The Lifting Scheme Based on the Second Generation Wavelets

The lifting scheme is a custom design construclion of Biorthogonal wavelets, a fast and efficient method to realize wavelet transform,which provides a wider range of application and efficiently reduces the computing time with its particular frame. This paper aims at introducing the second generation wavelets, begins with traditional Mallat algorithms, illustrates the lifting scheme and brings out the detail steps in the construction of Biorthogonal wavelets. Because of isolating the degrees of freedom remaining the biorthogonality relations, we can fully control over the lifting operators to design the wavelet for a particular application, such as increasing the number of the vanishing moments.

An Improved Algorithm for Image Edge Detection Based on Lifting Scheme

Wavelet transform is an ideal way for edge detection because of its multi-scale property, localization both in time and frequency domain, sensitivity to the abrupt change of signals, and so on. An improved algorithm for image edge detection based on Lifting Scheme is proposed in this paper. The simulation results show that our improved method can better reflect edge information of images.

Lifting Scheme Based SPIHT Still Image Coding

In order to eliminate float-point operations for fast wavelet transform, an integer D9/7 biorthogonal reversible wavelet transform was accomplished by lifting scheme. The lifting scheme based wavelet transform can be finished by addition and shift simply. It improved the quality of reconstructive image and greatly reduced the computational complexity due to integer operation. It is suitable for real-time image coding on hardware such as DSP. The simulation results show that the lifting scheme based SPIHT is prior to traditional wavelet based SPHIT in quality and complexity.

Lifting Scheme and Its Application to Edge Detection

Lifting scheme is a useful and very general technique for constructing wavelet decomposition. The paper adapts the lifting into redundant lifting to obtain shift invariant wavelet transform. In prediction and update stages of the lifting morphological operator is adopted for preserving local maxima of a signal over several scales, which is particularly useful in wavelet\|based signal detec tion. The new transform presented in the paper is applied in multiresoluti on edge detection of medical image and experim ent results are given to show better performance and applicable potentiali ty.

Lifting scheme of symmetric tight wavelets frames

This paper proposes a method to realize the lifting scheme of tight frame wavelet filters. As for 4-channel tight frame wavelet filter, the tight frame transforms＇ matrix is 2×4, but the lifting scheme transforms＇ matrix must be 4×4. And in the case of 3-channel tight frame wavelet filter, the transforms＇ matrix is 2×3, but the lifting scheme transforms＇ matrix must be 3×3. In order to solve this problem, we introduce two concepts： transferred polyphase matrix for 4-channel filters and transferred unitary matrix for 3-channel filters. The transferred polyphase matrix is symmetric/antisymmetric. Thus, we use this advantage to realize the lifting scheme.

Fault Diagnosis of a Rotor Based on a Lifting Wavelet and Local Wave

Aiming at the mode mixture in local wave decomposition（LWD） caused by a noise signal, the original data is preprocessed using the lifting wavelet transformation to suppress abnormal interference of noise and improve the quality of decomposition. It is employed to analyze the vibration signal of rotor rub-impact for extracting the weak impulsive feature. The signal is decomposed into intrinsic mode functions by LWD, then the high-frequency components are analyzed by Hilbert envelop demodulation. The period of the impulse response can be achieved, and the modulate fault feature of the vibration signal of a rotor system with rub-impact fault can be extracted exactly. Analysis results show that the proposed method is accurate and efficient, and is expected to be applied in engineering practice effectively.

APPLICATION OF WEIGHTED NONOSCILLATORY AND NON-FREE-PARAMETER DISSIPATION DIFFERENCE SCHEME IN CALCULATING THE FLOW OF VIBRATING FLAT CASCADE

A dual-time method is introduced to calculate the unsteady flow in a certain vibrating flat cascade. An implicit lower-upper symmetric-gauss-seidel scheme（LU-SGS） is applied for time stepping in pseudo time domains, and the convection items are discretized with the spatial three-order weighted non-oscillatory and non-free-parameter dissipation difference （WNND） scheme. The turbulence model adopts q-co low-Reynolds-number model. The frequency specmuns of lift coefficients and the unsteady pressure-difference coefficients at different spanwise heights as well as the entropy contours at blade tips on different vibrating instants, are obtained. By the analysis of frequency specmuns of lift coefficients at three spanwise heights, it is considered that there exist obvious non-linear perturbations in the flow induced by the vibrating, and the perturbation frequencies are higher than the basic frequency. The entropy contours at blade tips at different times display an intensively unsteady attribute of the flow under large amplitudes.

