Denoising and extracting background from fringe patterns using midpoint-based bidimensional empirical mode decomposition

The performance of interpolation algorithm used in bi-dimensional empirical mode decomposition directly affects its popularization and application. Therefore, the research on interpolation algorithm is more reasonable, accurate and fast. So far, in the interpolation algorithm adopted by the bi-dimensional empirical mode decomposition, an adaptive interpolation algorithm can be proposed according to the image characteristics. In view of this, this paper proposes an image interpolation algorithm based on the particle swarm and fractal. Its procedure includes: to analyze the given image by using the fractal brown function, to pick up the feature quantity from the image, and then to operate the adaptive image interpolation in terms of the obtained feature quantity. The parameters involved in the interpolation process are optimized by particle swarm optimization algorithm, and the optimal parameters are obtained, which can solve the problem of low efficiency and low precision of interpolation algorithm used in bi-dimensional empirical mode decomposition. It solves the problem that the image cannot be decomposed to obtain accurate and reliable bi-dimensional intrinsic modal function, and realize the fast decomposition of the image. It lays the foundation for the further popularization and application of the bi-dimensional empirical mode decomposition algorithm.

The arrangement of plant cortical microtubules can reflect the physiological state of cells. However, little attention has been paid to the image quantitative analysis of plant cortical microtubules so far. In this paper, Bidimensional Empirical Mode Decomposition (BEMD) algorithm was applied in the image preprocessing of the original microtubule image. And then Intrinsic Mode Function 1 (IMF1) image obtained by decomposition was selected to do the texture analysis based on Grey-Level Cooccurrence Matrix (GLCM) algorithm. Meanwhile, in order to further verify its reliability, the proposed texture analysis method was utilized to distinguish different images of Arabidopsis microtubules. The results showed that the effect of BEMD algorithm on edge preserving accompanied with noise reduction was positive, and the geometrical characteristic of the texture was obvious. Four texture parameters extracted by GLCM perfectly reflected the different arrangements between the two images of cortical microtubules. In summary, the results indicate that this method is feasible and effective for the image quantitative analysis of plant cortical microtubules. It not only provides a new quantitative approach for the comprehensive study of the role played by microtubules in cell life activities but also supplies references for other similar studies.

Synthetic aperture radar (SAR) produces ocean SAR solitary images which include the information of internal solitary waves (ISWs), surface wave, terraininfo and noise. Based on wavelet transform (WT) and bidimensional empirical mode decomposition (BEMD), we give a new algorithm, named wBEMD, to obtain information of ISWs from the SAR images, and apply it on two SAR images to extract ISWs features. The ISWs information layer obtained from wBEMD shows more intact ISW features, from which we retrieve the characteristic width and phase velocity of ISWs and analyse other detailed information. The closeness between the retrieved parameters and observed data verifies wBEMD's practicability.

Time-frequency analysis is of necessity for wrist pulse signal due to its complexity, among which, empirical mode decomposition (EMD) algorithm and its improved noise-assisted versions (such as ensemble EMD, noise-assisted multivariate EMD (NA-MEMD) and very recently median EMD) are deemed to be the most representative ones. In this study, we provide an in-depth evaluation of these well-established noise-assisted EMD algorithms in computational pulse analysis for the first time. In particular, we compare the performance of the different algorithms systematically and quantitatively based on objective quantitative criteria: number and central frequency of intrinsic mode function (IMF) components, total orthogonality index and mode mixing. Rather than using synthetic signals with visual inspection in most existing literature, the wrist pulse signals used in the evaluation are real recorded samples acquired from both healthy and patient subjects. Through extensive experiments, we found that: 1) Advanced EMD algorithm that has the best performance in other areas may not be the most suitable method for pulse signal analysis, which indicates its high dependence on the type of signal to be analyzed; 2) Adding noise can significantly improve algorithm performance, but tends to produce physiologically not relevant components, which however are usually neglected throughout the intelligent pulse diagnosis literature. Therefore, excluding redundant components and then extracting features is expected to improve performance further. Together, currently NA-MEMD achieves a better performance consistently, potential to become a powerful tool for computational pulse analysis, which in itself have not been applied in wrist pulse analysis before. We believe our works can bring up a new perspective to application of EMD-like algorithms in computational pulse analysis/diagnosis with effective information and guidance. Additionally, considering the similarity between physiological signals, especially such as photoplethysmogram/electrocardiogram, our research can be extended to wearable health monitoring technologies, including smart watches and fitness trackers, and their potential future applications, such as in heart rate estimation and evaluate various cardiovascular-related diseases. The present study underscored the necessity of evaluation noise-assisted EMDs or other adaptive decomposition algorithms based on real recorded signals with more objective measures. Especially, caution the possible redundant components that are introduced.

