Speech frame recognition based on less shift sensitive wavelet filter banks

The wavelet transform possesses multi-resolution property and high localization performance; hence, it can be optimized for speech recognition. In our previous work, we show that redundant wavelet filter bank parameters work better in speech recognition task, because they are much less shift sensitive than those of critically sampled discrete wavelet transform (DWT). In this paper, three types of wavelet representations are introduced, including features based on dual-tree complex wavelet transform (DT-CWT), perceptual dual-tree complex wavelet transform, and four-channel double-density discrete wavelet transform (FCDDDWT). Then, appropriate filter values for DT-CWT and FCDDDWT are proposed. The performances of the proposed wavelet representations are compared in a phoneme recognition task using special form of the time-delay neural networks. Performance evaluations confirm that dual-tree complex wavelet filter banks outperform conventional DWT in speech recognition systems. The proposed perceptual dual-tree complex wavelet filter bank results in up to approximately 9.82 % recognition rate increase, compared to the critically sampled two-channel wavelet filter bank.     

Multiple Hypothesis Mapping of Functional MRI Data in Orthogonal and Complex Wavelet Domains

We are interested in methods for multiple hypothesis testing that optimize power to refute the null hypothesis while controlling the false discovery rate (FDR). The wavelet transform of a spatial map of brain activation statistics can be tested in two stages to achieve this objective: First, a set of possible wavelet coefficients to test is reduced, and second, each hypothesis in the remaining subset is formally tested. We show that a Bayesian bivariate shrinkage operator (BaybiShrink) for the first step provides a powerful and expedient alternative to a subband adaptive chi-squared test or an enhanced FDR algorithm based on the generalized degrees of freedom. We also investigate the dual-tree complex wavelet transform (CWT) as an alternative basis to the orthogonal discrete wavelet transform (DWT). We design and validate a test for activation based on the magnitude of the complex wavelet coefficients and show that this confers improved specificity for mapping spatial signals. The methods are applied to simulated and experimental data, including a pharmacological magnetic resonance imaging (MRI) study. We conclude that using BaybiShrink to define a reduced set of complex wavelet coefficients, and testing the magnitude of each complex pair to control the FDR, represents a competitive solution for multiple hypothesis mapping in fMRI.     

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DT-CWT与TVAR的多雷达信号融合

针对目标散射回波数据非平稳的特点,本文提出了一种基于DT-CWT与TVAR的雷达信号融合方法。本文利用复小波对雷达信号进行分解,然后对各个小波子空间上的信号进行TVAR建模预测,最后再通过复小波重构雷达信号, 并对两部雷达信号进行幅相补偿和融合,从而获得了超分辨的雷达一维距离像。     

Application of the dual-tree wavelet transform for digital filtering of noisy audio signals

The problem of refinement of the quality of filtering of noisy audio signals with the help of the methods based on a discrete wavelet transform with real bases and a dual-tree (complex) wavelet transform using analytical wavelets as basis functions is considered. Test examples and processing of experimental data have shown that, in the case of the optimum selection of the threshold level, the approach using the dual-tree wavelet transform ensures the minimum signal reconstruction error after correction of wavelet coefficients.     

基于双树复小波变换和形态学的脉搏信号去噪

常见的医学信号（如脉搏信号）包含大量的噪声,具有强烈的非线性和非平稳性。针对传统的小波变换去噪方法的缺陷,提出了一种基于双树复小波变换和形态学的去噪算法,具有结构简单、计算复杂度低等优点,有效地克服了离散小波变换的平移敏感性和频率混淆。实验表明,该算法可以有效地去除脉搏信号中工频干扰及肌电干扰等高频噪声,其信噪比及均方差等定量指标均明显优于传统的阈值去噪算法,能得到较干净的脉搏信号波形。     

一种有效的双树复小波-Wiener滤波去噪算法

为了有效恢复被高斯白噪声污染的图像,将双树复小波变换和自适应Wiener滤波结合起来,提出了一种双树复小波-Wiener滤波去噪算法.仿真结果表明,利用该算法去噪后恢复的图像主观质量和峰值信噪比比基于正交小波变换的门限法和Wiener滤波法都要好.     

