Reconstruction from 2-D wavelet transform modulus maxima usingprojection

Wavelet transform modulus maxima can be used to characterise sharp variations such as edges and contours in an image. The authors analyse the a priori constraints present in the wavelet transform modulus maxima representation. A new projection-based algorithm which enforces all the a prior constraints in the representation is proposed. Quadratic programming is used to obtain a sequence which satisfies the maxima constraint. Thus realising the projection onto the maxima constraint space. To save computation, an approximate method to obtain a sequence which satisfies the maxima constraint is given. The new algorithm is shown to provide better solution than the original reconstruction algorithm of Mallat and Zhong (1992). The authors also propose a simple method to accelerate the algorithm. The acceleration is achieved by the incorporation of a momentum term which exploits the high correlation between the difference images between two consecutive iterations. The simulation results show that the proposed algorithm gives good reconstruction and the simple acceleration method can significantly improve the convergence rate     

基于二叉树搜索的小波变换信号压缩

正交离散小波变换由于缺乏平移不变性,会对信号压缩的性能造成很大的影响。为避免这一缺陷,该文在每个变换尺度上均对偶采样和奇采样的结果进行保留,产生一个三叉树结构,由此二叉树的任意一路径均可重构原信号,按照一定的准则可以确定最优分解路线。仿真结果表明,该变换方式较标准正交离散小波变换有更高的压缩性能。     

Signal recovery and wavelet reproducing kernels

A class of signal recovery problems can be formulated as finding missing data at the finest scale of a discrete wavelet transform. A unique and stable recovery can be obtained by solving the regularized wavelet-reproducing equation. We show that this approach has close relations to unconstrained and constrained least-squares techniques and derive a family of regularizing operators adapted to the degrading operator. Experimental results present restored images using regularizing operators of this type     

Signal and image approximation using interval wavelet transform.

In signal approximation, classical wavelet synthesis are known to produce Gibbs-like phenomenon around discontinuities when wavelet coefficients in the cone of influence of the discontinuities are quantized. By analyzing a function in a piecewise manner, filtering across discontinuities can be avoided. Using this principle, the interval wavelet transform can generate sparser representations in the vicinity of discontinuities than classical wavelet transforms. This work introduces two new constructions of interval wavelets and shows how they can be used for image compression and upscaling.     

芯片毛细管电泳信号的小波消噪

采用小波消噪方法对芯片毛细管电泳信号进行了处理,研究了小波基的选择,噪音在不同细节中的特征以及噪音阈值的确定。结果显示,与Fourier消噪算法相比,运用小波消噪算法不仅能够更有效地消除噪声,而且能使峰形不变,峰高不受影响。     

Uniqueness issue of wavelet transform modulus maxima representationand a least squares reconstruction algorithm

The authors show that the problem of uniqueness of the wavelet transform modulus maxima representation is related to the completeness of the wavelet basis set; i.e. it must be a frame of the function space of interest. The authors present a least squares reconstruction method that is optimum with respect to the basis set     

Detection of microcalcifications in mammograms using local maxima and adaptive wavelet transform analysis

A method for computer-aided diagnosis of microcalcification clusters in mammogram images is presented. Microcalcification clusters which are an early sign of breast cancer appear as isolated bright spots in mammograms. Therefore they correspond to local maxima of the image. The local maxima of the image is first detected and they are ranked according to a higher-order statistical test performed over the subband domain data.     

基于小波变换模极大值的LiDAR风切变预警算法

为了更好地检测低空风切变, 保障飞机的飞行安全, 提出了一种基于小波变换模极大值的激光雷达风切变预警算法。先用小波变换求取重组逆风廓线上的模极大值, 找到"拐点"后再利用风切变判断标准来判断。在进行数值仿真和来自湖北郧西气象站、四川攀枝花机场的现场检测验证后, 确认新算法在准确性及效率方面都有良好的性能, 且脉冲型数据使用biorthogonal系中双数小波检测结果较准确, 而阶跃型和斜坡型数据需使用Daubechies系中Db5小波。结果表明, 鄂西北郧西县和攀枝花保安营机场均有风切变发生, 风切变强度为重度。该算法能检测不同类型的风切变, 不用考虑风切变的尺度, 较好地弥补了现有算法的不足, 为飞机的起降提供技术保障, 对实时检测和预警也有重大的意义。     

基于提升小波与粒子群相结合的混沌信号降噪

提升小波变换用于混沌信号降噪具有良好的效果,阈值选取与混沌信号降噪后信号的畸变具有紧密联系。为了提高混沌信号中提升小波的自适应能力,降低降噪后信号的畸变率,提出了一种基于提升小波和粒子群相结合的混沌信号降噪方法。该方法在对提升小波变换后的细节部分进行阈值处理时,采用阈值自适应选择方法,并结合粒子群算法全局搜索最优阈值。通过对Colpitts模型进行仿真分析,与标准的软阈值降噪相比,能更好地对混沌信号降噪,并且降噪后信号失真度较小,具有很好的应用价值。     

二代小波降噪在激光陀螺信号滤波中的应用

为了抑制激光陀螺的随机漂移,提高其使用精度,提出了一种改进的第二代小波变换降噪方法对陀螺随机漂移测试数据进行滤波处理.该方法在二代小波变换时采用多组预测器和更新器,根据变换样本与相邻样本之间的相关性检测信号的局部特征,确定每个尺度上的每个变换样本的最佳预测器和更新器,使小波能够较好地适应信号的局部特征.该方法克服了传统小波变换降噪方法的缺陷,不仅可以有效地去除原始信号中的噪声,而且能够保留原始信号的局部特征.运用该方法对激光陀螺测试数据进行了滤波降噪实验,并用Allan方差法对不同降噪算法的降噪效果进行了比较分析,实验结果验证了该方法的有效性和优越性.     

