Embolic Doppler ultrasound signal detection using discrete wavelet transform

Asymptomatic circulating emboli can be detected by Doppler ultrasound. Embolic Doppler ultrasound signals are short duration transient like signals. The wavelet transform is an ideal method for analysis and detection of such signals by optimizing time-frequency resolution. We propose a detection system based on the discrete wavelet transform (DWT) and study some parameters, which might be useful for describing embolic signals (ES). We used a fast DWT algorithm based on the Daubechies eighth-order wavelet filters with eight scales. In order to evaluate feasibility of the DWT of ES, two independent data sets, each comprising of short segments containing an ES (N=100), artifact (N=100) or Doppler speckle (DS) (N=100), were used. After applying the DWT to the data, several parameters were evaluated. The threshold values used for both data sets were optimized using the first data set. While the DWT coefficients resulting from artifacts dominantly appear at the higher scales (five, six, seven, and eight), the DWT coefficients at the lower scales (one, two, three, and four) are mainly dominated by ES and DS. The DWT is able to filter out most of the artifacts inherently during the transform process. For the first data set, 98 out of 100 ES were detected as ES. For the second data set, 95 out of 100 ES were detected as ES when the same threshold values were used. The algorithm was also tested with a third data set comprising 202 normal ES; 198 signals were detected as ES.     

Multiview image coding using depth layers and an optimized bit allocation

In this paper, we present a novel wavelet-based compression algorithm for multiview images. This method uses a layer-based representation, where the 3-D scene is approximated by a set of depth planes with their associated constant disparities. The layers are extracted from a collection of images captured at multiple viewpoints and transformed using the 3-D discrete wavelet transform (DWT). The DWT consists of the 1-D disparity compensated DWT across the viewpoints and the 2-D shape-adaptive DWT across the spatial dimensions. Finally, the wavelet coefficients are quantized and entropy coded along with the layer contours. To improve the rate-distortion performance of the entire coding method, we develop a bit allocation strategy for the distribution of the available bit budget between encoding the layer contours and the wavelet coefficients. The achieved performance of our proposed scheme outperforms the state-of-the-art codecs for several data sets of varying complexity.     

Application of the robust discrete wavelet transform to signal detection in underwater sound

This paper applies the notion of robust discrete wavelet transform (robust DWT) to recursive density estimation as a solution to detecting multipath signals underwater. Though there are no obvious distribution assumptions that can be made to model underwater noise, a recursive density estimator of the initial background noise reconstructed by the discrete wavelet transform (DWT) can be established as an empirical model. Observations that are identified as an outlier are then flagged as potential signals. In a multipath environment, where many signal components arrive with arbitrary delays, the DWT's lack of translation invariance is a problem for processing multipath signals. We adopt a robust DWT as a solution. Using an iterative algorithm in the Zak domain, a scaling function can be turned to a robust one. By designing a robust scaling function we can obtain a robust DWT. The performance of the robust DWT, exhibiting much better shift invariance than the conventional DWT, is illustrated. Utilizing the robust DWT reconstruction to establish the recursive density estimator of the underwater background noise, the ability to detect a multipath signal in an underwater environment is improved compared to that of the conventional DWT.     

9/7提升小波变换图像处理算法的高速FPGA实现

提升结构(Lifting Scheme)是一种新的双正交小波变换构造方法.这种方法使得计算复杂度大大降低,有效地减少了运行时间.介绍了基于FPGA的高速9/7提升小波变换的设计,提出采用多级流水线硬件结构实现一维离散小波变换(1-D DWT).该结构使系统吞吐量提高到原来的3倍,面积仅增加40%.在实现二维离散小波变换(2-D DWT)时采用基于行的结构,可以提高片内资源利用率和运行速度,满足小波变换实时性的要求.     

A novel wavelet transform-based transient current analysis for fault detection and localization

Transient current (IDD) testing has been often cited and investigated as an alternative and/or supplement to quiescent current (IDDQ) testing. In this correspondence, we present a novel integrated method for fault detection and localization using wavelet transform-based IDD waveform analysis. The time-frequency resolution property of wavelet transform helps us detect as well as localize faults in digital CMOS circuits. Experiments performed on measured data from a fabricated 8-bit shift register, and simulation data from more complex circuits show promising results for both detection and localization. Wavelet-based detection method shows better sensitivity than spectral and time-domain methods. Effectiveness of the localization method in presence of complex power supply network, measurement noise, and process variation is also addressed.     

