Phase extraction from randomly phase-shifted interferograms by combining principal component analysis and least squares method

In surface shape measurement with phase-shifting interferometry, the extraction accuracy of initial phase is significant and it will influence the correct of measurement result. A least-squares algorithm is proposed to solve the parameters of interferograms with random and known phase shifts. It can rapidly extract the initial phase, modulation amplitude and background intensity without any iteration. Numerical simulations and optical experiments are implemented to demonstrate the performance of the proposed method. The simulation and experiment results show that the presented method is effective, rapid and accurate.

IQ imbalance (IQI) of radio-frequency (RF) Chains is one of the key factors that limits the performance of wireless communications systems, especially in high order modulation modes. Traditional methods usually estimate the IQI parameters with dedicated feedback circuits and compensate the distortion of RF Chains with extra compensation circuits. Moreover, they do not consider the random carrier phase shift between transceivers, which increases the difficulty of estimating IQI parameters. In the paper, we propose a CNN-based auto fully-digital calibration technique with no dedicated feedback and compensation circuits to compensate for IQI and the random phase shift. We train the CNN using the pilot signals to obtain the compensation matrix. Since only the pilot signal is adopted, the algorithm can work with current wireless communications systems automatically. Compared to user equipment (UE) with ideal RF chains, the simulation results show that our algorithm can help UEs with IQI and the random phase shift achieve similar performance even in 1024-QAM modulation mode.

Head-related transfer function (HRTF) plays an important role in the construction of 3D auditory display. This paper presents an individual HRTF modeling method using deep neural networks based on spatial principal component analysis. The HRTFs are represented by a small set of spatial principal components combined with frequency and individual-dependent weights. By estimating the spatial principal components using deep neural networks and mapping the corresponding weights to a quantity of anthropometric parameters, we predict individual HRTFs in arbitrary spatial directions. The objective and subjective experiments evaluate the HRTFs generated by the proposed method, the principal component analysis (PCA) method, and the generic method. The results show that the HRTFs generated by the proposed method and PCA method perform better than the generic method. For most frequencies the spectral distortion of the proposed method is significantly smaller than the PCA method in the high frequencies but significantly larger in the low frequencies. The evaluation of the localization model shows the PCA method is better than the proposed method. The subjective localization experiments show that the PCA and the proposed methods have similar performances in most conditions. Both the objective and subjective experiments show that the proposed method can predict HRTFs in arbitrary spatial directions.

This paper proposes a new method that reconstructs the information of specimen by using random phase shift step in digital holographic microscopy (DHM). The principles of the method are described and discussed in detail. In practical experiment, because the phase shifter is neither perfectly linear nor calibrated, digital holograms with inaccurate phase shift step are recorded by the charge-coupled device (CCD). The phase could be accurately reconstructed from the recorded digital holograms by using the random phase-shifting algorithm, which makes up for reconstructed phase error caused by ordinary phase-shifting algorithm. The phase aberration compensation is also discussed. In order to verify the flexibility of the proposed method, numerical simulation of random phase-shifting DHM was carried out. The simulation results illustrated that the presented method is effective when the phase shift step is unknown or random in DHM.

Data-driven simulation of multivariate nonstationary winds: A hybrid multivariate empirical mode decomposition and spectral representation method

We consider a thin superconducting film with randomly magnetized dots on top of it. The dots produce a disordered pinning potential for vortices in the film. We show that for dots with permanent and random magnetization normal or parallel to the film surface, our system is an experimental realization of the two-dimensional XY model with random phase shifts. The low-temperature superconducting phase, that exists without magnetic dots, survives in the presence of magnetic dots for sufficiently small disorder.

The stability of the ordered phase of the three-dimensional XY-model with random phase shifts is studied by considering the roughening of a single stretched vortex line due to the disorder. It is shown that the vortex line may be described by a directed polymer Hamiltonian with an effective random potential that is long range correlated. A Flory argument estimates the roughness exponent to $\zeta=3/4$ and the energy fluctuation exponent to $\omega=1/2$, thus fulfilling the scaling relation $\omega=2\zeta-1$. The Schwartz-Edwards method as well as a numerical integration of the corresponding Burger's equation confirm this result. Since $\zeta<1$ the ordered phase of the original XY-model is stable.

