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     

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     

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。     

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.     

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.     

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.     

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.     

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.     

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     

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     

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     

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.     

小波变换在傅立叶变换轮廓术中的应用

从小波变换本质、原理出发 ,说明它在提取条纹位相方面的应用 ,通过阐述小波变换与傅立叶变换两者之间的内在联系 ,将小波变换应用到傅立叶变换轮廓术中 ,并着重用傅立叶变换的原理对小波提取位相的原理进行详细解释。模拟结果表明 :小波变换在傅立叶变换轮廓术中的应用是正确的、可行的。     

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     

JPEG2000小波变换仿真

提出一种基于JPEG2000中推荐的提升结构的5/3小波变换硬件实现方案。该方案在加载数据的同时进行边界扩展,无须对运算电路进行逻辑控制,可以复用加法器,提高了资源利用率。该方案在FPGA上仿真通过。     

VLSI implementation of discrete wavelet transform

This paper presents a VLSI implementation of discrete wavelet transform (DWT). The architecture is simple, modular, and cascadable for computation of one or multidimensional DWT. It comprises of four basic units: input delay, filter, register bank, and control unit. The proposed architecture is systolic in nature and performs both high- and low-pass coefficient calculations with only one set of multipliers. In addition, it requires a small on-chip interface circuitry for interconnection to a standard communication bus. A detailed analysis of the effect of finite precision of data and wavelet filter coefficients on the accuracy of the DWT coefficients is presented. The architecture has been simulated in VLSI and has a hardware utilization efficiency of 87.5%. Being systolic in nature, the architecture can compute DWT at a data rate of N×10⁶ samples/s corresponding to a clock speed of N MHz