Fuzzy rule based multiwavelet ECG signal denoising

Since different multiwavelets, pre- and post-filters have different impulse responses and frequency responses, different multiwavelets, pre- and post-filters should be selected and applied at different noise levels for signal denoising if signals are corrupted by additive white Gaussian noises. In this paper, some fuzzy rules are formulated for integrating different multiwavelets, pre- and post-filters together so that expert knowledge on employing different multiwavelets, pre- and post-filters at different noise levels on denoising performances is exploited. When an ECG signal is received, the noise level is first estimated. Then, based on the estimated noise level and our proposed fuzzy rules, different multiwavelets, pre- and post-filters are integrated together. A hard thresholding is applied on the multiwavelet coefficients. According to extensive numerical computer simulations, our proposed fuzzy rule based multiwavelet denoising algorithm outperforms traditional multiwavelet denoising algorithms by 30%

Mine gearbox fault diagnosis based on multiwavelets and maximum correlated kurtosis deconvolution

As the mine gearbox working conditions are poor, the fault signal is weak and usually drowned in background noise when gearbox occurring fault. The fault feature is very difficult to extract. Aiming at solving this problem, this paper proposed a mine gearbox fault feature extraction method which combines multiwavelets decomposition with maximum correlated kurtosis deconvolution (MCKD).The component of multiwavelets decomposing was processed by MCKD method, MCKD suppress the noise in the signal and enhance the weak impact feature of fault signal, the envelope of its deconvolution signal was calculated, then the fault could be judged by analyzing the prominent frequency component of envelope spectrum. Thus, the experiment analysis and engineering application verify the effectiveness of the proposed method

Fuzzy multiwavelet denoising on an ECG signal

Since different multiwavelets, pre- and post-filters have different impulse and frequency responses characteristics, different multiwavelets, pre- and post-filters should be selected, integrated and applied at different noise levels if a signal is corrupted by an additive white Gaussian noise (AWGN). In this letter, some fuzzy rules on selecting and integrating different multiwavelets, pre- and post-filters together are proposed. These fuzzy rules are setup based on the training results of the denoising performances of applying different multiwavelets, pre- and post-filters at different noise levels. When a new electrocardiogram (ECG) signal is applied, the appropriate multiwavelets, pre- and post-filters are selected and integrated based on fuzzy rules and the noise level of the signal. A hard thresholding is applied on the multiwavelet coefficients. According to an extensive simulation, we found that our proposed fuzzy rule-based multiwavelet denoising algorithm achieves 30% improvement compared to the traditional multiwavelet denoising algorithms

A multi-wavelet based technique for calculating dense 2D disparity maps from stereo

A vision based approach for calculating accurate 3D models of the objects is presented. Generally industrial visual inspection systems capable of accurate 3D depth estimation rely on extra hardware tools like laser scanners or light pattern projectors. These tools improve the accuracy of depth estimation but also make the vision system costly and cumbersome. In the proposed algorithm, depth and dimensional accuracy of the produced 3D depth model depends on the existing reference model instead of the information from extra hardware tools. The proposed algorithm is a simple and cost effective software based approach to achieve accurate 3D depth estimation with minimal hardware involvement. The matching process uses the well-known coarse to fine strategy, involving the calculation of matching points at the coarsest level with consequent refinement up to the finest level. Vector coefficients of the wavelet transform-modulus are used as matching features, where wavelet transform-modulus maxima defines the shift invariant high-level features with phase pointing to the normal of the feature surface. The technique addresses the estimation of optimal corresponding points and the corresponding 2D disparity maps leading to the creation of accurate depth perception model. <br /

Disparity estimation using TI multi-wavelet transform

A multi-resolution image matching technique based on translation invariant discrete multi-wavelet transform followed by a coarse to fine matching strategy is presented. The technique addresses the estimation of optimal corresponding points and the corresponding disparity maps in the presence of occlusion, ambiguity and illuminative variations in the two perspective views taken by two different cameras or at different lighting conditions. The problem of occlusion and ambiguity is addressed explicitly by a geometric optimization approach along with the uniqueness constraint whereas the illuminative variation is dealt with by using windowed normalized correlation on the discrete multi-wavelet coefficients.<br /

Improving the performance of translation wavelet transform using BMICA

Research has shown Wavelet Transform to be one of the best methods for denoising biosignals. Translation-Invariant form of this method has been found to be the best performance. In this paper however we utilize this method and merger with our newly created Independent Component Analysis method – BMICA. Different EEG signals are used to verify the method within the MATLAB environment. Results are then compared with those of the actual Translation-Invariant algorithm and evaluated using the performance measures Mean Square Error (MSE), Peak Signal to Noise Ratio (PSNR), Signal to Distortion Ratio (SDR), and Signal to Interference Ratio (SIR). Experiments revealed that the BMICA Translation-Invariant Wavelet Transform out performed in all four measures. This indicates that it performed superior to the basic Translation- Invariant Wavelet Transform algorithm producing cleaner EEG signals which can influence diagnosis as well as clinical studies of the brain

