Wavelet Decomposition Level Research Articles

Operational rate-distortion modeling for wavelet video coders

Based on our statistical investigation of a typical three-dimensional (3-D) wavelet codec, we present a unified mathematical model to describe its operational rate-distortion (RD) behavior. The quantization distortion of the reconstructed video frames is assessed by tracking the quantization noise along the 3-D wavelet decomposition trees. The coding bit-rate is estimated for a class of embedded video coders. Experimental results show that the model captures sequence characteristics accurately and reveals the relationship between wavelet decomposition levels and the overall RD performance. After being trained with offline RD data, the model enables accurate prediction of real RD performance of video codecs and therefore can enable optimal RD adaptation of the encoding parameters according to various network conditions

Fundamental wave extraction and frequency measurement based on IIR wavelet filter banks

A wavelet function with good frequency response was adopted and the optimal decomposition level of wavelet transform was studied in order to improve the accuracy of fundamental wave extraction and frequency measurement in signal processing. In frequency measurements, an evaluating method was proposed to determine right maximal value points, and the fundamental frequency of signal was estimated by the least squares method, which could reduce the influence of low frequency noises. An interpolation method in parabola form was used to eliminate the error of the non-integral period sampling. A digital signal processing system was developed with a digital signal processor (DSP) to realise the wavelet filter and frequency measurement algorithms in real time. The testing results show that both the methods and system proposed by this paper are effective.

Wavelet techniques: A suitable tool to characterise and optimize encoders’ based systems

Calibration data together with the approximation and details of wavelet decomposition functions can be used to obtain important parameters of digital transducers based systems. Besides offset and gain errors that are usually easy to evaluate and compensate, digital transducers exhibit differential and integral nonlinearity errors whose estimation, whenever possible, can be used to increase measurement’s system accuracy. An error compensated system can easily be implemented by adding to the digital transducer, a microcontroller and a memory with a code conversion table. The proposed technique, based on wavelet data processing, can also be applied to estimated analogue-to-digital converters parameters, namely differential and integral nonlinearity errors. In the present paper, simulation and experimental results, obtained from a low-cost angular encoder, are used to validate the proposed characterisation method for different wavelet decomposition levels and wavelet mother function types.

Method and application of wavelet shrinkage denoising based on genetic algorithm

Genetic algorithm (GA) based on wavelet transform threshold shrinkage (WTS) and translation-invariant threshold shrinkage (TIS) is introduced into the method of noise reduction, where parameters used in WTS and TIS, such as wavelet function, decomposition levels, hard or soft threshold and threshold can be selected automatically. This paper ends by comparing two noise reduction methods on the basis of their denoising performances, computation time, etc. The effectiveness of these methods introduced in this paper is validated by the results of analysis of the simulated and real signals.

Resolve of overlapping voltammetric signals in using a wavelet packet transform based Elman recurrent neural network

A novel method named wavelet packet transform based Elman recurrent neural network (WPTERNN) was applied to differential pulse voltammetric techniques for simultaneous determination of Ni(II), Zn(II) and Co(II) by combining wavelet packet denoising with Elman recurrent neural network (ERNN). The performances of the WPT methods were compared with seven other filtering techniques in terms of root mean square deviations between reconstructed and original mean voltammogram. The visual inspection of filtering effects was supplied by figure. Wavelet packet representations of signals provided a local time–frequency description, thus in the wavelet domain, the quality of the noise removal can be improved. Elman recurrent network was applied for non-linear multivariate calibration and together with the whole voltammogram to improve predictive ability. In this case, by trials wavelet function, decomposition level and numbers of hidden nodes for WPTERNN method were selected as Daubechies 4, 6 and 8, respectively. A program PWPTERNN was designed to perform simultaneous determination of Ni(II), Zn(II) and Co(II). The relative standard errors of prediction (RSEP) for all components with WPTERNN, ERNN, PLS, PCR, TTFA and MLR were 9.53, 9.82, 12.3, 17.0, 16.7 and 1.46 × 10 5%, respectively. Experimental results demonstrated that the WPTERRN method had the best performance among the six methods and the two ANN methods had the clear superiority over the three factor-based method.