A novel Empirical mode decomposition (EMD) profilometry has been developed for dynamic measurement, which can reconstruct the 3D shape of an object by projecting only fringe pattern. The distinctive technique of the system is the newly developed Sinusoids-assisted Bidimensional EMD (SBEMD) algorithm, which can decompose an image into different pure scales. As even very detailed information can be purely extracted for analysis, EMD profilometry is able to measure the object with complex or discontinuous surface. However, the Gamma errors of the system become more obvious just due to these advantages of SBEMD, which also can be represented as high harmonics. In this paper, a simple yet effective phase filtering method is proposed also based on the SBEMD, which can filter the gamma errors but meantime avoid losing detailed phase. Experiments show the effectiveness of the method.

The data interpolation is an essential part of Bidimensional Empirical Mode Decomposition (BEMD) of an image. In the decomposition process, local maxima and minima of the image are extracted at each iteration and then interpolated to form the upper and lower envelopes, respectively. Because of the properties of radial basis function (RBF) interpolators, they are good candidates for use in BEMD. However, only one or two of the RBF interpolators have been utilized for BEMD so far. This paper employs many RBF interpolators for BEMD, compares their performances, and finds out the useful ones for BEMD especially in the image filtering application. We propose to apply the BEMD approach with the adequate interpolation function in the image denoising domain. After that, we combine the BEMD with the DWT to improve the BEMD denoising method. The analysis is done using real images. Simulations are made to focus mainly on the effect of interpolation methods by providing less or negligible control on the other parameters of the BEMD process. The study is believed to work as a guideline in the area of BEMD based real image in the filtering application.

A braking intention identification method based on empirical mode decomposition (EMD) algorithm and entropy theory for electric vehicles is proposed. EMD algorithm is given to decompose nonstationary brake pedal signal to stationary intrinsic mode function (IMF), which is the base of data mining. After that, entropy theory is used to extract brake pedal signal features. A braking intention identification model is built based on fuzzy c-means clustering algorithm. The hardware and software for braking intention identification system based on this method is set up to do offline and real-time experiments. The results show that the identification method proposed in this paper has good real-time quality and can distinguish moderate braking intention and gentle braking intention better.

In the present study, an adaptive Fourier Decomposition Method (FDM) is applied to identify damage at connections. For that purpose, an experimental single-story plane frame model is considered. The beam and columns of the frame are connected by angles and bolts, and the damage is introduced by loosening bolts at different locations. The frame is excited at the right top corner using a hammer, and strain time histories are collected from different points. The FDM and Empirical Mode Decomposition (EMD) algorithm are applied to characterize the damage sensitive features. The results obtained from the FDM are compared with the EMD algorithm, which shows that the performance of FDM is better, which motivates to extend its application further to estimate the amount of bolt loosening in terms of extracted damage sensitive features.

This paper reports an innovative pattern recognition technique for fracture microstructure images based on Bi-dimensional empirical mode decomposition (BEMD) and nonconvex penalty minimization L q (q = 0.5) regular sparse representation-based classification (NPMLq-SRC) algorithm. The detailed procedures of this work can be divided into three steps, i.e., the preprocessing stage, the feature extraction stage and the image classification stage. We test and validate the proposed method through real data from metallic alloy fracture images. The case verification results show that our proposal can obtain a much higher recognition accuracy than the conventional Back Propagation Neural Networks (BPNN for short), the L1-norm minimization sparse representation-based classification (L1-SRC) and the BEMD combined with L1-norm minimization sparse representation-based classification (BEMD+L1-SRC) methods, respectively. Specifically, the proposed BEMD+NPMLq-SRC (q = 0.5) method outperforms the BEMD+L1-SRC method by 3.33% improvement of the average recognition accuracy, and outperforms L1-SRC method by 14.06% improvement of the average recognition accuracy, respectively.

