The pairing of a wavelet basis with a mildly redundant analysis via subband regression

A distinction is usually made between wavelet bases and wavelet frames. The former are associated with a one-to-one representation of signals, which is somewhat constrained but most efficient computationally. The latter are over-complete, but they offer advantages in terms of flexibility (shape of the basis functions) and shift-invariance. In this paper, we propose a framework for improved wavelet analysis based on an appropriate pairing of a wavelet basis with a mildly redundant version of itself (frame). The processing is accomplished in four steps: 1) redundant wavelet analysis, 2) wavelet-domain processing, 3) projection of the results onto the wavelet basis, and 4) reconstruction of the signal from its nonredundant wavelet expansion. The wavelet analysis is pyramid-like and is obtained by simple modification of Mallat's filterbank algorithm (e.g., suppression of the down-sampling in the wavelet channels only). The key component of the method is the subband regression filter (Step 3) which computes a wavelet expansion that is maximally consistent in the least squares sense with the redundant wavelet analysis. We demonstrate that this approach significantly improves the performance of soft-threshold wavelet denoising with a moderate increase in computational cost. We also show that the analysis filters in the proposed framework can be adjusted for improved feature detection; in particular, a new quincunx Mexican-hat-like wavelet transform that is fully reversible and essentially behaves the (gamma/2)th Laplacian of a Gaussian.     

Iterative learning algorithms for linear Gaussian observation models

In this paper, we consider a signal/parameter estimation problem that is based on a linear model structure and a given setting of statistical models with unknown hyperparameters. We consider several combinations of Gaussian and Laplacian models. We develop iterative algorithms based on two typical machine learning methods - the evidence-based method and the integration-based method - to deal with the hyperparameters. We have applied the proposed algorithms to adaptive prediction and wavelet denoising. In linear prediction, we show that the proposed algorithms are efficient tools for tackling a difficult problem of adapting simultaneously the order and the coefficients of the predictor. In wavelet denoising, we show that by using the proposed algorithms, the noisy wavelet coefficients are subject to shrinkage and thresholding.     

基于均值量化的小波域自同步数字音频水印算法研究

文中提出了一种基于均值量化的小波域自同步数字音频水印算法。该算法是一种盲水印算法,水印提取不需要原始音频信号的参与。算法设计中运用了均值量化的策略,音频信号小波分解后,在低频系数中隐藏水印信息;引入了同步信号的思想,利用同步信号定位水印隐藏位置。实验表明,该算法具有较强的鲁棒性、抗攻击性、抗裁剪性。     

Bayesian tree-structured image modeling using wavelet-domain hiddenMarkov models

Wavelet-domain hidden Markov models have proven to be useful tools for statistical signal and image processing. The hidden Markov tree (HMT) model captures the key features of the joint probability density of the wavelet coefficients of real-world data. One potential drawback to the HMT framework is the need for computationally expensive iterative training to fit an HMT model to a given data set (e.g., using the expectation-maximization algorithm). We greatly simplify the HMT model by exploiting the inherent self-similarity of real-world images. The simplified model specifies the HMT parameters with just nine meta-parameters (independent of the size of the image and the number of wavelet scales). We also introduce a Bayesian universal HMT (uHMT) that fixes these nine parameters. The uHMT requires no training of any kind, while extremely simple, we show using a series of image estimation/denoising experiments that these new models retain nearly all of the key image structure modeled by the full HMT. Finally, we propose a fast shift-invariant HMT estimation algorithm that outperforms other wavelet-based estimators in the current literature, both visually and in mean square error.     

Fast wavelet estimation of weak biosignals

Wavelet-based signal processing has become commonplace in the signal processing community over the past decade and wavelet-based software tools and integrated circuits are now commercially available. One of the most important applications of wavelets is in removal of noise from signals, called denoising, accomplished by thresholding wavelet coefficients in order to separate signal from noise. Substantial work in this area was summarized by Donoho and colleagues at Stanford University, who developed a variety of algorithms for conventional denoising. However, conventional denoising fails for signals with low signal-to-noise ratio (SNR). Electrical signals acquired from the human body, called biosignals, commonly have below 0 dB SNR. Synchronous linear averaging of a large number of acquired data frames is universally used to increase the SNR of weak biosignals. A novel wavelet-based estimator is presented for fast estimation of such signals. The new estimation algorithm provides a faster rate of convergence to the underlying signal than linear averaging. The algorithm is implemented for processing of auditory brainstem response (ABR) and of auditory middle latency response (AMLR) signals. Experimental results with both simulated data and human subjects demonstrate that the novel wavelet estimator achieves superior performance to that of linear averaging.     