Image Segmentation with Fast Wavelet-Based Color Segmenting and Directional Region Growing

This investigation proposes a fast wavelet-based color segmentation (FWCS) technique and a modified directional region-growing (DRG) technique for semantic image segmentation. The FWCS is a subsequent combination of progressive color truncation and histogram-based color extraction processes for segmenting color regions in images. By exploring specialized centroids of segmented fragments as initial growing seeds, the proposed DRG operates a directional 1-D region growing on pairs of color segmented regions based on those centroids. When the two examined regions are positively confirmed by DRG, the proposed framework subsequently computes the texture features extracted from these two regions to further check their relation using texture similarity testing (TST). If any pair of regions passes double checking with both DRG and TST, they are identified as associated regions. If two associated regions/areas are connective, they are unified to a union area enclosed by a single contour. On the contrary, the proposed framework merely acknowledges a linking relation between those associated regions/areas highlighted with any linking mark. Particularly, by the systematic integration of all proposed processes, the critical issue to decide the ending level of wavelet decomposition in various images can be efficiently solved in FWCS by a quasi-linear high-frequency analysis model newly proposed. The simulations conducted here demonstrate that the proposed segmentation framework can achieve a quasi-semantic segmentation without priori a high-level knowledge.

Wavelet de-noising for IMU alignment

Inertial navigation system (INS) is presently used in several applications related to aerospace systems and land vehicle navigation. An INS determines the position, velocity, and attitude of a moving platform by processing the accelerations and angular velocity measurements of an inertial measurement unit (IMU). Accurate estimation of the initial attitude angles of an IMU is essential to ensure precise determination of the position and attitude of the moving platform. These initial attitude angles are usually estimated using alignment techniques. Due to the relatively low signal-to-noise ratio of the sensor measurement (especially for the gyroscopes), the initial attitude angles may not be computed accurately enough. In addition, the estimated initial attitude angles may have relatively large uncertainties that may affect the accuracy of other navigation parameters. This article suggests processing the gyro and accelerometer measurements with multiple levels of wavelet decomposition to remove the high frequency noise components. The proposed wavelet de-noising method was applied on a navigational grade inertial measurement unit (LTN90-100). The results showed that accurate alignment procedure and fast convergence of the estimation algorithm, in addition to reducing the estimation covariance of the three attitude angles, could be obtained.

IMPROVING POSITIONING ACCURACY DURING KINEMATIC DGPS OUTAGE PERIODS USING SINS/DGPS INTEGRATION AND SINS DATA DE-NOISING

In the standard integration of a Differential Global Positioning System (DGPS) and a Strapdown Inertial Navigation System (SINS), the DGPS provides position information while the SINS provides attitude information. In addition, the DGPS measurements are used to estimate the inertial sensors systematic errors and the SINS is used to detect and correct GPS cycle slips. In case of GPS signal blockages, the SINS is used instead for positioning as a stand-alone system until the GPS signals are available again. To obtain accurate positions during DGPS outages, near real-time (or post-mission) techniques should be applied, where these techniques are known as bridging algorithms. In such algorithms, new and improved positions of the outage periods are estimated. In this paper, two different bridging methods are used namely: backward smoothing and parametric modeling. An SINS/DGPS data collected with a van has been used in the analysis. The results show that both bridging algorithms reduce the SINS positional errors for DGPS outages of 75 to 100 seconds with an average of 1.35 m to an RMSE of 19 cm in case of backward smoothing and 10 cm in case of parametric modeling. To separate between the actual motion dynamics and other disturbing vibrations, a de-noising of the SINS raw data is required. Therefore, a de-noising of the van SINS data has been applied using a wavelet decomposition technique to eliminate or minimize the effect of sensor noise and other high frequency disturbances (such as engine vibrations). An analysis of the SINS sensor kinematic raw data in the frequency domain shows clearly that the majority of the van motion dynamics are contained in the low frequency portion of the spectrum (below 3.0 Hz). Consequently, several levels of wavelet decomposition can be performed without losing any motion information. The application of both bridging methods after the SINS data de-noising reduces the positional RMSE to 11 cm and 7.7 cm using backward smoothing and parametric modeling, respectively.

