A Globally Optimal Bilinear Programming Approach to the Design of Approximate Hilbert Pairs of Orthonormal Wavelet Bases

It is understood that the Hilbert transform pairs of orthonormal wavelet bases can only be realized approximately by the scaling filters of conjugate quadrature filter (CQF) banks. In this paper, the approximate FIR realization of the Hilbert transform pairs is formulated as an optimization problem in the sense of the lp (p=1, 2, or infinite) norm minimization on the approximate error of the magnitude and phase conditions of the scaling filters. The orthogonality and regularity conditions of the CQF bank pairs are taken as the constraints of such an optimization problem. Whereafter the branch and bound technique is employed to obtain the globally optimal solution of the resulting bilinear program optimization problem. Since the orthogonality and regularity conditions are explicitly taken as the constraints of our optimization problem, the attained solution is an approximate Hilbert transform pair satisfying these conditions exactly. Some orthogonal wavelet bases designed herein demonstrate that our design scheme is superior to those that have been reported in the literature. Moreover, the designed orthogonal wavelet bases show that minimizing the l ₁ norm of the approximate error should be advocated for obtaining better approximated Hilbert pairs.     

Construction of Hilbert Transform Pairs of Wavelet Bases and Gabor-Like Transforms

We propose a novel method for constructing Hilbert transform (HT) pairs of wavelet bases based on a fundamental approximation-theoretic characterization of scaling functions—the B-spline factorization theorem. In particular, starting from well-localized scaling functions, we construct HT pairs of biorthogonal wavelet bases of ${rm L}^2({BBR})$ by relating the corresponding wavelet filters via a discrete form of the continuous HT filter. As a concrete application of this methodology, we identify HT pairs of spline wavelets of a specific flavor, which are then combined to realize a family of complex wavelets that resemble the optimally-localized Gabor function for sufficiently large orders. Analytic wavelets, derived from the complexification of HT wavelet pairs, exhibit a one-sided spectrum. Based on the tensor-product of such analytic wavelets, and, in effect, by appropriately combining four separable biorthogonal wavelet bases of ${rm L}^2({BBR}^2)$, we then discuss a methodology for constructing 2-D directional-selective complex wavelets. In particular, analogous to the HT correspondence between the components of the 1-D counterpart, we relate the real and imaginary components of these complex wavelets using a multidimensional extension of the HT—the directional HT. Next, we construct a family of complex spline wavelets that resemble the directional Gabor functions proposed by Daugman. Finally, we present an efficient fast Fourier transform (FFT)-based filterbank algorithm for implementing the associated complex wavelet transform.      

用余弦调制PR－FIR方法构造正交小波基

离散小波变换将离散时间信号分解为一系列不同分辨率下的离散近似信号和离散细节，紧支的正交规范小波与完全重构正交镜象滤波器（ＰＲ－ＱＭＦ）相对应。本文在“二带”正交小波基的构造条件下，利用余弦调制完全重构滤波器组的方法，实现了正交小波基的构造，计算模拟表明该方法非常简单、有效。     

一种基于双正交小波变换的静止图像编码算法

本文研究了基于双正交小波变换的静止图像编码算法，提出了一种新的数据结构即扩展子树，从而实现了一种性能较好复杂度较低的静止图像编码方案。     

二维正交子波变换的VLSI并行计算

本文提出一个二维离散正交子波变换的ＶＬＳＩ并行结构，该结构将二维输入信号分解成不重叠的若干行组，从而使每组中的所有行被并行处理，而不同组的行的处理、不同级上的计算，以至不同信号的计算可以在此结构上流水线地进行。     

一种高效的二维提升小波变换方法

基于对通用处理器L1 Cache命中机制和二维提升小波变换结构的分析,提出一种在Intel通用处理器平台上,采用Streaming SIMD Extensions 2(SSE2)实现高效快速二维提升小波变换的方法.此法对原始小波系数存储层次进行调整,充分利用SSE2的SIMD并行处理能力,尽量保持列变换时数据读取与Cache命中方向一致,有效缩短了二维提升小波变换的执行时间.     

