Principal component analysis based simultaneous dual-wavelength phase-shifting interferometry

Within the last years various principal component analysis (PCA) algorithms have been proposed. In this paper we use a general framework to describe those PCA algorithms which are based on Hebbian learning. For an important subset of these algorithms, the local algorithms, we fully describe their equilibria, where all lateral connections are set to zero and their local stability. We show how the parameters in the PCA algorithms have to be chosen in order to get an algorithm which converges to a stable equilibrium which provides principal component extraction.

Remote sensing technology provides an unprecedented tool for the continuous and real-time monitoring of atmospheric SO2 from volcanic eruption and anthropogenic emission. The Global Ozone Monitoring Experiment (GOME), SCanning Imaging Absorption spectroMeter for Atmospheric CHartographY (SCIAMACHY), and Ozone Monitoring Instrument (OMI) have high SO2 monitoring capability. The OMI, which was launched on the EOS/Aura platform in July 2004, has the same hyperspectral measurements as the GOME and SCIAMACHY, but offers the improved spatial resolution at nadir (1324 km2) and daily global coverage for short-lifetime SO2. For OMI operational SO2 planetary boundary layer (PBL) retrieval, the previous band residual difference (BRD) algorithm has been replaced by principal component analysis (PCA) algorithm, which effectively reduces the systematic biases in SO2 column retrievals. However, there are few studies on the evaluations and validations of PCA SO2 retrievals over China, and the long-term comparisons with BRD SO2 retrievals also need to be conducted. In this study, the accuracies of PCA and BRD SO2 retrievals are validated by using ground-based multi axis differential optical absorption spectroscopy (MAX-DOAS) located in Beijing, and regional atmospheric modeling system, community multi-scale air quality (RAMS-CMAQ) modeling system model which can simulate the vertical distribution of atmospheric SO2. Moreover, BRD and PCA SO2 retrievals from oceanic area, eastern China and Reunion volcanic eruption are compared to find the long-term trend and spatiotemporal differences between SO2 columns. Finally, the uncertainty of SO2 retrieval, caused by measurement errors, band selection and input parameter errors in radiative transfer model, are analysed to understand the limitations of BRD and PCA algorithms. Results show that both PCA and BRD SO2 retrievals over Beijing are lower than ground-based MAX-DOAS measurements of SO2. PCA and BRD SO2 retrievals over eastern China are lower than the simulated SO2 columns from RAMS-CMAQ in winter 2008, but in July and August BRD SO2 columns are higher than RAMS-CMAQ simulations. The values of SO2 columns from BRD over China are more consistent with those from ground-based MAX-DOAS and RAMS-CMAQ model than from PCA. Although PCA algorithm effectively reduces the noise in SO2 column retrieval, SO2 columns from PCA over China are lower than those from BRD. For oceanic area where SO2 amount is nearly zero, the standard deviation of PCA results is lower than that of BRD, but the absolute value of averaged PCA SO2 column is larger than that of BRD. In the case of Reunion volcanic eruption with SO2 columns larger than 25 DU, the BRD SO2 columns are lower than PCA retrievals. Meanwhile, with the increase of SO2 column, the difference between BRD and PCA SO2 retrievals increases. Detailed uncertainty analysis shows the influences of measurement errors, band selection and inputs of radiative transfer model on the retrieval results. This study is important for developing the retrieval algorithm, and can also improve the application of OMI SO2 products.

In this study, an iterative k-t principal component analysis (PCA) algorithm with nonrigid frame-to-frame motion correction is proposed for dynamic contrast-enhanced three-dimensional perfusion imaging. An iterative k-t PCA algorithm was implemented with regularization using training data corrected for frame-to-frame motion in the x-pc domain. Motion information was extracted using shape-constrained nonrigid image registration of the composite of training and k-t undersampled data. The approach was tested for 10-fold k-t undersampling using computer simulations and in vivo data sets corrupted by respiratory motion artifacts owing to free-breathing or interrupted breath-holds. Results were compared to breath-held reference data. Motion-corrected k-t PCA image reconstruction resolved residual aliasing. Signal intensity curves extracted from the myocardium were close to those obtained from the breath-held reference. Upslopes were found to be more homogeneous in space when using the k-t PCA approach with motion correction. Iterative k-t PCA with nonrigid motion correction permits correction of respiratory motion artifacts in three-dimensional first-pass myocardial perfusion imaging.

Face recognition is one technology that is commonly used now. Therefore, various algorithms continue to be developed to obtain maximum results with minimum costs. One of them is the Deep Neural Network or DNN algorithm. While DNN requires a large dataset to train the algorithm, another algorithm called the Principal Component Analysis (PCA) algorithm works good in a smaller dataset. These algorithms are compared to know which algorithm has the better result in given circumstances. Later the accuracy, speed, and optimality of the algorithms are analyzed. By comparing these algorithms, we could know which algorithm is preferable in given circumstances. After the experiment is done, we can assume that the two algorithms have a slight difference in terms of accuracy. Also, the time used for running the PCA implementation code is slightly longer than DNN. However, that does not mean that the PCA algorithm is not great. If the dataset to be used is limited, PCA is going to be a good choice.