基于KL距离和双密度小波变换的纹理图像检索

为了进一步提纹理图像的检索性能，提出了一种基于双密度小波的算法。该算法根据双密度小波分解的特点。从系数角度出发首先进行子带组合，然后提取子带小波系数直方图分布特性作为纹理特征。利用最大似然估计规则将特征提取和相似计算结合起来．采用KL距离进行度量．与单小波和双密度小波方法比较．该算法具有时移不变性、特证数少等特点。理论分析和纹理图像检索的对比实验数据说明了组合双密度小波在纹理特征提取方面的性能优于单小波和双密度小波。检索率分别提高了。     

The phaselet transform-an integral redundancy nearly shift-invariant wavelet transform

This paper introduces an approximately shift invariant redundant dyadic wavelet transform - the phaselet transform - that includes the popular dual-tree complex wavelet transform of Kingsbury (see Phil. R. Soc. London A, Sept. 1999) as a special case. The main idea is to use a finite set of wavelets that are related to each other in a special way - and hence called phaselets - to achieve approximate shift-redundancy; the bigger the set, the better the approximation. A sufficient condition on the associated scaling filters to achieve this is that they are fractional shifts of each other. Algorithms for the design of phaselets with a fixed number vanishing moments is presented - building on the work of Selesnick (see IEEE Trans. Signal Processing) for the design of wavelet pairs for Kingsbury's dual-tree complex wavelet transform. Construction of two-dimensional (2-D) directional bases from tensor products of one-dimensional (1-D) phaselets is also described. Phaselets as a new approach to redundant wavelet transforms and their construction are both novel and should be interesting to the reader, independent of the approximate shift invariance property that this paper argues they possess.     

复轮廓波包变换及其在SAR图像去斑中的应用

利用解析的双树复小波包变换(DT-CWPT)与非抽样方向滤波器组(NSDFB),构造了一种复轮廓波包变换(CCPT),并将其应用于合成孔径雷达(SAR)图像去斑。新的变换由于对信号的低频和高频部分都进行了分解,因此除了具有多分辨率、局部性、方向性和各向异性的特点外,还具有平移不变性和更丰富的方向分量。实验结果表明,本文构造的CCPT能够有效地抑制斑点噪声,达到较好的边缘保持效果,并且在图像的细节和纹理表现方面具有一定的优势。     

The double-density dual-tree DWT

This paper introduces the double-density dual-tree discrete wavelet transform (DWT), which is a DWT that combines the double-density DWT and the dual-tree DWT, each of which has its own characteristics and advantages. The transform corresponds to a new family of dyadic wavelet tight frames based on two scaling functions and four distinct wavelets. One pair of the four wavelets are designed to be offset from the other pair of wavelets so that the integer translates of one wavelet pair fall midway between the integer translates of the other pair. Simultaneously, one pair of wavelets are designed to be approximate Hilbert transforms of the other pair of wavelets so that two complex (approximately analytic) wavelets can be formed. Therefore, they can be used to implement complex and directional wavelet transforms. The paper develops a design procedure to obtain finite impulse response (FIR) filters that satisfy the numerous constraints imposed. This design procedure employs a fractional-delay allpass filter, spectral factorization, and filterbank completion. The solutions have vanishing moments, compact support, a high degree of smoothness, and are nearly shift-invariant.     

基于局部方向能量的鲁棒图像融合算法

针对现有小波类图像融合算法在特征表达上的不足,将对偶树复数小波变换引入图像融合中。Robins等的研究表明,局部能量对各类图像特征的表达和定位具有稳健性。基于对偶树复数小波变换,定义了局部方向能量和局部能量,结合人类视觉系统对图像特征的响应特性,定义了局部带限对比度,表达特征的显著性。实时图像融合系统中,输入可能被随机噪声污染。根据图像特征和噪声局部方向能量分布不同的特点,定义了局部方向能量熵,用以自适应改善带限对比度,提高融合过程对噪声的鲁棒性。对融合算法仿真结果的主客观性能分析,充分验证了本文提出的鲁棒的图像融合算法的卓越性能。     

Face Recognition Using Dual-Tree Complex Wavelet Features

We propose a novel facial representation based on the dual-tree complex wavelet transform for face recognition. It is effective and efficient to represent the geometrical structures in facial image with low redundancy. Moreover, we experimentally verify that the proposed method is more powerful to extract facial features robust against the variations of shift and illumination than the discrete wavelet transform and Gabor wavelet transform.     

