Single-shot fringe pattern phase retrieval using improved period-guided bidimensional empirical mode decomposition and Hilbert transform

Fringe pattern analysis is the central aspect of numerous optical measurement methods, e.g., interferometry, fringe projection, digital holography, quantitative phase microscopy. Experimental fringe patterns always contain significant features originating from fluctuating environment, optical system and illumination quality, and the sample itself that severely affect analysis outcome. Before the stage of phase retrieval (information decoding) interferogram needs proper filtering, which minimizes the impact of mentioned issues. In this paper we propose fully automatic and adaptive fringe pattern pre-processing technique - improved period guided bidimensional empirical mode decomposition algorithm (iPGBEMD). It is based on our previous work about PGBEMD which eliminated the mode-mixing phenomenon and made the empirical mode decomposition fully adaptive. In present work we overcame key problems of original PGBEMD – we have considerably increased algorithm’s application range and shortened computation time several-fold. We proposed three solutions to the problem of erroneous decomposition for very low fringe amplitude images, which limited original PGBEMD significantly and we have chosen the best one among them after comprehensive analysis. Several acceleration methods were also proposed and merged to ensure the best results. We combined our improved pre-processing algorithm with the Hilbert Spiral Transform to receive complete, consistent, and versatile fringe pattern analysis path. Quality and effectiveness evaluation, in comparison with selected reference methods, is provided using numerical simulations and experimental fringe data

BEMDEC: An Adaptive and Robust Methodology for Digital Image Feature Extraction

The intriguing study of feature extraction, and edge detection in particular, has, as a result of the increased use of imagery, drawn even more attention not just from the field of computer science but also from a variety of scientific fields. However, various challenges surrounding the formulation of feature extraction operator, particularly of edges, which is capable of satisfying the necessary properties of low probability of error (i.e., failure of marking true edges), accuracy, and consistent response to a single edge, continue to persist. Moreover, it should be pointed out that most of the work in the area of feature extraction has been focused on improving many of the existing approaches rather than devising or adopting new ones. In the image processing subfield, where the needs constantly change, we must equally change the way we think. In this digital world where the use of images, for variety of purposes, continues to increase, researchers, if they are serious about addressing the aforementioned limitations, must be able to think outside the box and step away from the usual in order to overcome these challenges. In this dissertation, we propose an adaptive and robust, yet simple, digital image features detection methodology using bidimensional empirical mode decomposition (BEMD), a sifting process that decomposes a signal into its two-dimensional (2D) bidimensional intrinsic mode functions (BIMFs). The method is further extended to detect corners and curves, and as such, dubbed as BEMDEC, indicating its ability to detect edges, corners and curves. In addition to the application of BEMD, a unique combination of a flexible envelope estimation algorithm, stopping criteria and boundary adjustment made the realization of this multi-feature detector possible. Further application of two morphological operators of binarization and thinning adds to the quality of the operator

Multidimensional and multivariate empirical mode decomposition

Over the last decade, Empirical Mode Decomposition (EMD) has developed into a versatile tool for adaptive, scale-based modal decomposition. EMD has proven to be capable of decomposing multivariate signals with cross-channel mode alignment. However, the algorithms for envelope identification in multivariate EMD come with a computational burden rendering it unsuitable for the large computational demands of multidimensional signal processing. The current work introduces an alternative approach to multivariate EMD, and by combining it with existing fast and adaptive algorithms, paves the way for performing multivariate EMD on multidimensional signals. The application of the algorithm developed through the current study, when applied to the Direct Numerical Simulation (DNS) of a flat-plate boundary layer (a large dataset), revealed the desired scale separation behaviour across multiple data channels. This proves that the algorithm could be useful for a broad range of future problems

Statistical Properties and Applications of Empirical Mode Decomposition

Signal analysis is key to extracting information buried in noise. The decomposition of signal is a data analysis tool for determining the underlying physical components of a processed data set. However, conventional signal decomposition approaches such as wavelet analysis, Wagner-Ville, and various short-time Fourier spectrograms are inadequate to process real world signals. Moreover, most of the given techniques require \emph{a prior} knowledge of the processed signal, to select the proper decomposition basis, which makes them improper for a wide range of practical applications. Empirical Mode Decomposition (EMD) is a non-parametric and adaptive basis driver that is capable of breaking-down non-linear, non-stationary signals into an intrinsic and finite components called Intrinsic Mode Functions (IMF). In addition, EMD approximates a dyadic filter that isolates high frequency components, e.g. noise, in higher index IMFs. Despite of being widely used in different applications, EMD is an ad hoc solution. The adaptive performance of EMD comes at the expense of formulating a theoretical base. Therefore, numerical analysis is usually adopted in literature to interpret the behavior. This dissertation involves investigating statistical properties of EMD and utilizing the outcome to enhance the performance of signal de-noising and spectrum sensing systems. The novel contributions can be broadly summarized in three categories: a statistical analysis of the probability distributions of the IMFs and a suggestion of Generalized Gaussian distribution (GGD) as a best fit distribution; a de-noising scheme based on a null-hypothesis of IMFs utilizing the unique filter behavior of EMD; and a novel noise estimation approach that is used to shift semi-blind spectrum sensing techniques into fully-blind ones based on the first IMF. These contributions are justified statistically and analytically and include comparison with other state of art techniques

