The PCA Algorithm in Digital Holographic Microscopy under Structured Illumination

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

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OMI operational SO2 planetary boundary layer (PBL) retrieval, the previous band residual difference (BRD) algorithm has been replaced by principal component analysis (PCA) algorithm, which effectively reduces the systematic biases in SO2 column retrievals.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.

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.

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.

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.

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.

A method to improve the radial resolution using special structured light is proposed in the field of digital holographic microscopy (DHM). A specimen is illuminated with circular symmetrical structured light that makes the spectrum have radial movement, so that high frequency components of the specimen are moved into the passband of the receiver to overcome the diffraction limit. In the DHM imaging system, Computer Generated Hologram (CGH) technology is used to generate the required structured light grating. Then the grating is loaded into a spatial light modulator (SLM) to obtain specific structured illumination. After recording the hologram, digital reconstruction, for the microstructure of a binary optical element that needs to observe radial distribution, the radial resolution of the specimen is improved experimentally compare it with the result of one-dimensional sinusoidal structured light imaging. And a method of designing structured light is presented.

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.

This paper describes the novel method related to correcting color distortion in color imaging apparatus. Color images acquired from CMOS or CCD digital sensors can suffer from color distortion, which means that images from the sensors are different from those human being sees in the color space. The one of main reasons of this color distortion is crosstalk between adjacent pixels. To correct this kind of color distortion, existing methods are generally to multiply some gain coefficients in each color channel and this multiplication can cause noise boost and loss of detail information. This paper proposes the novel method which can not only preserve color distortion correction accuracy, but also suppress noise boost and loss of detail information based on the image fusion. Specifically the color and low frequency information in luminance channel are extracted from the color transformed image. And high frequency information is from the original image before color transform. The method to extract the low and high frequency information is based on the multi-resolution analysis with edge preserving filters.

In recent year, stock investor in Indonesia increased rapidly, so it is required to do analysis about the stock that helps the investor in their investment plan. Clustering is beneficial to select the appropriate stock for investors. Unfortunately, stock prices keep varying from time to time. Consequently, it is not an easy work to select the stock for investment. In addition, stock price time series data are high dimensional data that influenced by many factors. In this study, high dimensional data are obtained by the time frame of each factor. Therefore, it is important to use a suitable technique to cluster high dimensional data. This paper presents High Dimensional Data Clustering (HDDC), a model-based clustering based on Gaussian Mixture Model, using the Expectation-Maximization (EM) algorithm. HDDC via EM algorithm gives a more robust result, and it possible to make an additional assumption. Moreover, this paper combines a high-dimensional clustering technique HDDC via EM algorithm and the most popular feature extraction technique Principal Component Analysis (PCA). This paper comparing methods of clustering technique HDDC and the combination between HDDC and PCA to know the most effective method which gives better result in clustering high-dimensional time series data. The 155 data features are reduced to 7 principal components using PCA analysis. Despite PCA has increased the time efficiency of building the model, clustering technique HDDC via EM algorithm enables to handle the high-dimensional data better than the combination with PCA.

A de-noising method based on PCA (Principal Component Analysis) is proposed to suppress the noise of LLL (Low-Light Level) image. At first, the feasibility of de-noising with the algorithm of PCA is analyzed in detail. Since the image data is correlated in time and space, it is retained as principal component, while the noise is considered to be uncorrelated in both time and space and be removed as minor component. Then some LLL images is used in the experiment to confirm the proposed method. The sampling number of LLL image which can lead to the best de-noising effects is given. Some performance parameters are calculated and the results are analyzed in detail. To compare with the proposed method, some traditional de-noising algorithm are utilized to suppress noise of LLL images. Judging from the results, the proposed method has more significant effects of de-noising than the traditional algorithm. Theoretical analysis and experimental results show that the proposed method is reasonable and efficient.

Gram-Schmidt and Ehlers fusion, which are well known for spectral fidelity, are described. Selecting a sandrock mine using SPOT5 as study area, spectral fidelity and high spatial information gain are used to assess the two fusion methods, which are compared with multiplication and Andorr fusion. In the whole, the Gram-Schmidt method is the best, preserving highly the original spectral information, and can provide spectrum control foundation for interpreting mine targets in the complex geology environment. Ehlers method is the second. Then Andorr method is the third, and it has the highest spatial information gain, but high frequency information is enlarged excessively, effecting on the identification of mine exploitation state. The multiplication method is the worst, because it loses the high and low frequency information, which is the most important for mine targets recognition.

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.

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.