IMPROVING POSITIONING ACCURACY DURING KINEMATIC DGPS OUTAGE PERIODS USING SINS/DGPS INTEGRATION AND SINS DATA DE-NOISING

In the standard integration of a Differential Global Positioning System (DGPS) and a Strapdown Inertial Navigation System (SINS), the DGPS provides position information while the SINS provides attitude information. In addition, the DGPS measurements are used to estimate the inertial sensors systematic errors and the SINS is used to detect and correct GPS cycle slips. In case of GPS signal blockages, the SINS is used instead for positioning as a stand-alone system until the GPS signals are available again. To obtain accurate positions during DGPS outages, near real-time (or post-mission) techniques should be applied, where these techniques are known as bridging algorithms. In such algorithms, new and improved positions of the outage periods are estimated. In this paper, two different bridging methods are used namely: backward smoothing and parametric modeling. An SINS/DGPS data collected with a van has been used in the analysis. The results show that both bridging algorithms reduce the SINS positional errors for DGPS outages of 75 to 100 seconds with an average of 1.35 m to an RMSE of 19 cm in case of backward smoothing and 10 cm in case of parametric modeling. To separate between the actual motion dynamics and other disturbing vibrations, a de-noising of the SINS raw data is required. Therefore, a de-noising of the van SINS data has been applied using a wavelet decomposition technique to eliminate or minimize the effect of sensor noise and other high frequency disturbances (such as engine vibrations). An analysis of the SINS sensor kinematic raw data in the frequency domain shows clearly that the majority of the van motion dynamics are contained in the low frequency portion of the spectrum (below 3.0 Hz). Consequently, several levels of wavelet decomposition can be performed without losing any motion information. The application of both bridging methods after the SINS data de-noising reduces the positional RMSE to 11 cm and 7.7 cm using backward smoothing and parametric modeling, respectively.

WAVELET-BASED MEDICAL IMAGE COMPRESSION USING EZW: OBJECTIVE AND SUBJECTIVE EVALUATIONS

Recently, the wavelet transform has emerged as a cutting edge technology within the field of image compression research. Wavelet methods involve overlapping transforms with varying-length basis functions. This overlapping nature of the transform alleviates blocking artifacts, while the multi-resolution character of the wavelet decomposition leads to superior energy compaction and perceptual quality of the decompressed image. Embedded zerotree wavelet (EZW) coder is the first algorithm to show the full power of wavelet-based image compression. The main purpose of this paper is to investigate the impact and quality of orthogonal wavelet filter in compressing medical image by using EZW. Meanwhile, we also look into the effect of the level of wavelet decomposition towards compression efficiency. The wavelet filters used are Haar and Daubechies. The compression simulations are done on three modalities of medical images. The objective (based on PSNR) and subjective (perceived image quality) results of these simulations are presented.

Extracting symptoms of bearing faults in the wavelet domain

Improving the signal-to-noise (S/N) ratio is one of the classic machinery failure diagnostic problems. A new failure detection procedure using a wavelet-based estimator is proposed for extracting the symptoms of bearing faults under environmental noise conditions. The paper discusses the relationship between de-noising efficiency and S/N ratio under different threshold values and wavelet decompositions. Efficient ranges of wavelet coefficients and levels of wavelet decomposition for extracting the symptoms of bearing faults are obtained. A comparison of the failure detection capabilities of an envelope detector and a wavelet-based estimator under significant environmental noise is performed and the results show that the wavelet-based estimator is an effective method for extracting the symptoms of a bearing fault under such conditions.

Extracting symptoms of bearing faults in the wavelet domain

Improving the signal-to-noise (S/N) ratio is one of the classic machinery failure diagnostic problems. A new failure detection procedure using a wavelet-based estimator is proposed for extracting the symptoms of bearing faults under environmental noise conditions. The paper discusses the relationship between de-noising efficiency and S/N ratio under different threshold values and wavelet decompositions. Efficient ranges of wavelet coefficients and levels of wavelet decomposition for extracting the symptoms of bearing faults are obtained. A comparison of the failure detection capabilities of an envelope detector and a wavelet-based estimator under significant environmental noise is performed and the results show that the wavelet-based estimator is an effective method for extracting the symptoms of a bearing fault under such conditions.