一种新的融合小波变换与低秩矩阵恢复的图像去噪算法

针对小波阈值图像去噪会引入量化噪声和阈值选取不当会损失图像本身有用信息的问题,提出一种新的融合小波变换与低秩矩阵恢复(Low Rank Matrtix Recovery,LRMR)的图像去噪算法.不同于传统的单一阈值的去噪算法,所提出的算法在单一阈值上结合了低秩矩阵恢复算法,这样不仅能进一步消除噪声,同时还能修复被噪声损坏的数据,而且更能适应各种不同的噪声环境.首先,选取固定阈值对图像矩阵进行小波去噪处理.其次,采用增广拉格朗日乘子算法最小化矩阵核范数.最后,将矩阵分解为低秩逼近矩阵和稀疏误差矩阵.实验结果表明,算法获得了较高的峰值信噪比,在不同噪声环境下有较高的鲁棒性.     

Signal reconstruction from cosine transform magnitude

In this letter, we prove that any real, causal, and finite-duration sequence can be reconstructed from samples of its cosine transform magnitude. In addition, a simple numerical algorithm is developed for the signal reconstruction.     

Signal extrapolation from Hartley transform magnitudes

A novel approach to the problem of signal extrapolation from its Hartley transform magnitudes is presented. Using a newly defined function, it is proved that using only one known sample and the associated Hartley transform magnitudes a finite extended signal can be completely reconstructed. An algorithm for signal reconstruction from short-time Hartley transform (STHT) magnitudes with minimal window overlap can consequently be derived.<>     

基于小波变换的信号滤波在探地雷达中的应用

利用小波变换的时频局域性,提出了一种探地雷达信号处理的滤波方法.在连续小波变换的基础上,同时联合尺度和频率,通过能量分析确定回波信号主要分量所在区间,通过尺度分解和频域滤波剔除干扰分量,在此基础上重构信号,提高了信噪比.并针对不同连续小波基对信号处理的性能进行分析,对比结果表明与雷达发射母波相似的小波基在探地雷达信号处理中更有效.     

Three-dimensional discrete wavelet transform architectures

The three-dimensional (3-D) discrete wavelet transform (DWT) suits compression applications well, allowing for better compression on 3-D data as compared with two-dimensional (2-D) methods. This paper describes two architectures for the 3-D DWT, called the 3DW-I and the 3DW-II. The first architecture (3DW-I) is based on folding, whereas the 3DW-II architecture is block-based. Potential applications for these architectures include high definition television (HDTV) and medical data compression, such as magnetic resonance imaging (MRI). The 3DW-I architecture is an implementation of the 3-D DWT similar to folded 1-D and 2-D designs. It allows even distribution of the processing load onto 3 sets of filters, with each set performing the calculations for one dimension. The control for this design is very simple, since the data are operated on in a row-column-slice fashion. Due to pipelining, all filters are utilized 100% of the time, except for the start up and wind-down times. The 3DW-II architecture uses block inputs to reduce the requirement of on-chip memory. It has a central control unit to select which coefficients to pass on to the lowpass and highpass filters. The memory on the chip will be small compared with the input size since it depends solely on the filter sizes. The 3DW-I and 3DW-II architectures are compared according to memory requirements, number of clock cycles, and processing of frames per second. The two architectures described are the first 3-D DWT architectures     

Programmable wavelet packet transform processor

A programmable one-dimensional discrete wavelet packet transform processor is presented. Compared with existing architectures, the proposed processor can carry out both wavelet transforms and wavelet packet transforms, and is suitable for high-tap filters and high decomposition levels. It is small, and is especially suitable for on-chip or single-chip implementation     

Image coding using wavelet transform

A scheme for image compression that takes into account psychovisual features both in the space and frequency domains is proposed. This method involves two steps. First, a wavelet transform used in order to obtain a set of biorthogonal subclasses of images: the original image is decomposed at different scales using a pyramidal algorithm architecture. The decomposition is along the vertical and horizontal directions and maintains constant the number of pixels required to describe the image. Second, according to Shannon's rate distortion theory, the wavelet coefficients are vector quantized using a multiresolution codebook. To encode the wavelet coefficients, a noise shaping bit allocation procedure which assumes that details at high resolution are less visible to the human eye is proposed. In order to allow the receiver to recognize a picture as quickly as possible at minimum cost, a progressive transmission scheme is presented. It is shown that the wavelet transform is particularly well adapted to progressive transmission.     

Zero-crossings of a wavelet transform

The completeness, stability, and application to pattern recognition of a multiscale representation based on zero-crossings is discussed. An alternative projection algorithm is described that reconstructs a signal from a zero-crossing representation, which is stabilized by keeping the value of the wavelet transform integral between each pair of consecutive zero-crossings. The reconstruction algorithm has a fast convergence and each iteration requires O( N log² (N)) computation for a signal of N samples. The zero-crossings of a wavelet transform define a representation which is particularly well adapted for solving pattern recognition problems. As an example, the implementation and results of a coarse-to-fine stereo-matching algorithm are described     

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.     

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