Multiscale autoregressive processes. I. Schur-Levinsonparametrizations

In many applications it is of interest to analyze and recognize phenomena occurring at different scales. The recently introduced wavelet transforms provide a time-and-scale decomposition of signals that offers the possibility of such analysis. A corresponding statistical framework to support the development of optimal, multiscale statistical signal processing algorithms is described. The theory of multiscale signal representation leads naturally to models of signals on trees, and this provides the framework for investigation. In particular, the class of isotropic processes on homogeneous trees is described, and a theory of autoregressive models is developed in this context. This leads to generalizations of Schur and Levinson recursions, associated properties of the resulting reflection coefficients, and the initial pieces in a system theory for multiscale modeling     

Improved hidden Markov models in the wavelet-domain

Wavelet-domain hidden Markov models (HMMs), in particular the hidden Markov tree (HMT) model, have been introduced and applied to signal and image processing, e.g., signal denoising. We develop a simple initialization scheme for the efficient HMT model training and then propose a new four-state HMT model called HMT-2. We find that the new initialization scheme fits the HMT-2 model well. Experimental results show that the performance of signal denoising using the HMT-2 model is often improved over the two-state HMT model developed by Crouse et al. (see ibid., vol.46, p.886-902, 1998)     

Multiscale autoregressive models and wavelets

The multiscale autoregressive (MAR) framework was introduced to support the development of optimal multiscale statistical signal processing. Its power resides in the fast and flexible algorithms to which it leads. While the MAR framework was originally motivated by wavelets, the link between these two worlds has been previously established only in the simple case of the Haar wavelet. The first contribution of this paper is to provide a unification of the MAR framework and all compactly supported wavelets as well as a new view of the multiscale stochastic realization problem. The second contribution of this paper is to develop wavelet-based approximate internal MAR models for stochastic processes. This will be done by incorporating a powerful synthesis algorithm for the detail coefficients which complements the usual wavelet reconstruction algorithm for the scaling coefficients. Taking advantage of the statistical machinery provided by the MAR framework, we will illustrate the application of our models to sample-path generation and estimation from noisy, irregular, and sparse measurements     

强噪声背景下车辆震动信号检测算法研究

针对强噪声背景下车辆震动信号检测问题,结合车辆震动信号特点,提出了2种检测算法:基于功率谱分布的检测算法和基于负熵的检测算法,并将小波去噪用于强噪声背景下地震动信号的提取。该算法与一般检测算法相比具有环境适应性强、检测准确率高和运算量小的特点,这些优点使得该算法更适用于能量受限、工作环境复杂的无线传感网络。仿真结果表明该算法具有很高的检测准确率。     

The application of multiwavelet filterbanks to image processing

Multiwavelets are a new addition to the body of wavelet theory. Realizable as matrix-valued filterbanks leading to wavelet bases, multiwavelets offer simultaneous orthogonality, symmetry, and short support, which is not possible with scalar two-channel wavelet systems. After reviewing this theory, we examine the use of multiwavelets in a filterbank setting for discrete-time signal and image processing. Multiwavelets differ from scalar wavelet systems in requiring two or more input streams to the multiwavelet filterbank. We describe two methods (repeated row and approximation/deapproximation) for obtaining such a vector input stream from a one-dimensional (1-D) signal. Algorithms for symmetric extension of signals at boundaries are then developed, and naturally integrated with approximation-based preprocessing. We describe an additional algorithm for multiwavelet processing of two-dimensional (2-D) signals, two rows at a time, and develop a new family of multiwavelets (the constrained pairs) that is well-suited to this approach. This suite of novel techniques is then applied to two basic signal processing problems, denoising via wavelet-shrinkage, and data compression. After developing the approach via model problems in one dimension, we apply multiwavelet processing to images, frequently obtaining performance superior to the comparable scalar wavelet transform.     