Introduction: Saffron is one of the most important economic plants in the Khorasan province. Awareness of soil quality in agricultural lands is essential for the best management of lands and for obtaining maximum economic benefit. In general, plant growth is a function of environmental factors especially chemical and physical properties of soil (20). It has been demonstrated that there was a positive and high correlation between soil organic matter and saffron yield. Increasing the yield of saffron due to organic matter is probably due to soil nutrient, especially phosphorous and nitrogen and also improvement of soil physical quality (6, 28, 29). The yield of saffron in soils with high nitrogen as a result of vegetative growth is high (8). Shahandeh (6) found that most of the variation of saffron yield depends on soil properties. Due to the economic importance of saffron and the role of soil properties on saffron yield, this research was conducted to find the relationship between saffron yield and some soil physical and chemical properties, and to determine the contribution of soil properties that have the greatest impact on saffron yield in the Ghayenat area. Materials and Methods: This research was performed in 30 saffron fields (30 soil samples) of the Ghayenat area (longitude 59° 10΄ 10.37˝ - 59° 11΄ 38.41˝ and latitude 33° 43΄ 35.08˝ - 33΄ 44΄ 02.78˝), which is located in the Khrasan province of Iran. In this research, 21 soil properties were regarded as the total data set (TDS). Then the principal component analysis (PCA) was used to determine the most important soil properties affecting saffron yield as a minimum data set (MDS) and the stepwise regression to estimate saffron yield. To estimate the yield of saffron in stepwise regression method, saffron yield was considered as a dependent variable and soil physical and chemical properties were considered to be independent variables. Results and Discussion: According to the PCA method, among the 21 studied properties, 7 out of them including calcium, iron, zinc contents, sand, calcium carbonate equivalent percent, mean weight diameter of aggregates (MWD) and manganese (Mn) had the higher Eigenvalues. Therefore, the above properties were introduced as the most important soil properties in saffron fields. Calcium carbonate had the negative effect on the availability of micro-nutrients (26). Christensen et al. (15) found that by increasing the calcium carbonate in soil due to high pH and formation of insoluble components, the uptake of micro-nutrients is especially limited. The results of stepwise regression method (equation 1) showed that soil acidity (pH), zinc content, bulk density, MWD, iron content, salinity (EC), organic carbon and available potassium in soil were the most important properties that affect the yield of saffron, so that the determination coefficient (R2) of the regression model was high (Table 2) and it can explain 74% of the variation of saffron yield. Y = 6924.51 – 1187.31 pH – 89.65 EC + 71.6 Fe – 826.02 Zn + 471.55 OC, + 5490.96 K + 1353.56 BD + 752.82 MWD (1) where Y: saffron yield (kgha-1), pH: soil acidity, EC: electoral conductivity (dSm-1), Fe: iron concentration (mgkg-1), Zn: zinc concentration (mgkg-1), OC: organic carbon (%), K: soil potassium (%), BD: soil bulk density (Mgm-3), and MWD: mean weight diameter of aggregates (MM). Based on the absolute values of standard s in the regression model (Table 3), pH value and then after Zn concentration had the most effect on saffron yield. In general, responses of different plants to soil pH is varied, and saffron grows satisfactory in pH = 7.8 (5). Soil pH influences the uptake of soil nutrients by plants (15), so that this parameter had the most effect on saffron yield and by increasing the soil pH, the yield of saffron decreases. According to the regression model, Zn concentration was the second parameter in saffron yield. Zn has the important role in structure of plant enzymes (30). After these 2 parameters, Bd, MWD, Fe concentration, EC, Organic carbon and K concentration in soil had more effect on saffron yield (Table 3). Conclusion: According to both PCA and regression methods, the concentration of iron and zinc and MWD were determined as the important and effective soil properties on saffron yield in the Ghayenat area. In addition, soil pH in stepwise regression method and calcium carbonate in PCA method were determined as the effective properties on saffron yield. Therefore, it is suggested that the parameters of Zn, Fe, and MWD along with soil pH and calcium carbonate which were regarded individually in two methods, were considered as the most soil properties in saffron yield.