基于混合变换域的数字水印算法

提出了一种基于二维离散小波变换(DWT)和离散余弦变换(DCT)的混合变换域数字水印算法。通过小波变换得到载体图像的高频和低频系数,将低频系数作为一个子图像;再将二值水印图像置乱并编码,在子图像的离散余弦变换得到的系数中嵌入水印。该方法在水印检测和提取过程中都不需要原始图像。实验表明该方法水印隐藏性好,鲁棒性较好,抵抗放缩和局部攻击有很好的表现。     

基于小波分析和人工免疫算法的模拟电路故障诊断

受生物免疫系统自己-非己识别过程的启发,提出了一种基于小波分析和人工免疫算法的模拟电路故障诊断的新方法。该方法首先利用小波变换,归一化和主元分析法作为预处理提取模拟电路的最优故障特征向量,然后利用反面选择算法的检测器对故障信息进行检测,从而实现模拟电路故障的分类。计算机仿真证明该方法是可行的。     

Discrete wavelet transform: data dependence analysis and synthesisof distributed memory and control array architectures

We perform a thorough data dependence and localization analysis for the discrete wavelet transform algorithm and then use it to synthesize distributed memory and control architectures for its parallel computation. The discrete wavelet transform (DWT) is characterized by a nonuniform data dependence structure owing to the decimation operation it is neither a uniform recurrence equation (URE) nor an affine recurrence equation (ARE) and consequently cannot be transformed directly using linear space-time mapping methods into efficient array architectures. Our approach is to apply first appropriate nonlinear transformations operating on the algorithm's index space, leading to a new DWT formulation on which application of linear space-time mapping can become effective. The first transformation of the algorithm achieves regularization of interoctave dependencies but alone does not lead to efficient array solutions after the mapping due to limitations associated with transforming the three-dimensional (3-D) algorithm onto one-dimensional (1-D) arrays, which is also known as multiprojection. The second transformation is introduced to remove the need for multiprojection by formulating the regularized DWT algorithm in a two-dimensional (2-D) index space. Using this DWT formulation, we have synthesized two VLSI-amenable linear arrays of LPEs computing a 6-octave DWT decomposition with latencies of M and 2M-1, respectively, where L is the wavelet filter length, and M is the number of samples in the data sequence. The arrays are modular, regular, use simple control, and can be easily extended to larger L and J. The latency of both arrays is independent of the highest octave J, and the efficiency is nearly 100% for any M with one design achieving the lowest possible latency of M     

A Programmable Parallel VLSI Architecture for 2-D Discrete Wavelet Transform

Many VLSI architectures for computing the discrete wavelet transform (DWT) were presented, but the parallel input data sequence and the programmability of the 2-D DWT were rarely mentioned. In this paper, we present a parallel-processing VLSI architecture to compute the programmable 2-D DWT, including various wavelet filter lengths and various wavelet transform levels. The proposed architecture is very regular and easy for extension. To eliminate high frequency components, the pixel values outside the boundary of the image are mirror-extended as the symmetric wavelet transform (SWT) and the mirror-extension is realized via the routing network. Owing to the property of the parallel processing, we adopt the row-based recursive pyramid algorithm (RPA), similar to 1-D RPA, as the data scheduling. This design has been implemented and fabricated in a 0.35 m 1P4M CMOS technology and the working frequency is 50 MHz. The chip size is about 5200 m × 2500 m. For a 256 × 256 image, the chip can perform 30 frames per second with the filter length varying from 2 to 20 and with various levels. The proposed architecture is suitable for real-time applications such as JPEG 2000.     

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

The two-band discrete wavelet transform (DWT) provides an octave-band analysis in the frequency domain, but this might not be ldquooptimalrdquo 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 , 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 , extending the 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 . Lastly, we show how to extend the two-band to an -band (provided that ) using the same method.     

基于小波变换的自适应QRS-T对消P波检测算法

该文提出一种基于小波变换的自适应QRS-T对消P波检测算法。首先采用二进Marr小波的Mallat算法对心电信号作多尺度分解,在每个尺度下只保留超过一定阈值的小波模极大值点,其它点置零处理。在小波分解的3,4尺度下检测QRS波群,并根据心拍节律信息和QT间期,将QRS-T波群所对应的小波模极大值点进行自适应对消,最后对包含P波的剩余信号进行非线性放大,利用小波模极大值的自适应阈值检测方法定位P波。该方法经MIT-BIH心电数据库数据验证,取得了满意的结果。     

Image compression using bit-plane coding of wavelet coefficients

The authors propose new simple image coder based on a discrete wavelet transform (DWT). The DWT coefficients are coded in bit-planes. They use an improved version of the JBIG bi-level image compression method to code the DWT coefficient bit-planes. The experimental results are shown, both in distortion measurement and visual comparison, and are very promising     

Asymptotic decorrelation of between-Scale Wavelet coefficients

In recent years there has been much interest in the analysis of time series using a discrete wavelet transform (DWT) based upon a Daubechies wavelet filter. Part of this interest has been sparked by the fact that the DWT approximately decorrelates certain stochastic processes, including stationary fractionally differenced (FD) processes with long memory characteristics and certain nonstationary processes such as fractional Brownian motion. It is shown that, as the width of the wavelet filter used to form the DWT increases, the covariance between wavelet coefficients associated with different scales decreases to zero for a wide class of stochastic processes. These processes are Gaussian with a spectral density function (SDF) that is the product of the SDF for a (not necessarily stationary) FD process multiplied by any bounded function that can serve as an SDF on its own. We demonstrate that this asymptotic theory provides a reasonable approximation to the between-scale covariance properties of wavelet coefficients based upon filter widths in common use. Our main result is one important piece of an overall strategy for establishing asymptotic results for certain wavelet-based statistics.     