Wavelet packet transform and artificial neural network applied to simultaneous kinetic multicomponent determination

This paper presents a novel method, named wavelet packet transform based multilayer feedforward neural network with Levenberg-Marquardt and back propagation algorithm (WPTLMBP), developed for simultaneous kinetic determination of Cu(II), Fe(III), and Ni(II). Wavelet packet representations of signals provided a local time-frequency description, thus in the wavelet packet domain the quality of noise removal can be improved. The artificial neural network was applied for non-linear multivariate calibration. In this study, by optimization, wavelet packet function, decomposition level and number of hidden nodes for WPTLMBP method were selected as Db2, 2, and 4 respectively. A program PWPTLMBP was designed to perform simultaneous kinetic determination of Cu(II), Fe(III), and Ni(II). The relative standard error of prediction (RSEP) for all components with WPTLMBP, LM-BP-MLFN, and PLS methods were 6.39, 10.4, and 8.30%, respectively. Experimental results showed the proposed method to be successful and better than the others.

Beamlet dose distribution compression and reconstruction using wavelets for intensity modulated treatment planning.

Intensity modulated radiation therapy (IMRT) treatment planning is often formulated as the optimization of weights of fixed-geometry subfields (beamlets). Efficient optimization techniques can be based on direct storage of the influence matrix relating beamlet weights to dose values. However, direct storage of beamlet dose distributions for IMRT treatment planning can easily exceed several gigabytes, and is therefore often not feasible. We present a method for rapidly calculating full three-dimensional IMRT dose distributions, based on a vector of beamlet weights. The method is based on compressed beamlet dose distributions using fast digital wavelet transforms and so-called hard thresholding. We studied the method with a rectangular beamlet of 0.5 cm x 0.5 cm cross section from a monoenergetic 6 MeV photon point source simulated in homogeneous (water) and heterogeneous (CT-data) phantoms. Dose was calculated using the accurate VMC+ + Monte Carlo engine. The beamlet dose distributions were wavelet transformed and compressed by dropping wavelet coefficients below a given threshold value. Dose is then computed using the remaining wavelets. Selection of the wavelet basis function, decomposition level, and threshold values, for different slice orientations (transverse or parallel to the beam) and varying angles of beamlet incidence are studied. A typical in-slice compression ratio for a plane containing a beamlet was 32:1 using the sym2 wavelet and a threshold of 0.01, with a typical root-mean-square error, for voxels above 50% of the maximum dose, of about 0.04%. The overall compression performance, which includes many planes with little information content, is on the order of 100:1 or greater compared to full matrix storage. Although other methods are available to make the use of stored influence matrix values more feasible in IMRT treatment planning (such as using coarse grids or restricting values to defined volumes of interest) we conclude that wavelet compression facilitates the storage and use of full pencil dose deposition (influence matrix) data in IMRT treatment planning.

Statistical modelling of the wavelet coefficients with different bases and decomposition levels

Various wavelet coefficient statistics are useful to increase the compression efficiency of images. The distribution of the wavelet coefficients within a sub-band affects how the decompression values should be adjusted. A generalised Gaussian distribution model is seen to be applicable from a theoretical point of view, and a convenient way is provided to estimate the parameters from the empirical data. This knowledge is applied to examine the best statistical modelling of the wavelet coefficients for different wavelet bases and decomposition levels.

Identifying the characteristic scale of scene variation in fine spatial resolution imagery with wavelet transform-based sub-image statistics

Understanding the spatial structure of fine spatial resolution images is instrumental for either pixel- or object-based image analysis. In this Letter, the characteristic scale of scene variation in images is evaluated using statistics of sub-images produced by a wavelet transform. Six statistics, namely mean, variance, standard deviation (SD), coefficient of variation, skewness and kurtosis, were calculated for three directional sub-images and their derivative energy signature image at a sequence of wavelet decomposition levels. A simulated image, an aerial AUSIMAGE™ image (spatial resolution 0.2 m) and a recent Système Probatoire de l'Observation de la Terre (SPOT)-5 High Resolution Geometric (HRG) panchromatic image (spatial resolution 2.5 m) were analysed. It was found that with energy signature images, the change rate of SD over spatial resolution ranges between two successive decomposition levels ( ( SD/ ( R) suggested a synoptic and approximate description for the characteristic scale of scene variation. However, by comparing the result with the ranges of geostatistical variograms, it is suggested that the geostatistical method can correctly identify the characteristic scales of scene variation; semivariances can be calculated at any lag and orientation, while standard wavelet transforms are decomposed at only limited spatial resolution and orientation levels.