Mangroves are coastal plants influenced by tidal cycles. One of the regions in South Sumatra Province with a mangrove ecosystem is Sembilang National Park. As a national park, this location is strategically positioned for research related to mangrove species. The utilization of the Principal Component Analysis (PCA) method is considered to enhance the capabilities of remote sensing data in mangrove mapping. However, its application has been limited to the mangrove level. The research objective is to identify mangrove species in Sembilang National Park using the PCA method by leveraging Landsat-8 image data acquired on September 9, 2019. Mangrove distribution is obtained through the Mangrove Vegetation Index (MVI) and vector data from Global Mangrove Watch. The image is then overlaid with field species data to obtain species spectral patterns. Additionally, the correlation between spectral band values and eigenvalues (PC) is analyzed to detect parameters correlated with eigenvalues. The research results show that PC values correlate with mangrove species and can be used for mangrove species identification. This is demonstrated by Bruguiera Gymnorrhiza species with canopy coverage of 60.8% and 62.46% at ST7 and ST8 having the same PC values, while mangroves with canopy coverage of 62.5% in different species have different PC values. Moreover, the PCA method can indicate two crucial factors in identifying mangrove species, namely vegetation and soil factors. Mangrove merupakan tumbuhan pesisir yang dipengaruhi oleh pasang surut. Salah satu wilayah di Provinsi Sumatera Selatan yang memiliki ekosistem mangrove adalah Taman Nasional Sembilang. Sebagai taman nasional, lokasi ini sangat strategis untuk dilakukan penelitian terkait spesies mangrove. Pemanfaatan metode principal component analysis (PCA) dinilai mampu meningkatkan kemampuan data penginderaan jauh dalam pemetaan mangrove. Namun selama ini, pemanfaatan terbatas pada level mangrove. Adapun tujuan penelitian adalah mengidentifikasi spesies mangrove di Taman Nasional Sembilang menggunakan metode PCA dengan memanfaatkan data citra Landsat-8 yang diakusisi pada 09 September 2019. Sebaran mangrove diperoleh melalui indeks vegetasi mangrove (MVI) dan data vektor dari Global Mangrove Watch. Citra tersebut kemudian di overlay dengan data spesies lapangan untuk mendapatkan pola spektral species. Selain itu, korelasi nilai spektral band dan eigen (PC) dianalisis untuk mendeteksi parameter yang berkorelasi dengan nilai eigen. Hasil penelitian menunjukkan nilai PC memiliki korelasi dengan spesies mangrove dan dapat digunakan untuk mengidentifikasi spesies mangrove. Hal ini ditunjukkan spesies Bruguiera Gymnorrhiza dengan tutupan kanopi 60,8% dan 62,46% pada ST7 dan ST8 memiliki nilai PC yang sama serta mangrove dengan besaran tutupan kanopi 62,5% pada spesies nilai PC berbeda. Selain itu, metode PCA mampu menunjukkan dua faktor penting dalam mengidentifikasi spesies mangrove, yaitu faktor vegetasi dan tanah.

The development of artificial neural networks is related to statistical and biometric analysis which is one of the applications that can require artificial neural network models. Recognition of facial patterns is an important part of identifying a person. The face can be divided into areas such as the nose, eyes and mouth. Face pattern recognition is a research area that can be applied to the principal component analysis (PCA) method. The training process carried out by the eigenface calculation uses PCA and the results of this study show that facial pattern recognition based on the proportion of memorization and generalization for the use of the method without PCA is better than facial pattern recognition using PCA. Pattern recognition without using the PCA method, the level of memorization and generalization reaches 100% at the 40th iteration and 0.0099 error with a learning rate and momentum of 0.8, while facial pattern recognition using the PCA method, the memorization and generalization level reaches 100% in the iteration. to -1000 and error 0.00103 with learning rate and momentum 0.9.

Systematic principal component analysis (PCA) methods are presented in this paper for reliable islanding detection for power systems with significant penetration of distributed generations (DGs), where synchrophasors, recorded by phasor measurement units, are used for system monitoring. Existing islanding detection methods, such as rate-of-change-of-frequency and vector shift are fast for processing local information; however, with the growth in installed capacity of DGs, they suffer from several drawbacks. Incumbent genset islanding detection cannot distinguish a system-wide disturbance from an islanding event, leading to maloperation. The problem is even more significant when the grid does not have sufficient inertia to limit frequency divergences in the system fault/stress due to the high penetration of DGs. To tackle such problems, this paper introduces PCA methods for islanding detection. A simple control chart is established for intuitive visualization of the transients. A recursive PCA scheme is proposed as a reliable extension of the PCA method to reduce the false alarms for time-varying process. To further reduce the computational burden, the approximate linear dependence condition errors are calculated to update the associated PCA model. The proposed PCA and RPCA methods are verified by detecting abnormal transients occurring in the U.K. utility network.

