Hilbert-Huang processing and analysis of complex fringe patterns

Optical interferometry is a popular technique for high precision measurement. It produces fringe patterns for analysis. The output fringe patterns usually have noises, and thus a filtering process for fringe patterns is necessary. A few filtering algorithms, such as windowed Fourier filtering (WFF), have been proposed specially for fringe pattern denoising. Meanwhile, filtering techniques have been intensively studied for a long time in the general image processing area. It is curious that how the filtering techniques in general image processing area perform on fringe pattern denoising. In this paper, a state-of-the-art filtering algorithm, block-matching 3D filtering (BM3D), is selected and compared with the WFF.

Parallel computing for fringe pattern processing: A multicore CPU approach in MATLAB ® environment

In 3D shape measurement, because deformed fringes often contain low-frequency information degraded with random noise and background intensity information, a new fringe-projection profilometry is proposed based on 2D empirical mode decomposition (2D-EMD). The fringe pattern is first decomposed into numbers of intrinsic mode functions by 2D-EMD. Because the method has partial noise reduction, the background components can be removed to obtain the fundamental components needed to perform Hilbert transformation to retrieve the phase information. The 2D-EMD can effectively extract the modulation phase of a single direction fringe and an inclined fringe pattern because it is a full 2D analysis method and considers the relationship between adjacent lines of a fringe patterns. In addition, as the method does not add noise repeatedly, as does ensemble EMD, the data processing time is shortened. Computer simulations and experiments prove the feasibility of this method.

We propose a 2D generalization to the midpoint-based empirical mode decomposition algorithm (MBEMD). Unlike with the regular bidimensional empirical mode decomposition algorithm (BEMD), we do not interpolate the upper and lower envelopes, but rather directly find the mean envelope, utilizing well defined points between two extrema of different kind (midpoints). This approach has several advantages such as improved spectral selectivity and better time performance over the regular BEMD process. The MBEMD algorithm is then applied to the task of the interferometric fringe pattern analysis, to identify its distinct components. This allows to separate the oscillatory pattern component, which is of interest, from the background, noise and possibly other spurious interferometric patterns. In result, the phase demodulation error is reduced. Flexibility of the adaptive method allows for processing correlation fringe patterns met in the digital speckle pattern interferometry as well as the regular interferometric fringe patterns without any special tuning of the algorithm.

Conjugated wavefront fidelity has been evaluated using an interferometer with a phase conjugate mirror and fringe pattern computer processing. The quantitative interpretation of the fringe patterns is performed using direct spatial phase reconstruction methods (in the space and Fourier domain). A set of algorithms for fast and accurate phase evaluation, by fringe pattern processing, were derived. The result of optical interferograms evaluation appears in terms of different phase representations. These methods have been verified by studies of the optical phase conjugation fidelity in photorefractive crystals.

This work aims to define Sonine filters and introduce them for digital image processing. Their fundamental properties are described and an optimizing performance procedure is explained, exploiting the unique advantage that this kind of filters possess, which consists of having simple analytical finite Fourier transforms for circular, elliptical and rectangular domains. A comparison with various existing filters is also presented, like Gaussian, Hann, Hamming, Blackmann, etc. Some relations are provided to facilitate their applicability. Also, comprehensive optimized filter designs are provided. Finally, an experimental application for intensity normalization and noise reduction of fringe patterns is described, showing that this kind of filters could be helpful in digital image processing and particularly in the analysis of fringe patterns.

A principled approach, based on Bayesian estimation theory and complex-valued Markov random-field prior models, is introduced for the design of a new class of adaptive quadrature filters. These filters are capable of adapting their tuning frequency to the local dominant spatial frequency of the input image while maintaining an arbitrarily narrow local frequency response; therefore they may be effectively used for the accurate recovery of the phase of broadband spatial-carrier fringe patterns, even when they are corrupted by a significant amount of noise. Also, by constraining the spatial variation of the adaptive frequency to be smooth, they permit the completely automatic recovery of local phase from single closed fringe pattern images, since the spurious discontinuities and sign reversals that one obtains from the classical Fourier-based methods are avoided in this case. Although the applications discussed here come from fringe pattern analysis in optics, these filters may also be useful in the solution of other problems, such as texture characterization and segmentation and the recovery of depth from stereoscopic pairs of images.