Wavelet Packet Compression of Medical Images

Tolba, A. S., Wavelet Packet Compression of Medical Images, Digital Signal Processing 12 (2002) 441–470 The increasing need for efficient image storage and transmission in hospitals imposes heavy requirements on the design of picture archiving and communication systems. Thus new methods are needed for efficient image compression. Recent reviews of wavelets in biomedical applications showed that wavelets should be used with caution and that a particular solution should always be motivated by the problem itself. This study discovers the best design parameters for a data compression scheme applied to medical images of different imaging modalities. The proposed technique aims at reducing the transmission cost while preserving the diagnostic integrity. By selecting the wavelet packet's filters, decomposition level and subbands that are better adapted to the frequency characteristics of the image, one may achieve better image representation in the sense of lower entropy or minimum distortion. Experimental results show that the selection of the best parameters has a dramatic effect on the data compression rate of medical images. Statistical significance tests were performed on the experimental measures to conduct the most suitable wavelet shape for each imaging modality. Image quality measures are used to evaluate the performance of different wavelet filters for different imaging modalities. Image resolution is found to have a remarkable effect on the compression rate.

Ball grid array (BGA) substrate conduct paths inspection using two-dimensional wavelet transform

The objective of this paper is to implement two-dimensional wavelet transform (2-D WT) in the detection of mousebite, spur, open, and short defect candidates on ball grid array (BGA) substrate conduct paths. Once the defect candidates are located, traditional BGA substrate inspection algorithms can further detect true defects among these suspicious defects. Therefore, the scope and effort during the inspection stage can be significantly reduced. The binary BGA substrate image is processed that shows only conduct path boundaries, which are decomposed directly by 2-D WT. Then, the inter-scale ratio from the wavelet transform modulus sum (WTMS) across adjacent decomposition levels for the edge pixels on BGA substrate conduct path boundaries is calculated. Since irregular edges in a small domain can preserve much more wavelet energy, an edge pixel is considered as an abnormal one or a defect candidate if its inter-scale ratio is less than a predefined threshold. The proposed approach is template-free and easy to implement, so it is suitable for small batch production. Real BGA substrates with synthetic boundary defects are used as testing samples to evaluate the performance of the proposed approach. Experimental results show that the proposed method is able to capture all the true mousebite, spur, open, and short defects without any missing errors by appropriate wavelet basis, decomposition level, and image resolution.

Wavelet-based approach for ball grid array (BGA) substrate conduct paths inspection

The aim was to detect boundary defects such as open, short, mousebite and spur on ball grid array (BGA) substrate conduct paths using machine vision. The 2-D boundaries of BGA substrate conduct paths are initially represented by the 1-D tangent curve. The tangent angles were evaluated from the eigenvector of a covariance matrix constructed by the boundary coordinates over a small boundary segment. Since defective regions of boundaries result in irregular tangent variations, the wavelet transform was used to decompose the 1-D tangent curve and capture the irregular angle variations. A boundary defect can then be easily located by evaluating the wavelet coefficients of the 1-D tangent curve in its high-pass decomposition. The proposed method is invariant with respect to the rotation of the BGA substrates and does not require prestored templates for matching. Real BGA substrates with various boundary defects were used as test samples to evaluate the performance of the proposed method. Experimental results show that the proposed method achieves 100% correct identification for BGA substrate boundary defects by selecting appropriate wavelet basis and decomposition level.

EDGE EXTRACTION OF IMAGES BY RECONSTRUCTION USING WAVELET DECOMPOSITION DETAILS AT DIFFERENT RESOLUTION LEVELS

This paper describes a novel method for edge feature detection of document images based on wavelet decomposition and reconstruction. By applying the wavelet decomposition technique, a document image becomes a wavelet representation, i.e. the image is decomposed into a set of wavelet approximation coefficients and wavelet detail coefficients. Discarding wavelet approximation, the edge extraction is implemented by means of the wavelet reconstruction technique. In consideration of the mutual frequency, overlapping will occur between wavelet approximation and wavelet details, a multiresolution-edge extraction with respect to an iterative reconstruction procedure is developed to ameliorate the quality of the reconstructed edges in this case. A novel combination of this multiresolution-edge results in clear final edges of the document images. This multi-resolution reconstruction procedure follows a coarser-to-finer searching strategy. The edge feature extraction is accompanied by an energy distribution estimation from which the levels of wavelet decomposition are adaptively controlled. Compared with the scheme of wavelet transform, our method does not incur any redundant operation. Therefore, the computational time and the memory requirement are less than those in wavelet transform.