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.     

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.     

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.     

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.     

小波变换在图像数据压缩中的应用

小波变换的图像编码方法,不仅拥有传统编码的优点,能够消除图像中的统计冗余,并且,其多分辨率的特性提供了消除非统计冗余信息的良好机制。基于离散小波变换(DWT)理论,介绍了DWT在数字图像压缩中的应用,使用零树编码实现了数字图像压缩,并同时保持原图像在各种分辨率下的精细结构,该方法对消除图像中非统计冗余信息提供了有效途径。     

基于改进的K-L变换的多光谱图像压缩算法

融合离散小波变换(DWT,discrete wavelet tran sform)与Karhunen-Loeve变换(KLT),将图像的能量集中到少数系数上,以达到更好的 压缩效果。首先将多光谱图像的每个谱段进行快速9/72D DWT,消除多光谱图像的大部分 空间冗余;然后对所有谱段产生的小波系数进行改进的KLT,来消除光谱冗余和残存的空 间冗余;最后对所得谱段产生的小波系数进行改进的KLT,来消除光谱冗余和残存的空间冗 余;最后对所得系数进行熵编码,得到压缩码流。实验结果表明,在码率为0.25～2.0bit/ pixel范围内,平均信噪比(SNR)高于41dB,同时缩短了运 算时间,从而提升了多光谱图像压 缩算法的性能。     

基于方向小波变换的边缘检测算法

提出了一种基于方向小波变换的边缘检测算法.本文详细介绍了方向小波变换的原理、基于此的图像边缘检测算法,比较了方向小波变换和传统小波变换、Canny算子在图像边缘检测的效果.实验结果表明,方向小波变换更符合图像的方向、纹理特征,因此更能反映图像的边缘信息,对传统的小波变换、Canny边缘检测算法有一定程度的改进.     

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.     

基于非下采样轮廓小波变换的图像去噪

针对采用下采样滤波器结构的轮廓波、轮廓小波在图像去噪过程中会引入伪吉布斯现象,利用小波变换(WT)和非下采样方向滤波器组(NDFB)构造了一种新的多尺度、多分辨率图像的非下采样轮廓小波变换(NWCT)。WT去除了拉普拉斯金字塔滤波器(LPF)的计算冗余,NDFB保证了该变换具有平移不变性。为了验证该变换的有效性,对其进行了图像去噪实验。实验结果表明,所提出方法能获得比WT、轮廓波变换(CT)、轮廓小波变换(WCT)更高的峰值信噪比(PSNR),并且能够很好地抑制伪吉布斯现象。     

Analytic Wavelet Packets—Combining the Dual-Tree Approach With Wavelet Packets for Signal Analysis and Filtering

Real wavelets (or real basis functions in general) suffer from two major disadvantages: shift-variance and oscillating coefficients. This paper provides a review of these problems as well as the undecimated wavelet transform which solves the problem of shift-variance. However, undecimated transforms have very high computational costs and still have oscillating coefficients. The work of Kingsbury is summarized afterwards. They have presented a dual-tree complex wavelet transform (DTCWT) which is nearly shift-invariant and has smooth coefficients. Subsequently, a filter swapping scheme is developed in order to create complex wavelet packets with analytic basis functions. Finally, the effectiveness of the proposed method is demonstrated by five examples.      

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.     

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.     

基于双变量收缩函数的对偶树复小波图像去噪

常用离散小波变换缺乏平移不变性和良好的方向选择性,并且在图像去噪中使用的模型没有充分考虑系数间的相关性,导致去噪效果不理想.为了克服上述离散小波变换图像去噪的不足,提出了利用对偶树复小波变换与双变量收缩函数相结合的图像去噪算法.实验结果表明,该算法比传统算法有更好的去噪效果.     

A novel image hash algorithm resistant to print–scan

With the rapid development of multimedia technology, how to establish the integrity of images has become an unavoidable problem. The transform between a digital image and its hard-copy makes the problem more complex. To simplify the content based authentication, we propose a print–scan resistant image hashing algorithm based on the Radon and wavelet transform. The Radon transforms an image to its luminance distribution, before the wavelet extracts the relationship of the different areas from the luminance distribution. Experimental results show that our algorithm is not only robust to print–scan and other common content-preserving processing, but also discriminable to content changes.     