This article presents a method based on support vector machines (SVMs) and the Osuna–Platt algorithm used to diagnose the ischemic heart disease. It also includes the necessary concepts from the optimization theory which make it possible to formulate the problem for support vectors and the Osuna–Platt algorithm applied. Next, a principal component analysis (PCA) algorithm used is also presented. Heart images acquired using Single Photon Emission Computed Tomography (SPECT) have been used in the experimental part. Results of classifying cardiac SPECT images using SVM, PCA and neural networks are compared here with those obtained using another method of machine learning – CLIP3 – a combination of the decision tree algorithm and the rule induction algorithm. Tests against an SPECT image database have shown that SVMs are generally more accurate and specific, while the PCA algorithm is the most sensitive for all data sets analysed in this research project.

<p>This paper presents a simple and fast recognition system with various facial expressions, poses, and rotation. The proposed system performed in two phases. Face detection is the first phase. The front and profile face detected cropped face area from the image by Viola-Jones algorithm and the right side face is detected from the image by taking the flip of the profile image. Principal component analysis (eigenfaces) algorithm is used in the recognition phase and depends on created database models used to be compared with test face image input to the recognition procedure. For training and testing the system, two sets of the image of the file exchange interface (FEI) database have been used to identify the person. The experimental result shows the effectiveness and robustness of the method used for the detection of the face and achieves high accuracy of 96%, which improves the recognition performance with low execution time. Furthermore, the accuracy of 35 trained images for recognition is 97.143% with average time execution which is (0.323657s). Also, the accuracy of 15 tested images for recognition is 93.315% with average time execution which is (0.3348s) which indicates a good and strong success and accuracy method for facial recognition.</p>

This paper reviews the implementation of Principal Component Analysis (PCA) Algorithm to traveling wave distance protection with the addition of Type D locator for distance calculation of a three phase 400 kV doubly fed power system. When a fault occurs on the transmission line by detecting the traveling waves at substation based on the pattern recognition of the first wavefront that arrives at the location of relay is used to classify whether they are within the reach of the relay using PCA algorithm and by implementing Type D locator i.e. two terminal method in algorithm, the discrimination is verified. The idea is tested for different types of faults and is simulated using MATLAB/Simulink and the performance of the algorithm is reported.

Cancer is the most common disease to threaten human health. The ability to screen individuals with malignant tumours with only a blood sample would be greatly advantageous to early diagnosis and intervention. This study explores the possibility of discriminating between cancer patients and normal subjects with serum surface-enhanced Raman spectroscopy (SERS) and a support vector machine (SVM) through a peripheral blood sample. A total of 130 blood samples were obtained from patients with liver cancer, colonic cancer, esophageal cancer, nasopharyngeal cancer, gastric cancer, as well as 113 blood samples from normal volunteers. Several diagnostic models were built with the serum SERS spectra using SVM and principal component analysis (PCA) techniques. The results show that a diagnostic accuracy of 85.5% is acquired with a PCA algorithm, while a diagnostic accuracy of 95.8% is obtained using radial basis function (RBF), PCA–SVM methods. The results prove that a RBF kernel PCA–SVM technique is superior to PCA and conventional SVM (C-SVM) algorithms in classification serum SERS spectra. The study demonstrates that serum SERS, in combination with SVM techniques, has great potential for screening cancerous patients with any solid malignant tumour through a peripheral blood sample.

Shrimps are aquaculture products highly needed by the people and this is the reason their growth needs to be monitored using underwater digital images. However, the large dimensions of the shrimp digital images usually make the processing difficult. Therefore, this research focuses on reducing the dimensions of underwater shrimp digital images without reducing their information through the application of the Principal Component Analysis (PCA) algorithm. This was achieved using 4 digital shrimp images extracted from video data with the number of columns 398 for each image. The results showed that 12 PCs were produced and this means the reduced digital images with new dimensions have 12 variable columns with data diversity distributed based on a total variance of 95.61%. Moreover, the original and reduced digital images were compared and the lowest value of MSE produced was 94.12, the minimum value of RMSE was 9.54, and the highest value of PSNR was 8.06 db, and they were obtained in the 4th digital image. The experiment was conducted using 3 devices which include I3, I7, and Google Colab processor computers and the fastest computational result was produced at 2.1 seconds by the Google Colab processor. This means the PCA algorithm is good for the reduction of digital image dimensions as indicated by the production of 12 PC as the new variable dimensions for the reduced underwater image of shrimps.