To address the issue of spectrum overlapping in Fourier transform profilometry, a new method based on Bi-dimensional Empirical Mode Decomposition (BEMD) is proposed. BEMD is an adaptive data decomposition method, so it does not need filters or basic functions which are important for Fourier transform or wavelet transform. In this paper, the complicated original signal of distorted fringe pattern is decomposed into several Bi-dimensional Intrinsic Mode Functions (BIMFs) as well as the residual component, with which the background component and some other frequency noises of fringe pattern can be eliminated effectively. It is beneficial to extract the first frequency component exactly for the subsequent wrapped phase retrieval in Fourier transform. Simulation and experiments illustrate the feasibility and the exactness of the proposed method.

Youzhi Zheng Tsinghua University, Department of Computer Science and Technology, Beijing, China 100084 Zheng Qin Tsinghua University, School of Software, Beijing, China 100084 We propose a novel multiscale decomposition (MSD) image fusion algorithm, which is region-based image fusion using bidimensional empirical mode decomposition (BEMD). BEMD is a 2-D data-driven decomposition derived from the empirical mode decomposition (EMD), which does not require predetermined filter or wavelet function. The input images are decomposed into a number of intrinsic mode functions (IMFs) as well as a residual image. The fusion is performed region by region based on the segmentations of the input images to produce composite BEMD representation, and then the inverse BEMD transform is applied to obtain the fused image. Experiments show that the proposed image fusion algorithm provides superior performance over traditional fusion schemes in terms of both objective metrics and visual quality.

In this paper, we introduce a robust image watermarking method based on bi-dimensional empirical mode decomposition (BEMD) against geometric distortion. Based on the characteristics of the image theory and human visual system, the proposed method makes use of orthogonal properties of empirical mode decomposition to achieve the BEMD transform on the image. The image is decomposed into a series of IMFs and residue which contain the different frequency parts of the image. So the watermark is adaptively weighed to the different positions of the middle frequency IMF region. The method makes use of the multi-scale analysis characteristics of image BEMD theory and the person's sense of vision and shows excellent advantage against shearing attack. The method could show the watermark clearly when half of the image has been cut. Experimental results show this method excellent robustness for image shearing. The watermark thus generated is invisible and performs well in StirMark test and is robust to geometrical attacks. Compared with other watermarking algorithms, this algorithm is more robust, especially against geometric distortion, while having excellent frequency properties.

To better analyze images with the Gaussian white noise, it is necessary to remove the noise before image processing. In this paper, we propose a self-adaptive image denoising method based on bidimensional empirical mode decomposition (BEMD). Firstly, normal probability plot confirms that 2D-IMF of Gaussian white noise images decomposed by BEMD follow the normal distribution. Secondly, energy estimation equation of the ith 2D-IMF (i=2,3,4,......) is proposed referencing that of ith IMF (i=2,3,4,......) obtained by empirical mode decomposition (EMD). Thirdly, the self-adaptive threshold of each 2D-IMF is calculated. Eventually, the algorithm of the self-adaptive image denoising method based on BEMD is described. From the practical perspective, this is applied for denoising of the magnetic resonance images (MRI) of the brain. And the results show it has a better denoising performance compared with other methods.

The interpolation causes the frequency aliasing in intrinsic mode functions (IMF) in bi-dimensional empirical mode decomposition (BEMD). The local orthogonality or the computational complexity of the improved BEMDs can not be met. In this paper, a novel BEMD - local estimation empirical mode decomposition (LEEMD) is proposed. Particularly, the local estimation instead of the interpolation without changing the framework of EMD is proposed to solve the problem. LEEMD will be applied in image fusion based on the proposed background/detail rule. In experiments, the objective and subjective experiments show that LEEMD and its application is effective.

Empirical mode decomposition (EMD) based methods have been widely used in fringe pattern analysis, including denoising, detrending, normalization, etc. The common problem of using EMD and Bi-dimensional EMD is the mode mixing problem, which is generally caused by uneven distribution of extrema. In recent years, we have proposed some algorithms to solve the mode mixing problem and further applied these methods in fringe analysis. In this paper, we introduce the development of these methods and show the successful results of two most recent algorithms.