Generalized multivariate analysis of variance - A unified framework for signal processing in correlated noise

Generalized multivariate analysis of variance (GMANOVA) and related reduced-rank regression are general statistical models that comprise versions of regression, canonical correlation, and profile analyses as well as analysis of variance (ANOVA) and covariance in univariate and multivariate settings. It is a powerful and, yet, not very well-known tool. We develop a unified framework for explaining, analyzing, and extending signal processing methods based on GMANOVA. We show the applicability of this framework to a number of detection and estimation problems in signal processing and communications and provide new and simple ways to derive numerous existing algorithms. Many of the methods were originally derived "from scratch", without knowledge of their close relationship with the GMANOVA model. We explicitly show this relationship and present new insights and guidelines for generalizing these methods. Our results could inspire applications of the general framework of GMANOVA to new problems in signal processing. We present such an application to flaw detection in nondestructive evaluation (NDE) of materials. A promising area for future growth is image processing.     

Wavelet footprints: theory, algorithms, and applications

Wavelet-based algorithms have been successful in different signal processing tasks. The wavelet transform is a powerful tool because it manages to represent both transient and stationary behaviors of a signal with few transform coefficients. Discontinuities often carry relevant signal information, and therefore, they represent a critical part to analyze. We study the dependency across scales of the wavelet coefficients generated by discontinuities. We start by showing that any piecewise smooth signal can be expressed as a sum of a piecewise polynomial signal and a uniformly smooth residual (Theorem 1). We then introduce the notion of footprints, which are scale space vectors that model discontinuities in piecewise polynomial signals exactly. We show that footprints form an overcomplete dictionary and develop efficient and robust algorithms to find the exact representation of a piecewise polynomial function in terms of footprints. This also leads to efficient approximation of piecewise smooth functions. Finally, we focus on applications and show that algorithms based on footprints outperform standard wavelet methods in different applications such as denoising, compression, and (nonblind) deconvolution. In the case of compression, we also prove that at high rates, footprint-based algorithms attain optimal performance (Theorem 3).     

Genetic algorithm and wavelet hybrid scheme for ECG signal denoising

This paper introduces an effective hybrid scheme for the denoising of electrocardiogram (ECG) signals corrupted by non-stationary noises using genetic algorithm (GA) and wavelet transform (WT). We first applied a wavelet denoising in noise reduction of multi-channel high resolution ECG signals. In particular, the influence of the selection of wavelet function and the choice of decomposition level on efficiency of denoising process was considered. Selection of a suitable wavelet denoising parameters is critical for the success of ECG signal filtration in wavelet domain. Therefore, in our noise elimination method the genetic algorithm has been used to select the optimal wavelet denoising parameters which lead to maximize the filtration performance. The efficiency performance of our scheme is evaluated using percentage root mean square difference (PRD) and signal to noise ratio (SNR). The experimental results show that the introduced hybrid scheme using GA has obtain better performance than the other reported wavelet thresholding algorithms as well as the quality of the denoising ECG signal is more suitable for the clinical diagnosis.     

Electronic-nose for detecting environmental pollutants: signal processing and analog front-end design

Environmental monitoring relies on compact, portable sensor systems capable of detecting pollutants in real-time. An integrated chemical sensor array system is developed for detection and identification of environmental pollutants in diesel and gasoline exhaust fumes. The system consists of a low noise floor analog front-end (AFE) followed by a signal processing stage. In this paper, we present techniques to detect, digitize, denoise and classify a certain set of analytes. The proposed AFE reads out the output of eight conductometric sensors and eight amperometric electrochemical sensors and achieves 91 dB SNR at 23.4 mW quiescent power consumption for all channels. We demonstrate signal denoising using a discrete wavelet transform based technique. Appropriate features are extracted from sensor data, and pattern classification methods are used to identify the analytes. Several existing pattern classification algorithms are used for analyte detection and the comparative results are presented.     

An Improved Wavelet Denoising Algorithm for Wideband Radar Targets Detection

A novel denoising technique based on wavelet transform modulus maxima (WTMM) is proposed for processing wideband radar spread targets detection signal in a clutter environment. Combined with the improved adaptive Bayes–Shrink threshold and Lipschitz exponents, we propose the path pruned approach at each scale terms as full-scale to split the signal. The estimation of WTMM over each scale has been optimized, thus, the signal and the noise can be split effectively. Additionally, to improve the computational efficiency, a fast method based on a piecewise polynomial interpolation algorithm is applied for the split signal reconstruction. Statistical results are quite promising and perform better than the conventional denoising algorithms: compared with the classical WTMM algorithm, the improved WTMM full-scale denoising algorithm not only increases the signal-to-noise (SNR) ratio by over 10 % but also reduces the processing time by 88 % and reduces the root-mean-square-error (RMSE) by over 35 %. More generally, the proposed algorithm has better performance than that of several typical algorithms in its denoising quality and singularity detection.     