基于小波的多尺度边缘检测在遥感图像处理中的应用

本文引入小波多尺度边缘检测,将小波的尺度因子与不同方向的梯度联系起来在梯度大的方向(垂直边缘方向)采用小尺度的因子,突出细节.在梯度小的方向(沿着边缘方向)采用大尺度因子,可提高信噪比.试验结果表明:该算法具有很好的边缘细节的保持性,较常见的P-M模型滤波方法算法效果有明显优势.     

A Parallel Architecture for the 2-D Discrete Wavelet Transform with Integer Lifting Scheme

In this paper we propose a dedicated architecture to implement a 2-D discrete wavelet transform computed by adopting the new lifting scheme framework. Through this new construction tool it is possible to obtain integer versions of the wavelet transform. This is a very interesting issue when the goal is lossless compression of images, whose pixels are represented through integers. In the classical approach to the discrete wavelet, the filter coefficients are real numbers and so are the resulting coefficients. When pursuing hardware implementations for real time and embedded applications, this causes the need to manage fixed point operations and unavoidable quantization. If the output can be produced with integer values instead, perfect reconstruction and lossless compression are possible. Typical applications include scenarios with limited bandwidth and big image sizes, such as medical imaging for tele-medicine or satellite image transmission, not suited to lossy compression, or high quality images in digital cameras.We analyze the data flow and dependencies to define an architecture to implement the integer lifting wavelet transform. The paper covers all lifting implementations based on a single lifting stepr and uses the Deslauriers-Dubuc (4, 2) filter as a guiding example, but the approach is general and the results can be easily extended to other filters. We outline a very general framework, to be used either in a custom VLSI implementation, or in mappings onto existing computing cells. The overall resources needed are less than those for the equivalent classical FIR version computed through a systolic architecture.     

基于小波和余弦变换组合的图像水印方案

数字水印作为数字媒体版权保护的有效手段,近几年来在国际上引起了人们极大的兴趣.本文针对数字图像水印进行了研究,提出了一个基于离散小波变换和离散余弦变换组合的图像水印新方案.实验结果表明,该水印方案很好地体现了图像水印的鲁棒性和不可视性间的统一,在相同的水印图像质量条件下,对常规的图像处理和噪声干扰比其它图像水印方案具有更好的鲁棒性.     

一种基于小波变换的自适应图像降噪法

提出了一种基于二进小波变换的图像降噪方法,通过对小波变换系数进行阈值处理实现降噪。该方法结合图像的自身邻域信息,具有一定的自适应性。实验结果证明能够产生较好的效果。     

基于中值滤波和小波变换图像降噪的新算法

针对小波变换去噪方法仅适用于去除高斯白噪声,对于脉冲噪声得不到良好的降噪效果的问题,文中构造了一个新的小波阈值函数,并对中值滤波进行了改进,将此两者方法相结合进行图像去噪。仿真实验结果表明,新算法能够有效去除高斯白噪声和脉冲噪声,而且去噪后图像的峰值信噪比和均方误差都较单一算法得到改善,从而证明了该方法的有效性。     

基于Hilbert变换的电压凹陷检测方法

电压凹陷是严重的动态电能质量问题之一,补偿电压凹陷能带来巨大的经济效益.而实现电压凹陷特征量的快速、准确检测是电压凹陷补偿的前提,因此电压凹陷特征量的检测方法及补偿指令的产生成为目前对DVR研究的一个热点.采用Hilbert变换与后差分相结合的检测方法,首先利用Hilbert变换可对凹陷电压信号的幅值进行检测,然后采用后差分得到电压凹陷的起止时刻,不但提高了检测精度,还能实时产生电压补偿指令信号.通过Matlab对其进行仿真,仿真结果表明了该检测方法简单、快速、准确的优点.     