To address the issue of frequency regulation in AC‐islanded microgrids (MGs), this paper introduces a novel approach for adjusting primary controller gains for AC‐islanded MGs. The proposed approach uses the linear matrix inequality (LMI) for polytopic linear parameter varying (P‐LPV) modelling based on the H ∞ control theory and principal component analysis (PCA) algorithm. The objective is to regulate the MG frequency while considering the nonlinearity and uncertainty of the system. To achieve optimal control gains, the method considers all the system uncertainties in a P‐LPV modelling of the system. The PCA algorithm reduces the scheduling parameter region, and the optimal control gains are computed by solving the relevant LMIs defined on the obtained P‐LPV model based on H∞ performance and stability achievement. The primary control gains are optimised to minimise the errors between the optimal and actual control signals. Importantly, the suggested method preserves the order and structure of the primary control, making it applicable to implement on digital hardware devices. In addition, the MG is simulated in MATLAB/Simulink, and the simulation results demonstrate the authenticity, effectiveness, and efficiency of the proposed process for MG frequency regulation in the presence of uncertainties, disturbances, nonlinearity, and dynamic changes in MGs.

This paper analyzes and studies the task of traffic sign recognition in the complex traffic road environment, analyzes the defects of the traditional classification algorithm and CNN (convolutional neural network) algorithm, cannot maximize the elimination of the lack of use of image disturbance information and hidden image information. This paper proposes a traffic sign recognition algorithm based on CNN, PCA (Principal Component Analysis) and LVQ (Learning Vector Quantization) algorithm, and uses PCA algorithm and LVQ algorithm to perform eigenvectors generated by CNN model. Dimensionality reduction and classification processing eliminates picture interference information and in-depth use of hidden information in pictures, further improves the accuracy of identification of traffic signs in complex environments, validates the effectiveness of the proposed method on the GTSRB data set, and relates to depth volumes. The product network model, LeNet-5, performs comparative experiments and proves that this method can further improve the classification accuracy.

Principal component analysis (PCA) and minor component analysis (MCA) are two important statistical tools which have many applications in the fields of signal processing and data analysis. PCA and MCA neural networks (NNs) can be used to online extract principal component and minor component from input data. It is interesting to develop generalized learning algorithms of PCA and MCA NNs. Some novel generalized PCA and MCA learning algorithms are proposed in this paper. Convergence of PCA and MCA learning algorithms is an essential issue in practical applications. Traditionally, the convergence is studied via deterministic continuous-time (DCT) method. The DCT method requires the learning rate of the algorithms to approach to zero, which is not realistic in many practical applications. In this paper, deterministic discrete-time (DDT) method is used to study the dynamical behaviors of the proposed algorithms. The DDT method is more reasonable for the convergence analysis since it does not require constraints as that of the DCT method. It is proven that under some mild conditions, the weight vector in these proposed algorithms will converge exponentially to principal or minor component. Simulation results are further used to illustrate the theoretical results.

Principal component analysis (PCA) is a method of processing high-dimensional feature data, which can be decomposed into a set of unrelated variables called principal components. Digital holographic microscopy (DHM) is a powerful tool in the biomedical imaging for recording the amplitude and phase information of object simultaneously. Structured illumination (SI) has been introduced in DHM to improve the resolution, by which the resolution can be doubled. However, accurate phase-shifting is required to retrieve the low and high frequency information. Besides that, the aberration of imaging system makes DHM under SI cumbersome. This paper presents an algorithm based on PCA for DHM under SI. The aberration terms can be extracted from the first principal component of the exponential term of filtered hologram. Moreover, the low and high frequency information can be achieved from three images without prior knowledge of phase shift values. In synthesizing process, the spectrums are precisely shifted to the correct position in the spatial-frequency domain also based on the PCA. This paper verifies the feasibility of the PCA algorithm the experiment. It is an attractive and promising technology for DHM under SI.

In this study, a simultaneous dual-wavelength phase-shifting interferometry system using two reference arms was built, and a simple phase retrieval method for the system with blind phase shifts was proposed using five phase-shifted interferograms. First, the unknown phase shifts were controlled independently to separate the information of single wavelength, which can be calculated directly by using the Euclidean matrix norm algorithm. Second, a wrapped phase of a single wavelength was obtained using a three-step phase-shifting algorithm. Finally, a continuous phase of a synthetic wavelength was obtained. The simulation and experimental results indicated the feasibility and greater accuracy of the proposed method. Moreover, the strict requirement of the phase shifter was eliminated because of the use of arbitrary and unknown phase shifts, thereby making experimental operation easier.

Synthetic Aperture Radar (SAR) signal model is considered as a series of echo signals in range direction. The procedure of Principal Component Analysis (PCA) is introduced which is used as transformation basis to sparsify the SAR signals. The joint Compressive Sensing (CS) and PCA algorithm is derived to realize SAR raw data sparse and compressive measurement. The numerical simulation results demonstrate that the PCA method has good sparse performance and the joint CS and PCA algorithm is possible to online compressive measure the SAR raw data.