A denoising approach to multisensor signal estimation

Multisensor array processing of noisy measurements has received considerable attention in many areas of signal processing. The optimal processing techniques developed so far usually assume that the signal and noise processes are at least wide sense stationary, yet a need exists for efficient, effective methods for processing nonstationary signals. Although wavelets have proven to be useful tools in dealing with certain nonstationary signals, the way in which wavelets are to be used in the multisensor setting is still an open question. Based on the structure for optimal linear estimation of nonstationary multisensor data and statistical models of spatial signal coherence, we propose a multisensor denoising algorithm that fully exploits, in a statistically optimal fashion, the additional information afforded by multisensor measurements. Under certain conditions, we show that the proposed estimator can be realized efficiently and robustly in a completely blind fashion, employing only wavelet and discrete Fourier transforms while entailing only a small loss in performance     

Image Denoising Using Trivariate Shrinkage Filter in the Wavelet Domain and Joint Bilateral Filter in the Spatial Domain

This correspondence proposes an efficient algorithm for removing Gaussian noise from corrupted image by incorporating a wavelet-based trivariate shrinkage filter with a spatial-based joint bilateral filter. In the wavelet domain, the wavelet coefficients are modeled as trivariate Gaussian distribution, taking into account the statistical dependencies among intrascale wavelet coefficients, and then a trivariate shrinkage filter is derived by using the maximum a posteriori (MAP) estimator. Although wavelet-based methods are efficient in image denoising, they are prone to producing salient artifacts such as low-frequency noise and edge ringing which relate to the structure of the underlying wavelet. On the other hand, most spatial-based algorithms output much higher quality denoising image with less artifacts. However, they are usually too computationally demanding. In order to reduce the computational cost, we develop an efficient joint bilateral filter by using the wavelet denoising result rather than directly processing the noisy image in the spatial domain. This filter could suppress the noise while preserve image details with small computational cost. Extension to color image denoising is also presented. We compare our denoising algorithm with other denoising techniques in terms of PSNR and visual quality. The experimental results indicate that our algorithm is competitive with other denoising techniques.     

基于小波变换的光寻址电位传感器信号去噪研究

基于(LAPS)(光寻址电位传感器)技术的生化传感器中的光生电流是一种微弱的非平稳信号,信噪比(SNR)低。为了提取清晰的LAPS信号,且鉴于传统的傅里叶方法去噪后信号失真严重,本文采用小波变换的方法对LAPS信号进行去噪处理。通过小波变换将信号分解为3层,得到各层的小波系数以及阈值。根据每一层系数特点,按阈值进行分别处理,得到新的小波系数。最后根据新的小波系数,重构信号。对去噪后的信号进行频谱分析发现,信号频谱为有效的LAPS信号谱段。将傅里叶去噪和小波去噪方法进行对比发现,小波去噪得到信号的SNR和平滑度(SR)要高于傅里叶去噪,表明小波变换是LAPS信号去噪的有效方法。     

小波变换及其在信号去噪中的应用

介绍了小波变换理论及基于小波变换去除信号噪声的基本原理和方法.研究利用小波变换技术对噪声进行阈值处理和去除非平稳信号的噪声,并应用Matlab软件实现了小波去噪的计算机仿真,仿真结果表明小波变换去除噪声的效果优于传统的Fourier变换.     

Denoising by singularity detection

A new algorithm for noise reduction using the wavelet transform is proposed. Similar to Mallat's (1992) wavelet transform modulus maxima denoising approach, we estimate the regularity of a signal from the evolution of its wavelet transform coefficients across scales. However, we do not perform maxima detection and processing; therefore, complicated reconstruction is avoided. Instead, the local regularities of a signal are estimated by computing the sum of the modulus of its wavelet coefficients inside the corresponding “cone of influence”, and the coefficients that correspond to the regular part of the signal for reconstruction are selected. The algorithm gives an improved denoising result, as compared with the previous approaches, in terms of mean squared error and visual quality. The new denoising algorithm is also invariant to translation. It does not introduce spurious oscillations and requires very little a priori information of the signal or noise. Besides, we extend the method to two dimensions to estimate the regularity of an image by computing the sum of the modulus of its wavelet coefficients inside the so-called “directional cone of influence”. The denoising technique is applied to tomographic image reconstruction, where the improved performance of the new approach can clearly be observed