Nonlinear Adaptive Wavelet Transform for Lossless Image Compression

The paper presents a class of nonlinear adaptive wavelet transforms for lossless image compression. In update step of the lifting the different operators are chosen by the local gradient of original image. A nonlinear morphological predictor follows the update adaptive lifting to result in fewer large wavelet coefficients near edges for reducing coding. The nonlinear adaptive wavelet transforms can also allow perfect reconstruction without any overhead cost. Experiment results are given to show lower entropy of the adaptive transformed images than those of the non-adaptive case and great applicable potentiality in lossless image compresslon.

Seismic data compression based on integer wavelet transform

Due to the particularity of the seismic data, they must be treated by lossless compression algorithm in some cases. In the paper, based on the integer wavelet transform, the lossless compression algorithm is studied. Comparing with the traditional algorithm, it can better improve the compression rate. CDF (2, n) biorthogonal wavelet family can lead to better compression ratio than other CDF family, SWE and CRF, which is owe to its capability in can- celing data redundancies and focusing data characteristics. CDF (2, n) family is suitable as the wavelet function of the lossless compression seismic data.

AN EFFICIENT 3-DIMENSIONAL DISCRETE WAVELET TRANSFORM ARCHITECTURE FOR VIDEO PROCESSING APPLICATION

This paper presents an optimized 3-D Discrete Wavelet Transform (3-DDWT) architecture. 1-DDWT employed for the design of 3-DDWT architecture uses reduced lifting scheme approach. Further the architecture is optimized by applying block enabling technique, scaling, and rounding of the filter coefficients. The proposed architecture uses biorthogonal (9/7) wavelet filter. The architecture is modeled using Verilog HDL, simulated using ModelSim, synthesized using Xilinx ISE and finally implemented on Virtex-5 FPGA. The proposed 3-DDWT architecture has slice register utilization of 5%, operating frequency of 396 MHz and a power consumption of 0.45 W.

Low complexity reconfigurable architecture for the 5/3 and 9/7 discrete wavelet transform

Efficient reconfigurable VLSI architecture for 1-D 5/3 and 9/7 wavelet transforms adopted in JPEG2000 proposal, based on lifting scheme is proposed. The embedded decimation technique based on fold and time multiplexing, as well as embedded boundary data extension technique, is adopted to optimize the design of the architecture. These reduce significantly the required numbers of the multipliers, adders and registers, as well as the amount of accessing external memory, and lead to decrease efficiently the hardware cost and power consumption of the design. The architecture is designed to generate an output per clock cycle, and the detailed component and the approximation of the input signal are available alternately. Experimental simulation and comparison results are presented, which demonstrate that the proposed architecture has lower hardware complexity, thus it is adapted for embedded applications. The presented architecture is simple, regular and scalable, and well suited for VLSI implementation.

The Real-Time Image Processing Technique Based on DSP

This paper proposes a novel real time image processing technique based on digital singnal processor （DSP）. At the aspect of wavelet transform（WT） algorithm, the technique uses algorithm of second generation wavelet transform lifting scheme WT that has low calculation complexity property for the 2 D image data processing. Since the processing effect of lifting scheme WT for I D data is better than the effect of it for 2 D data obviously, this paper proposes a reformative processing method： Transform 2-D image data to 1 D data sequence by linearization method, then process the 1 D data sequence by algorithm of lifting scheme WT. The method changes the image convolution mode, which based on the cross filtering of rows and columns. At the aspect of hardware realization, the technique optimizes the program structure of DSP to exert the operation power with the iwchip memorizer of DSP. The experiment results show that the real time image processing techniquc proposed in this paper can meet the real-time requirement of videoimage transmitting in the video surveillance system of electric power. So the technique is a feasible and efficient DSP solution.

