapted to represent image entities like edges or textures, which means wavelet-based coding algorithms are suboptimal to image compression. In this paper, a novel tree-structured edge-directed orthogonal wavelet packet transform is proposed for SAR image compression. Inspired by the intrinsic geometric structure of images, the new transform improves the performance of standard wavelet by filtering along the regular direction first and then along the orthogonal direction with directional lifting structure. The cost function of best basis selection is designed by textural and directional information for tree-structured edge-directed orthogonal wavelet packet transform. The new transform including speckle reduction can be used to construct SAR image coder with the embedded block coding with optimal truncation for transform coefficients, and arithmetic coding for additional information. The experimental results show that the proposed approach outperforms JPEG2000 and Fast wavelet packet (FWP), both visually and item of PSNR values.     

Error-resilient packet header compression

Full packet headers consume valuable bitrate, which is especially costly in satellite links and some terrestrial wireless links. This has motivated the compression of packet headers by exploiting their correlation via using finite-state machines. The drawback is that compression in the presence of channel errors (packet loss) may result in error propagation. We offer several designs by adapting error control codes for the requirements of packet header compression in uni-directional and bi-directional links, and explore the tradeoffs in complexity, delay, and system performance. For the bi-directional link, we propose a new design called predictive hybrid ARQ and evaluate its performance. Experiments show significant gains in link-layer throughput as well as improved application layer performance demonstrated via video transfer experiments.     

Programmable wavelet packet transform processor

A programmable one-dimensional discrete wavelet packet transform processor is presented. Compared with existing architectures, the proposed processor can carry out both wavelet transforms and wavelet packet transforms, and is suitable for high-tap filters and high decomposition levels. It is small, and is especially suitable for on-chip or single-chip implementation     

Hierarchical quantization indexing for wavelet and wavelet packet image coding

In this paper, we introduce the quantization index hierarchy, which is used for efficient coding of quantized wavelet and wavelet packet coefficients. A hierarchical classification map is defined in each wavelet subband, which describes the quantized data through a series of index classes. Going from bottom to the top of the tree, neighboring coefficients are combined to form classes that represent some statistics of the quantization indices of these coefficients. Higher levels of the tree are constructed iteratively by repeating this class assignment to partition the coefficients into larger subsets. The class assignments are optimized using a rate-distortion cost analysis. The optimized tree is coded hierarchically from top to bottom by coding the class membership information at each level of the tree. Context-adaptive arithmetic coding is used to improve coding efficiency. The developed algorithm produces PSNR results that are better than the state-of-art wavelet-based and wavelet packet-based coders in literature.     

Ubiquitous packet networking and data compression

Recently clock and data synchronisation issues have prompted a rethink of how data should be communicated within embedded microprocessor systems, leading to the development of early standards for serial transmission of data using packets; these feature a symbol for delineating the end of a packet. Bounds are investigated on the potential advantage, in terms of extra data compression, if compression took place in conjunction with packetisation. The Shannon formula for a binary data source is re-derived, showing how the formula varies when compressing relatively small chunks of data into packets. Simulation results suggest that a non-trivial amount of extra compression can be obtained in this way, and that the advantage is greater for data with lower original entropy.     

最佳小波包多载波调制解调技术

本文利用离散小波包变换（ＤＷＰＴ）导出信号窨的诱导小波包基。在此基础上建立起基于ＤＷＰＴ的小波包多载波传输系统的概念,提出了最佳小波包多载波市制解调技术。技术根据给定的信道特性,采用类似于最佳基搜索城众多的小波包多载波市制解调方案中快速寻求出最佳方案,使得系统解调出的信号中所要信号与符号间干扰的信干比在不增强噪声的前提下达了最大。     

小波包分解对心理声学模型的改进

为了改变常用心理声学模型中均匀谱分析造成的时频分辨率不足的问题,采用小波包分解对信号进行分析.通过Matlab对信号进行小波包分解处理,代替常用心理声学模型的FFT,改善了时频分辨率不足的问题,且通过小波包分解得到的频带划分.比常用心理声学模型得到的频带划分更接近于人耳的临界频带,更适应于人耳的听觉特性.     

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.     

Wavelet packet modulation for orthogonally multiplexedcommunication

Utilizing multidimensional signaling techniques, a generalized multirate wavelet-based modulation format for orthogonally multiplexed communication systems is presented. Wavelet packet modulation (WPM) employs the basis functions from an arbitrary pruning of a dyadic tree structured filter bank as orthogonal pulse shapes for conventional quadrature amplitude modulation (QAM) symbols. This generalized framework affords an entire library of basis sets with increased flexibility in time-frequency (T-F) partitioning. The bandwidth efficiency and power spectral density figures of merit for the general signal are derived and shown to be that of standard QAM     

Wavelet packet modulation for wireless communications

As proven by the success of OFDM, multicarrier modulation has been recognized as an efficient solution for wireless communications. Waveform bases other than sine functions could similarly be used for multicarrier systems in order to provide an alternative to OFDM. In this paper, we study the performance of wavelet packet transform modulation (WPM) for transmission over wireless channels. This scheme is shown to be overall quite similar to OFDM but with some interesting additional features and improved characteristics. A detailed analysis of the system's implementation complexity as well as an evaluation of the influence of implementation‐related impairments are also reported. Copyright © 2004 John Wiley & Sons, Ltd.     

基于小波和小波包变换的医学图像融合比较

分别用小波变换和小波包变换对CT和PET图像进行融合,用常用的十种图像融合质量评价指标对融合效果进行比较.结果表明小波包变换的融合质量评价指标只有部分是优于小波变换的.在对CT和PET图像进行融合时,小波包并不一定更占优势,要根据自己的实际需求来决定选择使用小波变换还是小波包变换.     

Wavelet packet decomposition for spatial sound conditioning

It is well known that sound localisation is heavily dependent on frequency. Band-limited signals generally suffer from poor localisation potential. While significant effort has been invested in HRTF modelling, room acoustics and crosstalk filtering, research into alleviating the spatial system performance dependence on source spectral characteristics has been largely overlooked. The authors briefly consider how one can compensate source frequency-deficient bands that are critical to localisation with wavelet packet decomposition