Digital Filter Algorithm Based on Morphological Lifting Scheme and Median Filter

Abstract--When the circuits in which electronic products are fitted are disturbed by various interrupting signals, wave distortions occur to the normal voltage signals of these circuits. These wave distortions influence the normal operation and life cycle of electronic products. To eliminate the harmful effects of interrupting signals on electronic products, in this paper, a digital filter algorithm based on morphological lifting scheme and median filter （MLS-MF）, which will be used to filter various interrupting signals existing in the circuits in which electronic products are fitted, is proposed. A variety of interrupting sig- nals have been included in simulation studies, and simulation results have demonstrated the effectiveness and feasibility of the proposed digital filter algorithm in high frequency continuous interference, random background noise and damped oscillatory transient interference filter. Index Terms--Digital filter, lifting scheme, median filter, mor- phology.

Second-generation wavelet finite element based on the lifting scheme for GPR simulation

Ground-penetrating radar(GPR)is a highly efficient,fast and non-destructive exploration method for shallow surfaces.High-precision numerical simulation method is employed to improve the interpretation precision of detection.Second-generation wavelet finite element is introduced into the forward modeling of the GPR.As the finite element basis function,the second-generation wavelet scaling function constructed by the scheme is characterized as having multiple scales and resolutions.The function can change the analytical scale arbitrarily according to actual needs.We can adopt a small analysis scale at a large gradient to improve the precision of analysis while adopting a large analytical scale at a small gradient to improve the efficiency of analysis.This approach is beneficial to capture the local mutation characteristics of the solution and improve the resolution without changing mesh subdivision to realize the efficient solution of the forward GPR problem.The algorithm is applied to the numerical simulation of line current radiation source and tunnel non-dense lining model with analytical solutions.Result show that the solution results of the secondgeneration wavelet finite element are in agreement with the analytical solutions and the conventional finite element solutions,thereby verifying the accuracy of the second-generation wavelet finite element algorithm.Furthermore,the second-generation wavelet finite element algorithm can change the analysis scale arbitrarily according to the actual problem without subdividing grids again.The adaptive algorithm is superior to traditional scheme in grid refinement and basis function order increase,which makes this algorithm suitable for solving complex GPR forward-modeling problems with large gradient and singularity.

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.

An Image Fusion Algorithm Based on Lifting Scheme

Taking the advantage of the lifting scheme＇s characters that can build wavelet translorms tor transforming from integer to integer and the quality of the reconstructing image＇is independent of the topology way adopted by the boundary, an image fusion algorithm based on lifting scheme is proposed. This paper discusses the fundamental theory of lifting scheme firstly and then after taking transform analysis according to a kind of images that need to be confused.

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.

A COMPRESSION ALGORITHM FOR ECG BASED ON INTEGER LIFTING SCHEME WAVELET TRANSFORM

In view of the shortcomes of conventional ElectroCardioGram (ECG) compression algo- rithms,such as high complexity of operation and distortion of reconstructed signal,a new ECG compression encoding algorithm based on Set Partitioning In Hierarchical Trees (SPIHT) is brought out after studying the integer lifting scheme wavelet transform in detail.The proposed algorithm modifies zero-tree structure of SPIHT,establishes single dimensional wavelet coefficient tree of ECG signals and enhances the efficiency of SPIHT-encoding by distributing bits rationally,improving zero-tree set and ameliorating classifying method.For this improved algorithm,floating-point com- putation and storage are left out of consideration and it is easy to be implemented by hardware and software.Experimental results prove that the new algorithm has admirable features of low complexity, high speed and good performance in signal reconstruction.High compression ratio is obtained with high signal fidelity as well.

Feature extraction of gear-localized defect using adaptive lifting scheme and local gradient maps

In this paper,the adaptive lifting scheme (ALS) and local gradient maps (LGM) are proposed to isolate the transient feature components from the gearbox vibration signals. Based on entropy minimization rule,the ALS is employed to change properties of an initial wavelet and design adaptive wavelet. Then LGM is applied to characterize the transient feature components in detail signal of decomposition results using ALS. In the present studies, the orthogonal Daubechies 4 (Db 4) wavelet is used as the initial wavelet. The proposed method is applied to both simulated signals and vibration signals acquired from a gearbox for periodic impulses detection. The two conventional methods (cepstrum analysis and Hilbert envelope analysis) and the orthogonal Db4 wavelet are also used to analyze the same signals for comparison. The results demonstrate that the proposed method is more effective in extracting transient components from noisy signals.

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.

Denoising of SAR Images Based on Lifting Scheme Wavelet Packet Transform

According to the different characteristics that signal and noise exhibit during wavelet decomposition, a new denoising method based on the lifting scheme wavelet packet decomposition is presented. In this method, the SAR images are decom- posed by using the best wavelet packet and the norm of each sub-band are calculated; signals and noise can be discriminated based on the norm and soft-threshold method, and the images can be denoised. Experiments show that the proposed algorithm has excellent performance in denoising SAR images, and can remove most noise of images with well-kept texture detail informa- tion. The calculating speed of the method is twice the speed of the general wavelet packet transform algorithm.

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.

A Parallel-based Lifting Algorithm and VLSI Architecture for DWT

A novel Parallel-Based Lifting Algorithm （PBLA） for Discrete Wavelet Transform （DWT）, exploiting the parallelism of arithmetic operations in all lifting steps, is proposed in this paper. It leads to reduce the critical path latency of computation, and to reduce the complexity of hardware implementation as well. The detailed derivation on the proposed algorithm, as well as the resulting Very Large Scale Integration （VLSI） architecture, is introduced, taking the 9/7 DWT as an example but without loss of generality. In comparison with the Conventional Lifting Algorithm Based Implementation （CLABI）, the critical path latency of the proposed architecture is reduced by more than half from （4Tm ＋ 8Ta）to Tm ＋ 4Ta, and is competitive to that of Convolution-Based Implementation （CBI）, but the new implementation will save significantly in hardware. The experimental results demonstrate that the proposed architecture has good performance in both increasing working frequency and reducing area.

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.