Microarray image enhancement by denoising using decimated and undecimated multiwavelet transforms

In this paper, we present a new approach to deal with the noise inherent in the microarray image processing procedure. We use the denoising capabilities of decimated and undecimated multiwavelet transforms, DMWT and UMWT respectively, for the removal of noise from microarray data. Multiwavelet transforms, with appropriate initialization, provide sparser representation of signals than wavelet transforms so that their difference from noise can be clearly identified. Also, the redundancy of the UMWT transform is particularly useful in image denoising in order to capture the salient features such as noise or transients. We compare this method with the discrete and stationary wavelet transforms, denoted by DWT and SWT, respectively, and the Wiener filter for denoising microarray images. Results show enhanced image quality using the proposed approach, especially in the undecimated case in which the results are comparable and often outperform that of the stationary wavelet transform. Both multiwavelet transforms outperform the DWT and the Wiener filter.     

A translation- and scale-invariant adaptive wavelet transform

This paper presents a new approach to deal with the translation- and scale-invariant problem of the discrete wavelet transform (DWT). Using a signal-dependent filter, whose impulse response is calculated by the first two moments of the original signal and a scale function of an orthonormal wavelet, we adaptively renormalized a signal. The renormalized signal is then decomposed by using the algorithm of the conventional DWT. The final wavelet transform coefficients, called adaptive wavelet invariant moments (AWIM), are proved to be both translation- and scale-invariant. Furthermore, as an application, we define a new textural feature in the framework of our adaptive wavelet decomposition, show its stability to shift and scaling, and demonstrate its efficiency for the task of scale-invariant texture identification.     

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.     

CCSDS中二维整数小波变换的FPGA实现方法

CCSDS空间图像压缩标准(CCSDS 122.0-B-1)的核心算法之一是三级二维小波变换,此变换适合用可编程逻辑电路实现。文章介绍了整数9/7小波变换的特点,提出了一种基于FPGA的二维变换快速实现结构,该方法利用FPGA内部Block RAM进行行暂存,实现了行列同时变换的效果,节省了内部寄存器资源,并获得了较高的数据吞吐率。在此基础上,文章还给出了两种适用于不同需求的多级变换架构,并通过仿真验证了其合理性。     

Multitaper power spectrum estimation and thresholding: wavelet packets versus wavelets

It was suggested that spectrum estimation can be accomplished by applying wavelet denoising methodology to wavelet packet coefficients derived from the logarithm of a spectrum estimate. The particular algorithm we consider consists of computing the logarithm of the multitaper spectrum estimator, applying an orthonormal transform derived from a wavelet packet tree to the log multitaper spectrum ordinates, thresholding the empirical wavelet packet coefficients, and then inverting the transform. For a small number of tapers, suitable transforms/partitions for the logarithm of the multitaper spectrum estimator are derived using a method matched to statistical thresholding properties. The partitions thus derived starting from different stationary time series are all similar and easily derived, and any differences between the wavelet packet and discrete wavelet transform (DWT) approaches are minimal. For a larger number of tapers, where the chosen parameters satisfy the conditions of a proven theorem, the simple DWT again emerges as appropriate. Hence, using our approach to thresholding and the method of partitioning, we conclude that the DWT approach is a very adequate wavelet-based approach and that the use of wavelet packets is unnecessary.     

基于改进经验小波变换的时频分析方法及其在滚动轴承故障诊断中的应用

经验小波变换是最近提出的非平稳信号分析方法,针对其不足,提出了一种改进的经验小波变换方法;同时结合瞬时频率新定义,提出了一种非平稳信号时频分析新方法.该方法首先通过改进的经验小波变换将一个复杂的非平稳信号自适应地分解为若干个具有紧支集频谱的内禀模态函数之和;再通过对每个内禀模态函数进行解调,得到原始信号的时频分布.将提出的方法应用于滚动轴承试验数据分析,并将其与希尔伯特黄变换进行了对比,结果表明,论文提出的方法能够有效地诊断滚动轴承故障,且诊断效果优于希尔伯特黄变换方法.     

一种二维离散子波变换的滤波器结构

子波变换具有良好的时间（空间）频率局部化性能，在图象子带编码中二维离散子波变换是一种接近理想的子带分析／综合子系统．本文提出一种利用一维离散子波变换实现二维有限长离散子波变换的方法，同时给出了二维离散子波正变换（DWT）和反变换（IDWT）的滤波器实现结构．实验结果表明新的方法具有良好的重构性，完全适用于图象压缩编码系统中的分析／综合子系统．