A fringe analysis method, which combines the Fourier transform with the fractional fringe order method for measuring the absolute thickness of a block gauge, is presented. An approximate integer part of the fringe order is estimated by mechanical measurements, and the fractional part is determined by Fourier analysis of the interferometric fringe patterns. The fringe patterns are obtained with a Michelson interferometer by illumination of several selected wavelengths, respectively. The use of the fractional fringe order method can determine accurately more than 2ϖ phase jumps. The measured thickness of a block gauge is 5999115.0 ± 0.7 nm, which is comparable with the standard thickness of 6 mm. The influence of wavelength and approximate integer part of fringe order on the measurement accuracy is discussed.

Near-infrared spectroscopy (NIRS) can be used as the basis of non-invasive neuroimaging that may allow the measurement of haemodynamic changes in the human brain evoked by applied stimuli. Since this technique is very sensitive, physiological interference arising from the cardiac cycle and breathing can significantly affect the signal quality. Such interference is difficult to remove by conventional techniques because it occurs not only in the extracerebral layer but also in the brain tissue itself. Previous work on this problem employing temporal filtering, spatial filtering, and adaptive filtering have exhibited good performance for recovering brain activity data in evoked response studies. However, in this study, we present a time-frequency adaptive method for physiological interference reduction based on the combination of empirical mode decomposition (EMD) and Hilbert spectral analysis (HSA). Monte Carlo simulations based on a five-layered slab model of a human adult head were implemented to evaluate our methodology. We applied an EMD algorithm to decompose the NIRS time series derived from Monte Carlo simulations into a series of intrinsic mode functions (IMFs). In order to identify the IMFs associated with symmetric interference, the extracted components were then Hilbert transformed from which the instantaneous frequencies could be acquired. By reconstructing the NIRS signal by properly selecting IMFs, we determined that the evoked brain response is effectively filtered out with even higher signal-to-noise ratio (SNR). The results obtained demonstrated that EMD, combined with HSA, can effectively separate, identify and remove the contamination from the evoked brain response obtained with NIRS using a simple single source–detector pair.

Conditions of the digital recording of the fringe pattern determine the phase reconstruction procedure, which in turn directly shapes the final accuracy and throughput of the full-field (non-scanning) optical measurement technique and defines the system capabilities. In this way, the fringe pattern analysis plays a crucial role in the ubiquitous optical measurements and thus is under constant development focused on high temporal/spatial resolution. It is especially valuable in the quantitative phase imaging technology, which emerged in the high-contrast label-free biomedical microscopy. In this paper, I apply recently blossomed two-frame phase-shifting techniques to the QPI and merge them with advanced adaptive interferogram pre-filtering algorithms. Next, I comprehensively test such frameworks against classical and adaptive single-shot methods applied for phase reconstruction in dynamic QPI enabling highest phase time-space-bandwidth product. The presented study systematically tackles important question: what is the gain, if any, in QPI realized by recording two phase-shifted interferograms? Counterintuitively, the results show that single-shot demodulation exhibited higher phase reconstruction accuracy than two-frame phase-shifting methods in low and medium interferogram signal-to-noise ratio regimes. Thus, the single-shot approach is promoted due to not only high temporal resolution but also larger phase-information throughput. Additionally, in the majority of scenarios, the best option is to shift the paradigm and employ two-frame pre-filtering rather than two-frame phase retrieval. Experimental fringe analysis in QPI of LSEC/RWPE cell lines successfully corroborated all novel numerical findings. Hence, the presented numerical-experimental research advances the important field of fringe analysis solutions for optical full-field measurement methods with widespread bio-engineering applications.