Low Bit-rate Color Video Compression using Multiwavelets in Three Dimensions

In recent years, wavelet-based video compressions have become a major focus of research because of the advantages that it provides. More recently, a growing thrust of studies explored the use of multiple scaling functions and multiple wavelets with desirable properties in various fields, from image de-noising to compression. In term of data compression, multiple scaling functions and wavelets offer a greater flexibility in coefficient quantization at high compression ratio than a comparable single wavelet. The purpose of this research is to investigate the possible improvement of scalable wavelet-based color video compression at low bit-rates by using three-dimensional multiwavelets. The first part of this work included the development of the spatio-temporal decomposition process for multiwavelets and the implementation of an efficient 3-D SPIHT encoder/decoder as a common platform for performance evaluation of two well-known multiwavelet systems against a comparable single wavelet in low bitrate color video compression. The second part involved the development of a motion-compensated 3-D compression codec and a modified SPIHT algorithm designed specifically for this codec by incorporating an advantage in the design of 2D SPIHT into the 3D SPIHT coder. In an experiment that compared their performances, the 3D motion-compensated codec with unmodified 3D SPIHT had gains of 0.3dB to 4.88dB over regular 2D wavelet-based motion-compensated codec using 2D SPIHT in the coding of 19 endoscopy sequences at 1/40 compression ratio. The effectiveness of the modified SPIHT algorithm was verified by the results of a second experiment in which it was used to re-encode 4 of the 19 sequences with lowest performance gains and improved them by 0.5dB to 1.0dB. The last part of the investigation examined the effect of multiwavelet packet on 3-D video compression as well as the effects of coding multiwavelet packets based on the frequency order and energy content of individual subbands

Correspondence between Multiwavelet Shrinkage/Multiple Wavelet Frame Shrinkage and Nonlinear Diffusion

There are numerous methodologies for signal and image denoising. Wavelet, wavelet frame shrinkage, and nonlinear diffusion are effective ways for signal and image denoising. Also, multiwavelet transforms and multiple wavelet frame transforms have been used for signal and image denoising. Multiwavelets have important property that they can possess the orthogonality, short support, good performance at the boundaries, and symmetry simultaneously. The advantage of multiwavelet transform for signal and image denoising was illustrated by Bui et al. in 1998. They showed that the evaluation of thresholding on a multiwavelet basis has produced good results. Further, Strela et al. have showed that the decimated multiwavelet denoising provides superior results than decimated conventional (scalar) wavelet denoising. Mrazek, Weickert, and Steidl in 2003 examined the association between one-dimensional nonlinear diffusion and undecimated Haar wavelet shrinkage. They proved that nonlinear diffusion could be presented by using wavelet shrinkage. High-order nonlinear diffusion in terms of one-dimensional frame shrinkage and two-dimensional frame shrinkage were presented in 2012 by Jiang, and in 2013 by Dong, Jiang, and Shen, respectively. They obtained that the correspondence between both approaches leads to a different form of diffusion equation that mixes benefits from both approaches. The objective of this dissertation is to study the correspondence between one-dimensional multiwavelet shrinkage and high-order nonlinear diffusion, and to study high-order nonlinear diffusion in terms of one-dimensional multiple frame shrinkage also well. Further, this dissertation formulates nonlinear diffusion in terms of 2D multiwavelet shrinkage and 2D multiple wavelet frame shrinkage. From the experiment results, it can be inferred that nonlinear diffusion in terms of multiwavelet shrinkage/multiple frame shrinkage gives better results than a scalar case. On the whole, this dissertation expands nonlinear diffusion in terms of wavelet shrinkage and nonlinear diffusion in terms of frame shrinkage from the scalar wavelets and frames to the multiwavelets and multiple frames

A Hierarchical Bayesian Model for Frame Representation

In many signal processing problems, it may be fruitful to represent the signal under study in a frame. If a probabilistic approach is adopted, it becomes then necessary to estimate the hyper-parameters characterizing the probability distribution of the frame coefficients. This problem is difficult since in general the frame synthesis operator is not bijective. Consequently, the frame coefficients are not directly observable. This paper introduces a hierarchical Bayesian model for frame representation. The posterior distribution of the frame coefficients and model hyper-parameters is derived. Hybrid Markov Chain Monte Carlo algorithms are subsequently proposed to sample from this posterior distribution. The generated samples are then exploited to estimate the hyper-parameters and the frame coefficients of the target signal. Validation experiments show that the proposed algorithms provide an accurate estimation of the frame coefficients and hyper-parameters. Application to practical problems of image denoising show the impact of the resulting Bayesian estimation on the recovered signal quality

Noise Removal in Microarray Images Using Variational Mode Decomposition Technique

Microarray technology allows the simultaneous monitoring of thousands of genes in parallel. Based on the gene expression measurements, microarray technology have proven powerful in gene expression profiling for discovering new types of diseases and for predicting the type of a disease. Enhancement, Gridding, Segmentation and Intensity extraction are important steps in microarray image analysis. This paper presents a noise removal method in microarray images based on Variational Mode Decomposition (VMD). VMD is a signal processing method which decomposes any input signal into discrete number of sub-signals (called Variational Mode Functions) with each mode chosen to be its band width in spectral domain. First the noisy image is processed using 2-D VMD to produce 2-D VMFs. Then Discrete Wavelet Transform (DWT) thresholding technique is applied to each VMF for denoising.  The denoised microarray image is reconstructed by the summation of VMFs.  This method is named as 2-D VMD and DWT thresholding method. The proposed method is compared with DWT thresholding and BEMD and DWT thresholding methods. The qualitative and quantitative analysis shows that 2-D VMD and DWT thresholding method produces better noise removal than other two methods