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.     

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.     

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。     

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.     

A new framework for complex wavelet transforms

Although the discrete wavelet transform (DWT) is a powerful tool for signal and image processing, it has three serious disadvantages: shift sensitivity, poor directionality, and lack of phase information. To overcome these disadvantages, we introduce two-stage mapping-based complex wavelet transforms that consist of a mapping onto a complex function space followed by a DWT of the complex mapping. Unlike other popular transforms that also mitigate DWT shortcomings, the decoupled implementation of our transforms has two important advantages. First, the controllable redundancy of the mapping stage offers a balance between degree of shift sensitivity and transform redundancy. This allows us to create a directional, non-redundant, complex wavelet transform with potential benefits for image coding systems. To the best of our knowledge, no other complex wavelet transform is simultaneously directional and non-redundant. The second advantage of our approach is the flexibility to use any DWT in the transform implementation. As an example, we can exploit this flexibility to create the complex double-density DWT (CDDWT): a shift-insensitive, directional, complex wavelet transform with a low redundancy of (3/sup m/-1/2/sup m/-1) in m dimensions. To the best of our knowledge, no other transform achieves all these properties at a lower redundancy.     

Multidimensional, mapping-based complex wavelet transforms.

Although the discrete wavelet transform (DWT) is a powerful tool for signal and image processing, it has three serious disadvantages: shift sensitivity, poor directionality, and lack of phase information. To overcome these disadvantages, we introduce multidimensional, mapping-based, complex wavelet transforms that consist of a mapping onto a complex function space followed by a DWT of the complex mapping. Unlike other popular transforms that also mitigate DWT shortcomings, the decoupled implementation of our transforms has two important advantages. First, the controllable redundancy of the mapping stage offers a balance between degree of shift sensitivity and transform redundancy. This allows us to create a directional, nonredundant, complex wavelet transform with potential benefits for image coding systems. To the best of our knowledge, no other complex wavelet transform is simultaneously directional and nonredundant. The second advantage of our approach is the flexibility to use any DWT in the transform implementation. As an example, we exploit this flexibility to create the complex double-density DWT: a shift-insensitive, directional, complex wavelet transform with a low redundancy of (3M - 1)/(2M - 1) in M dimensions. No other transform achieves all these properties at a lower redundancy, to the best of our knowledge. By exploiting the advantages of our multidimensional, mapping-based complex wavelet transforms in seismic signal-processing applications, we have demonstrated state-of-the-art results.     

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.     

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.     

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.     

Combining the discrete wavelet transform and mixed-domain filtering

A novel filtering method is proposed that combines the discrete orthogonal wavelet transform (DWT) with the mixed-domain (mixed-D) filtering method. The method uses the DWT to pre- and postprocess those dimensions of the signal that are transformed to the discrete-frequency domain by mixed-D filtering. Using the DWT in this manner provides a controlled mechanism to partition the spectrum of the input signal into subband signals, which then may be selectively filtered during the linear difference equation (LDE) step of the mixed-D algorithm. It is shown that, when the DWT is computed using filters with ideal high- and lowpass frequency responses, the LDE filters used in the mixed-D filtering stage are unchanged by the introduction of the DWT (although the frequency tuple associated with each LDE filter is altered). This indicates that the mixed-D filtering scheme can be easily used in subband coding systems. Results are given for the filtering of a three-dimensional (3-D) linear trajectory signal, representing a common application in video processing.     

自适应的混合域音频水印新算法

本文结合小波包变换和离散余弦变换，提出了一种基于听觉模型的混合域自适应音频盲水印算法，在不引入听觉失真的前提下，实现了自适应的水印嵌入。算法首先对音频信号进行小波包分解，使得分解后的子带更接近人耳临界频带。其次对每个子带的小波包系数进行离散余弦变换，计算出子带掩蔽阈值。根据子带掩蔽阈值自适应的选取噪声敏感度小的音频段作为水印嵌入段，选取功率值低于掩蔽阈值的频域系数作为水印嵌入位置，同时采用噪声掩蔽比调整水印嵌入强度。二值水印图像通过量化索引调制的方法嵌入到音频信号的中低频系数中，提取水印时不需要原始音频载体。本算法在水印容量、不可感知性和鲁棒性之间达到了很好的平衡，水印容量在576.7bps到689.5bps之间，算法对添加噪声、重新量化、重新采样、低通滤波和MP3压缩均具有很好的鲁棒性。      

Image denoising with anisotropic bivariate shrinkage

This paper presents a novel image denoising algorithm based on the modeling of wavelet coefficients with an anisotropic bivariate Laplacian distribution function. The anisotropic bivariate Laplacian model not only captures the child-parent dependency between wavelet coefficients, but also fits the anisotropic property of the variances of wavelet coefficients in different scales of natural images. With this statistical model, we derive a closed-form anisotropic bivariate shrinkage function in the framework of Bayesian denoising and a new image denoising approach with local marginal variance estimation based on this newly derived shrinkage function is proposed in the discrete wavelet transform (DWT) domain. The proposed anisotropic bivariate shrinkage approach is also extended to the dual-tree complex wavelet transform (DT-CWT) domain to further improve the performance of image denoising. To take full advantage of DT-CWT, a more accurate noise variance estimator is proposed and the way the anisotropic bivariate shrinkage function applied to the magnitudes of DT-CWT coefficients is presented. Experiments were carried out in both the DWT and the DT-CWT domain to validate the effectiveness of the proposed method. Using a representative set of standard test images corrupted by additive white Gaussian noise, the simulation results show that the proposed method provides promising results and is competitive with the best wavelet-based denoising results reported in the literature both in terms of peak signal-to-noise ratio (PSNR) and in visual quality.     

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.     

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.     

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。     

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     

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.     

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.     

The dual-tree complex wavelet transform

The paper discusses the theory behind the dual-tree transform, shows how complex wavelets with good properties can be designed, and illustrates a range of applications in signal and image processing. The authors use the complex number symbol C in CWT to avoid confusion with the often-used acronym CWT for the (different) continuous wavelet transform. The four fundamentals, intertwined shortcomings of wavelet transform and some solutions are also discussed. Several methods for filter design are described for dual-tree CWT that demonstrates with relatively short filters, an effective invertible approximately analytic wavelet transform can indeed be implemented using the dual-tree approach.     

基于最优小波包基的信号增强算法研究及应用

本文介绍了小波包分析的基本理论以及小波包信号降噪的基本原理,与小波变换相比,小波包变换则是对小波分解中所得到的高频部分再继续细分为一些子频带,具有更精细的信噪分离能力,所以对包含大量中、高频信息的信号能更好地进行时频局部化分析。小波包变换在信号去噪中有着非常重要的应用,因此利用小波包对信号进行消噪也越来越受到科学界的关注。本文的主旨在于研究最优小波包基函数的选取方法,以小波包分析为基础,根据最小代价原理研究信号分解的最佳小波包基,从而在最优小波包基的基础上获得最好的信号增强效果。