Primal sketch performs an important role in early vision. In this paper, we propose a novel method to obtain the primal sketch of natural images by integrating empirical mode decomposition (EMD) techniques and image gradient. 2D EMD approach can decompose the image into a finite number of intrinsic mode functions (IMF), and each one represents the original image in a different scale, with the 1st IMF representing the finest scale. To enhance the information represented by the IMF, we multiply the 1st IMF by the image gradient. This enhanced IMF highlights intensity changes in the image. By linking all the maximal points in the enhanced IMF, we obtain a primal sketch of the original image. Compared with the existed primal sketch extraction methods, our method is fully driven by the image data, and it needs neither to choose filters nor to learn the image bases. The experiment results show that our method is fast and 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.

In this paper, a novel approach has been proposed for fault diagnosis of internal combustion (IC) engine using Empirical Mode Decomposition (EMD) and Neural Network. Live signals from the engines were collected with and without faults by using four sensors. The vibration signals measured from the large number of faulty engines were decomposed into a number of Intrinsic Mode Functions (IMFs). Each IMF corresponds to a specific range of the frequency component embedded in the vibration signal. This paper proposes the use of EMD technique for finding IMFs. The Cumulative Mode Function (CMF) was chosen rather than IMFs since all the IMFs are not useful to reveal the vibration signal characteristics due to the effect of noise. Statistical parameters like shape factor, crest factor etc. of the envelope spectrum of CMF were investigated as an indicator for the presence of faults. These statistical parameters are used in turn for classification of faults using Neural Networks. Resilient Propagation which is a rapidly converging neural network algorithm is used for classification of faults. The accuracy obtained by using EMD-ANN technique effectively in IC engine diagnosis for various faults is more than 85% with each sensor. By using a majority voting approach 96% accuracy has been achieved in fault classification.

This paper proposes a new criterion for selecting the optimum number of Intrinsic Mode Functions (IMFs) from vibration signals measured on rotating machines. The criterion is based on calculating the variation of normalized Shannon entropy ([Formula: see text]) between two successive IMFs, enabling the optimization of the number of processed IMFs. The method combines Variational Mode Decomposition (VMD) with Wavelet Multi-Resolution Analysis (WMRA) using the newly introduced criterion. The key steps involve determining the optimal number of IMFs, decomposing the vibration signals using VMD, and applying WMRA to the selected IMFs. Numerical simulations and experimental results demonstrate its effectiveness in identifying various faults, including gear defects, shaft misalignment, insufficient backlash, and belt defects. These latter flaws are the primary cause of the elevated noise levels in the measured signals. Finally, to validate our approach in an industrial setting, we diagnosed a turbofan, which revealed the presence of several typical faults for this type of installation. The proposed approach addresses a critical industry need by increasing fault diagnosis accuracy in noisy environments. Its practical impact stems from its ability to improve early fault detection, which is critical for predictive maintenance strategies aimed at reducing equipment downtime and extending its lifespan.

A novel edge detection of image based on window empirical mode decomposition (WEMD) was proposed in this paper. WEMD was inherited all advantages from EMD and can decompose any nonlinear and non-stationary data into a number of intrinsic mode functions (IMFs). In WEMD, window mean function is employed to get the mean surface in the decomposition process instead of the surface interpolation, which enables fast decomposition. Meanwhile, the drawback of gray spots in IMF images has been avoided. Since the first IMF provides the highest local spatial variations and/or scales of the image, this IMF is then processed for obtaining the edge. 2D-Hilbert transform and non-maxima suppression, hysteresis threshold in canny method are applied to the first BIMF to achieve the desired edge map. The proposed method is compared with Canny and wavelet edge detection techniques. Simulation results with the real images demonstrate the efficacy of the proposed algorithm for edge detection.