Principal Component Analysis (PCA) is a widely used dimensional reduction method that aims to find a low dimension sub space of highly correlated data for its major information to be used in further analysis. Machine learning methods based on PCA are popular in high dimensional data analysis, such as video and image processing. In video processing, the Robust PCA (RPCA), which is a modified method of the traditional PCA, has good properties in separating moving objects from the background, but it may have difficulties in separating those when light intensity of the background varies significantly in time. To overcome the difficulties, a modified PCA method, called Regression PCA (RegPCA), is proposed. The method is developed by combining the traditional PCA and regression approaches together, and it can be easily combined with RPCA for video processing. We focus the presentation of RegPCA with the combination of RPCA on video processing and find that it is more reliable than RPCA only. We use RegPCA to separate moving object from the background in a color video and get a better result than that given by RPCA. In the implementation, we first derive the explanatory variables by the background information. we then process a number of frames of the video and use those as a set of response variables. We remove the impact of the background by regressing the response against the explanatory variables by a regression model. The regression model provides a set of residuals, which can be further analyzed by RPCA. We compare the results of RegRPCA against those of RPCA only. It is evident that the moving objects can be completely removed from the background using our method but not in RPCA. Note that our result is based on a combination of RegPCA with RPCA. Our proposed method provides a new implementation of RPCA under the framework of regression approaches, which can be used to account for the impact of risk factors. This problem cannot be addressed by the application of RPCA only.

A 3D object can be recovered from scanned point data, which requires accurate estimating normal directions of the object surface from the cloud data. Many point cloud processing algorithms rely on the accurate normal as input to generate an accurate 3D surface model. The neighborhood of a data point in its smooth region can be well approximated by a plane. However, the neighborhood of a feature point employed for the normal estimation is isotropic which would enclose points belonging to different surface patches across the sharp feature. In this paper, isotropic neighborhoods are segmented to search anisotropic neighborhoods for the accurate normal estimation. Normals and candidate feature points are first estimated by the principal component analysis (PCA) method. Neighborhoods of the feature point are then mapped into a Gaussian image. A k-means clustering algorithm is then used for the Gaussian image to identify an anisotropic sub-neighborhood for the data point. The normal of the candidate feature point is finally estimated by the anisotropic neighborhood with the PCA method. The proposed method can accurately estimate normal directions while preserving sharp features of the object surface. Applications have demonstrated the effectiveness of the proposed method.

This paper presents a novel Gabor-based kernel Principal Component Analysis (PCA) method by integrating the Gabor wavelet representation of face images and the kernel PCA method for face recognition. Gabor wavelets first derive desirable facial features characterized by spatial frequency, spatial locality, and orientation selectivity to cope with the variations due to illumination and facial expression changes. The kernel PCA method is then extended to include fractional power polynomial models for enhanced face recognition performance. A fractional power polynomial, however, does not necessarily define a kernel function, as it might not define a positive semidefinite Gram matrix. Note that the sigmoid kernels, one of the three classes of widely used kernel functions (polynomial kernels, Gaussian kernels, and sigmoid kernels), do not actually define a positive semidefinite Gram matrix either. Nevertheless, the sigmoid kernels have been successfully used in practice, such as in building support vector machines. In order to derive real kernel PCA features, we apply only those kernel PCA eigenvectors that are associated with positive eigenvalues. The feasibility of the Gabor-based kernel PCA method with fractional power polynomial models has been successfully tested on both frontal and pose-angled face recognition, using two data sets from the FERET database and the CMU PIE database, respectively. The FERET data set contains 600 frontal face images of 200 subjects, while the PIE data set consists of 680 images across five poses (left and right profiles, left and right half profiles, and frontal view) with two different facial expressions (neutral and smiling) of 68 subjects. The effectiveness of the Gabor-based kernel PCA method with fractional power polynomial models is shown in terms of both absolute performance indices and comparative performance against the PCA method, the kernel PCA method with polynomial kernels, the kernel PCA method with fractional power polynomial models, the Gabor wavelet-based PCA method, and the Gabor wavelet-based kernel PCA method with polynomial kernels.

Two-step phase extraction and random phase shift estimation in phase-shifting profilometry based on least-squared optical flow method