一种基于DWT_SVD的抗几何攻击彩色图像水印算法

针对传统离散小波变换(DWT)水印算法不能较好地抵抗几何攻击的缺点,提出了一种基于离散小波变换(DWT)和奇异值分解(SVD)相结合的彩色图像水印新算法。首先对原始彩色载体图像进行RGB三基色分解,然后进行离散小波变换,再选取四个子块的四分之一重构成新子块,并进行二次离散小波变换,最后对其低频部分进行奇异值分解嵌入水印信息,得到嵌入水印的彩色图像。实验结果表明,该算法能够较好地抵抗诸如高斯噪声、椒盐噪声、压缩等常规攻击,并对大角度旋转、任意角度旋转、剪切加旋转等几何攻击也表现出了较强的鲁棒性,其总体性能明显优于传统的DWT水印算法。     

Wavelet packet image coding using space-frequency quantization

We extend our previous work on space-frequency quantization (SFQ) for image coding from wavelet transforms to the more general wavelet packet transforms. The resulting wavelet packet coder offers a universal transform coding framework within the constraints of filterbank structures by allowing joint transform and quantizer design without assuming a priori statistics of the input image. In other words, the new coder adaptively chooses the representation to suit the image and the quantization to suit the representation. Experimental results show that, for some image classes, our new coder gives excellent coding performance.     

基于方向小波的弱尾迹检测

针对遥感图像中的弱尾迹检测,提出了一种基于方向小波变换的尾迹检测新算法,并且比较了方向小波和传统的小波变换在检测尾迹中的不同之处。分析得出方向小波变换更符合图像的方向、纹理特征,因而不仅可以有效检测出图像中的弱尾迹,而且可以检测出某一特定方向上的弱尾迹。仿真结果表明,检测效果十分良好。     

Block-based SVD image watermarking in spatial and transform domains

The idea of this paper is to implement an efficient block-by-block singular value (SV) decomposition digital image watermarking algorithm, which is implemented in both the spatial and transforms domains. The discrete wavelet transform (DWT), the discrete cosine transform and the discrete Fourier transform are exploited for this purpose. The original image or one of its transforms is segmented into non-overlapping blocks, and consequently the image to be inserted as a watermark is embedded in the SVs of these blocks. Embedding the watermark on a block-by-block manner ensures security and robustness to attacks such like Gaussian noise, cropping and compression. The proposed algorithm can also be used for colour image watermarking. A comparison study between the proposed block-based watermarking algorithm and the method of Liu is performed for watermarking in all domains. Simulation results ensure that the proposed algorithm is more effective than the traditional method of Liu, especially when the watermarking is performed in the DWT domain.     

Multiresolution Monogenic Signal Analysis Using the Riesz–Laplace Wavelet Transform

The monogenic signal is the natural 2D counterpart of the 1D analytic signal. We propose to transpose the concept to the wavelet domain by considering a complexified version of the Riesz transform which has the remarkable property of mapping a real-valued (primary) wavelet basis of L₂(R²) into a complex one. The Riesz operator is also steerable in the sense that it give access to the Hilbert transform of the signal along any orientation. Having set those foundations, we specify a primary polyharmonic spline wavelet basis of L₂(R²) that involves a single Mexican-hat-like mother wavelet (Laplacian of a B-spline). The important point is that our primary wavelets are quasi-isotropic: they behave like multiscale versions of the fractional Laplace operator from which they are derived, which ensures steerability. We propose to pair these real-valued basis functions with their complex Riesz counterparts to specify a multiresolution monogenic signal analysis. This yields a representation where each wavelet index is associated with a local orientation, an amplitude and a phase. We give a corresponding wavelet-domain method for estimating the underlying instantaneous frequency. We also provide a mechanism for improving the shift and rotation-invariance of the wavelet decomposition and show how to implement the transform efficiently using perfect-reconstruction filterbanks. We illustrate the specific feature-extraction capabilities of the representation and present novel examples of wavelet-domain processing; in particular, a robust, tensor-based analysis of directional image patterns, the demodulation of interferograms, and the reconstruction of digital holograms.     

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.