一种新的自适应子波预滤波器设计

基于一般的紧支撑尺度函数,本文设计了一咎单参数且具有良好逼近性能的新的自适应ＦＩＲ预滤波器,分析和模拟结果与表明这种预波滤算法具有较高的逼近精度和较快的逼近速度。     

一种小波域新颖鲁棒语音扩谱水印

文章提出一种基于小波变换的新颖的鲁棒语音扩谱水印算法。算法对原始语音进行离散小波变换．利用扩谱水印技术将水印隐藏到小波域。根据检测与估计理论，运用新的检测统计量进行相关检测。同时，通过引入抗异步攻击的机制和倒谱滤波，增强了算法的鲁棒性。实验结果表明，该算法对噪声、中值滤波、低通滤波、异步攻击等有较强的鲁棒性。     

A Configurable Architecture for the Wavelet Packet Transform

The standard Wavelet Transform (WT) has a wide range of applications, from signal analysis to image or video compression and communications. Most of these applications would be benefited if the transform provided good spectral and temporal resolution in arbitrary regions of the time-frequency plane. This flexible choice of the time-frequency tiling is provided by the Wavelet Packet Transform (WPT). Though many VLSI architectures have been proposed for the WT in the literature, it is not the case for the WPT. We present both word-serial and word-parallel real-time pipelined architectures capable of computing a complete WPT binary tree, but which are easily configurable to compute any required WPT subtree.     

基于近似小波变换与时频分析的SAR运动目标检测

本文针对地面匀速直线运动的目标，提出近似小波变换与时频分析相结合的检测方法，近似小波变换不仅可以检测出目标信号相位二次项中含有的运动参数，还可以为时频分析提供预处理，滤除杂波及其噪声，时频分析则可以同时检测相位一次项及二次项中含有的运动参数。     

小波提升算法及其在图像处理中的应用

小波提升算法是一种新的双正交小波构造方法，通过预测算子，确定高频信息，并初步确定低频信息，然后通过更新算子，对初步确定的低频信息进行修正，从而确定低频信息。它在空域对信号进行变换，完成了对信号频域的分析。在图像处理中，基于离散小波变换的提升算法比传统的卷积算法运算简单，实时性好，易于实现，因而被新一代图像压缩标准JPEG2000所采用。文中简要介绍了小波提升算法的原理，分析了其特点，并介绍了JPEG2000标准中采用的W5／3、D9／7两种小波的提升格式和实现算法。     

基于提升算法的离散小波变换FPGA实现

离散小波变换是当今许多图像处理和压缩技术的基础,并得到了广泛的应用.本文以4阶Daubechies小波为例阐述基于提升算法的离散小波变换的原理,并给出其硬件实现架构,然后进行仿真,将仿真结果与Matlab软件实现结果进行比较,结果表明硬件实现与软件实现基本一致,该硬件架构与基于传统的卷积方法实现相比,可以减小硬件实现面积,并利用插入流水线寄存器的方法,缩短关键路径,提高运算速度.     

Hardware-Efficient Systolic-Like Modular Design for Two-Dimensional Discrete Wavelet Transform

A systolic-like modular architecture is presented for hardware-efficient implementation of two-dimensional (2-D) discrete wavelet transform (DWT). The overall computation is decomposed into two distinct stages; where column processing is performed in stage-1, while row processing is performed in stage-2. Using a new data-access scheme and a novel folding technique, the computation of both the stages are performed concurrently for transposition-free implementation of 2-D DWT. The proposed design can offer nearly the same throughput rate, and requires the same or less the number of adders and multipliers as the best of the existing structures. The storage space is found to occupy most of the area in the existing 2-D DWT structures but the proposed structure does not require any on-chip or off-chip storage of input samples or storage/transposition of intermediate output. The proposed one, therefore, involves considerably less hardware complexity compared with the existing structures. Apart from that, it has less duration of cycle period in comparison to the existing structures, and has a latency of cycles while all the existing structures have latency of cycles, the filter order being small compared to the input size .