Singularity Detecting with the SecondGeneration Wavelet

Adopting the lifting scheme, introduced by Sweldens, a new wavelet is constructed. It overcomes the shortcoming of the classical wavelets that has no flexibility in the number of vanishing moment. Two examples are given to prove the second-generation wavelets's potentialities in the singularity detection of signal: a wavelet with vanishing moment and symmetry can be constructed according to the problem. Key words biorthogonal wavelet - lifting scheme - secondgeneration wavelets - singularity CLC number O 174.2 Foundation item: Supported by the National Natural Science Foundation of China (19602014)Biography: XU Bing-lian (1977-), female, Master candidate, research direction: the wavelets application.

Numerical solution of Poisson equation with wavelet bases of Hermite cubic splines on the interval

A new wavelet-based finite element method is proposed for solving the Poisson equation. The wavelet bases of Hermite cubic splines on the interval are employed as the multi-scale interpolation basis in the finite element analysis. The lifting scheme of the wavelet-based finite element method is discussed in detail. For the orthogonal characteristics of the wavelet bases with respect to the given inner product, the corresponding multi-scale finite element equation can be decoupled across scales, totally or partially, and suited for nesting approximation. Numerical examples indicate that the proposed method has the higher efficiency and precision in solving the Poisson equation.

An Approach to Integer Wavelet Transform for Medical Image Compression in PACS

We study an approach to integer wavelet transform for lossless compression of medical image in medical picture archiving and communication system (PACS). By lifting scheme a reversible integer wavelet transform is generated, which has the similar features with the corresponding biorthogonal wavelet transform. Experimental results of the method based on integer wavelet transform are given to show better performance and great applicable potentiality in medical image compression.

Improved Region Energy Based Image Fusion Rule for Multi-focus Image Fusion

In this paper,we propose a novel improved region energy based image fusion rule.The original images are firstly decomposed by using the lifting scheme of wavelet transform into four sub-bands:LL,LH,HL,HH,by studying principles and characteristics of the wavelet subbands,and we put emphasis on the high frequency subbands.Thus HH,HL,LH sub-bands,which represent three direction of high frequency details,are weighted by different size of three direction Gaussian kernel,then the energy based image fusion rule is applied with a optional size of window,thus the activity level of high frequency subbands are obtained,followed by a local region matching degree in the corresponding direction and resolution,an activity level of low frequency subband is calculated,then perform consistency verification on the selected wavelet coefficients,by doing the inverse wavelet transform the fused image is obtained.The performance of the proposed novel image fusion scheme is conducted and compared with a few existing image fusion algorithm,the experimental results show that the proposed method is an effective multi-focus image fusion algorithm.

A Study on Wavelet Data Compression of a Real-Time Monitoring System for Large Hydraulic Machines

The general concept of data compression consists in removing the redundancy existing in data to find a more compact representation. This paper is concerned with a new method of compression using the second generation wavelets based on the lifting scheme, which is a simple but powerful wavelet construction method. It has been proved by its successful application to a real-time monitoring system of large hydraulic machines that it is a promising compression method.

Segment-based coding of color images

Based on the idea of second generation image coding, a novel scheme for coding still images is pre- sented.At first, an image was partitioned with a pulse-coupled neural network; and then an improved chain code and the 2D discrete cosine transform was adopted to encode the shape and the color of its edges respectively.To code its smooth and texture regions, an improved zero-trees strategy based on the 2nd generation wavelet was chosen.After that, the zero-tree chart was selected to rearrange quantified coefficients.And finally some regulations were given according to psychology of various users.Experiments under noiseless channels demonstrate that the proposed method performs better than those of the current one, such as JPEG, CMP, EZW and JPEG2000.