Data-driven time-frequency analysis of multivariate data

Empirical Mode Decomposition (EMD) is a data-driven method for the decomposition and time-frequency analysis of real world nonstationary signals. Its main advantages over other time-frequency methods are its locality, data-driven nature, multiresolution-based decomposition, higher time-frequency resolution and its ability to capture oscillation of any type (nonharmonic signals). These properties have made EMD a viable tool for real world nonstationary data analysis. Recent advances in sensor and data acquisition technologies have brought to light new classes of signals containing typically several data channels. Currently, such signals are almost invariably processed channel-wise, which is suboptimal. It is, therefore, imperative to design multivariate extensions of the existing nonlinear and nonstationary analysis algorithms as they are expected to give more insight into the dynamics and the interdependence between multiple channels of such signals. To this end, this thesis presents multivariate extensions of the empirical mode de- composition algorithm and illustrates their advantages with regards to multivariate non- stationary data analysis. Some important properties of such extensions are also explored, including their ability to exhibit wavelet-like dyadic filter bank structures for white Gaussian noise (WGN), and their capacity to align similar oscillatory modes from multiple data channels. Owing to the generality of the proposed methods, an improved multi- variate EMD-based algorithm is introduced which solves some inherent problems in the original EMD algorithm. Finally, to demonstrate the potential of the proposed methods, simulations on the fusion of multiple real world signals (wind, images and inertial body motion data) support the analysis

Detection of pathologies in retina digital images an empirical mode decomposition approach

Accurate automatic detection of pathologies in retina digital images offers a promising approach in clinicalapplications. This thesis employs the discrete wavelet transform (DWT) and empirical mode decomposition (EMD) to extract six statistical textural features from retina digital images. The statistical features are the mean, standard deviation, smoothness, third moment, uniformity, and entropy. The purpose is to classify normal and abnormal images. Five different pathologies are considered. They are Artery sheath (Coat’s disease), blot hemorrhage, retinal degeneration (circinates), age-related macular degeneration (drusens), and diabetic retinopathy (microaneurysms and exudates). Four classifiers are employed; including support vector machines (SVM), quadratic discriminant analysis (QDA), k-nearest neighbor algorithm (k-NN), and probabilistic neural networks (PNN). For each experiment, ten random folds are generated to perform cross-validation tests. In order to assess the performance of the classifiers, the average and standard deviation of the correct recognition rate, sensitivity and specificity are computed for each simulation. The experimental results highlight two main conclusions. First, they show the outstanding performance of EMD over DWT with all classifiers. Second, they demonstrate the superiority of the SVM classifier over QDA, k-NN, and PNN. Finally, principal component analysis (PCA) was employed to reduce the number of features in hope to improve the accuracy of classifiers. We find that there is no general and significant improvement of the performance, however. In sum, the EMD-SVM system provides a promising approach for the detection of pathologies in digital retina

A study of information-theoretic metaheuristics applied to functional neuroimaging datasets

This dissertation presents a new metaheuristic related to a two-dimensional ensemble empirical mode decomposition (2DEEMD). It is based on Green’s functions and is called Green’s Function in Tension - Bidimensional Empirical Mode Decomposition (GiT-BEMD). It is employed for decomposing and extracting hidden information of images. A natural image (face image) as well as images with artificial textures have been used to test and validate the proposed approach. Images are selected to demonstrate efficiency and performance of the GiT-BEMD algorithm in extracting textures on various spatial scales from the different images. In addition, a comparison of the performance of the new algorithm GiT-BEMD with a canonical BEEMD is discussed. Then, GiT-BEMD as well as canonical bidimensional EEMD (BEEMD) are applied to an fMRI study of a contour integration task. Thus, it explores the potential of employing GiT-BEMD to extract such textures, so-called bidimensional intrinsic mode functions (BIMFs), of functional biomedical images. Because of the enormous computational load and the artifacts accompanying the extracted textures when using a canonical BEEMD, GiT-BEMD is developed to cope with such challenges. It is seen that the computational cost is decreased dramatically, and the quality of the extracted textures is enhanced considerably. Consequently, GiT-BEMD achieves a higher quality of the estimated BIMFs as can be seen from a direct comparison of the results obtained with different variants of BEEMD and GiT-BEMD. Moreover, results generated by 2DBEEMD, especially in case of GiT-BEMD, distinctly show a superior precision in spatial localization of activity blobs when compared with a canonical general linear model (GLM) analysis employing statistical parametric mapping (SPM). Furthermore, to identify most informative textures, i.e. BIMFs, a support vector machine (SVM) as well as a random forest (RF) classifier is employed. Classification performance demonstrates the potential of the extracted BIMFs in supporting decision making of the classifier. With GiT-BEMD, the classification performance improved significantly which might also be a consequence of a clearer structure for these modes compared to the ones obtained with canonical BEEMD. Altogether, there is strong believe that the newly proposed metaheuristic GiT-BEMD offers a highly competitive alternative to existing BEMD algorithms and represents a promising technique for blindly decomposing images and extracting textures thereof which may be used for further analysis