基于双树复小波变换的多聚焦图像融合方法

针对同一场景的多聚焦图像融合,提出了一种基于双树复小波变换(DT-CWT)的图像融合新算法.首先利用DT-CWT对图像进行多尺度和多方向分解,并根据双树复小波分解域各子带的系数特性定义了图像局部方向对比度,然后针对高频分量系数的选择,采用基于方向对比度的融合规则,而在低频域采用图像清晰度为测度的融合策略.实验结果表明,该算法能够很好地将多聚焦图像中的重要信息提取并注入到融合图像中,与其他方法相比较,取得了更好的融合效果,提高了融合图像的质量.     

Dual-tree complex wavelet hidden Markov tree model for image denoising

A new non-training complex wavelet hidden Markov tree (HMT) model, which is based on the dual-tree complex wavelet transform and a fast parameter estimation technique, is proposed for image denoising. This new model can mitigate the two problems (high computational cost and shift-variance) of the conventional wavelet HMT model simultaneously. Experiments show that the denoising approach with this new model achieves better performance than other related HMT- based image denoising algorithms.     

基于非抽样复轮廓波变换的图像去噪算法研究

将二维双树复小波变换(DT-CWT)与非抽样方向滤波器组(NSDFB)相结合,构造一种新的非抽样复轮廓波变换(NSCCT),并对其平移不变性作了相应证明。同时利用对称的正态逆高斯(NIG)分布先验概率模型和贝叶斯最小均方算法,提出一种基于NSCCT的图像去噪算法。实验结果表明,本文构造的NSCCT能够有效地抑制伪Gibbs现象,并且具有更丰富的方向分量,因而在图像的细节和纹理表现方面有一定的优势。     

Low-light image enhancement based on Retinex theory and dual-tree complex wavelet transform

In order to enhance the contrast of low-light images and reduce noise in them, we propose an image enhancement method based on Retinex theory and dual-tree complex wavelet transform (DT-CWT). The method first converts an image from the RGB color space to the HSV color space and decomposes the V-channel by dual-tree complex wavelet transform. Next, an improved local adaptive tone mapping method is applied to process the low frequency components of the image, and a soft threshold denoising algorithm is used to denoise the high frequency components of the image. Then, the V-channel is rebuilt and the contrast is adjusted using white balance method. Finally, the processed image is converted back into the RGB color space as the enhanced result. Experimental results show that the proposed method can effectively improve the performance in terms of contrast enhancement, noise reduction and color reproduction.     

基于Mellin变换的连续小波变换快速算法

连续小波变换（CWT）快速算法的研究对于小波变换在信号处理领域更加广泛，深入的应用有重要意义．本文提出一种基于Mellin变换的CWT快速算法，其特点是一次算出某一固定时刻各个灰度的变换结果．算法的计算量与待分析信号的数据长度成正比，在任一时刻下为两个2N点FFT和一次2N点复数乘法（N为分析尺度个数）．该算法适用于尺度跨度较小，对尺度分析要求较细的应用场合。     

Simple algorithm for wavelet maxima modulus extraction intime-scale representations

A simple algorithm is presented to extract the local maxima moduli from time-scale representations of the continuous wavelet transform (CWT). Local features of complex signals embedded in noise can be detected easily when applied to this algorithm     

一种敌我识别辐射源暂态信号指纹特征提取方法

信号的指纹特征是辐射源个体识别的重要依据。针对敌我识别辐射源的个体识别问题,提出了一种基于双树复小波和多重分形的信号暂态特征提取方法。该方法通过双树复小波变换实现信号多分辨率分解,求解分解信号Hilbert谱的信息熵和指数熵,计算信号的多重分形奇异指数和谱值,最终组成表征辐射源的特征向量。通过实验验证,提取的特征向量能充分代表辐射源个体之间的差异;被测信号的信噪比满足8 dB或9 dB的条件时,对辐射源的识别正确率能达到90%以上。统计分析表明该方法提取的特征具有很高的稳定性。