Model-driven CT reconstruction algorithm for nano-resolution x-ray phase contrast imaging

The low-density imaging performance of a zone plate-based nano-resolution hard x-ray computed tomography(CT)system can be significantly improved by incorporating a grating-based Lau interferometer. Due to the diffraction, however,the acquired nano-resolution phase signal may suffer splitting problem, which impedes the direct reconstruction of phase contrast CT(nPCT) images. To overcome, a new model-driven nPCT image reconstruction algorithm is developed in this study. In it, the diffraction procedure is mathematically modeled into a matrix B, from which the projections without signal splitting can be generated invertedly. Furthermore, a penalized weighted least-square model with total variation(PWLSTV) is employed to denoise these projections, from which nPCT images with high accuracy are directly reconstructed.Numerical experiments demonstrate that this new algorithm is able to work with phase projections having any splitting distances. Moreover, results also reveal that nPCT images of higher signal-to-noise-ratio(SNR) could be reconstructed from projections having larger splitting distances. In summary, a novel model-driven nPCT image reconstruction algorithm with high accuracy and robustness is verified for the Lau interferometer-based hard x-ray nano-resolution phase contrast imaging.

Ultrahigh spatiotemporal resolution beam signal reconstruction with bunch phase compensation

Various electromagnetic signals are excited by the beam in the acceleration and beam-diagnostic elements of a particle accelerator.It is important to obtain time-domain waveforms of these signals with high temporal resolution for research,such as the study of beam–cavity interactions and bunch-by-bunch parameter measurements.Therefore,a signal reconstruction algorithm with ultrahigh spatiotemporal resolution and bunch phase compensation based on equivalent sampling is proposed in this paper.Compared with traditional equivalent sampling,the use of phase compensation and setting the bunch signal zero-crossing point as the time reference can construct a more accurate reconstructed signal.The basic principles of the method,simulation,and experimental comparison are also introduced.Based on the beam test platform of the Shanghai Synchrotron Radiation Facility(SSRF)and the method of experimental verification,the factors that affect the reconstructed signal quality are analyzed and discussed,including the depth of the sampled data,quantization noise of analog-to-digital converter,beam transverse oscillation,and longitudinal oscillation.The results of the beam experiments show that under the user operation conditions of the SSRF,a beam excitation signal with an amplitude uncertainty of 2%can be reconstructed.

Heterogeneous information phase space reconstruction and stability prediction of filling body–surrounding rock combination

Traditional research believes that the filling body can effectively control stress concentration while ignoring the problems of unknown stability and the complex and changeable stress distribution of the filling body–surrounding rock combination under high-stress conditions.Current monitoring data processing methods cannot fully consider the complexity of monitoring objects,the diversity of monitoring methods,and the dynamics of monitoring data.To solve this problem,this paper proposes a phase space reconstruction and stability prediction method to process heterogeneous information of backfill–surrounding rock combinations.The three-dimensional monitoring system of a large-area filling body–surrounding rock combination in Longshou Mine was constructed by using drilling stress,multipoint displacement meter,and inclinometer.Varied information,such as the stress and displacement of the filling body–surrounding rock combination,was continuously obtained.Combined with the average mutual information method and the false nearest neighbor point method,the phase space of the heterogeneous information of the filling body–surrounding rock combination was then constructed.In this paper,the distance between the phase point and its nearest point was used as the index evaluation distance to evaluate the stability of the filling body–surrounding rock combination.The evaluated distances(ED)revealed a high sensitivity to the stability of the filling body–surrounding rock combination.The new method was then applied to calculate the time series of historically ED for 12 measuring points located at Longshou Mine.The moments of mutation in these time series were at least 3 months ahead of the roadway return dates.In the ED prediction experiments,the autoregressive integrated moving average model showed a higher prediction accuracy than the deep learning models(long short-term memory and Transformer).Furthermore,the root-mean-square error distribution of the prediction results peaked at 0.26,thus outperforming the no-prediction method in 70%of the cases.

Prediction of elevator traffic flow based on SVM and phase space reconstruction

To make elevator group control system better follow the change of elevator traffic flow (ETF) in order to adjust the control strategy,the prediction method of support vector machine (SVM) in combination with phase space reconstruction has been proposed for ETF.Firstly,the phase space reconstruction for elevator traffic flow time series (ETFTS) is processed.Secondly,the small data set method is applied to calculate the largest Lyapunov exponent to judge the chaotic property of ETF.Then prediction model of ETFTS based on SVM is founded.Finally,the method is applied to predict the time series for the incoming and outgoing passenger flow respectively using ETF data collected in some building.Meanwhile,it is compared with RBF neural network model.Simulation results show that the trend of factual traffic flow is better followed by predictive traffic flow.SVM algorithm has much better prediction performance.The fitting and prediction of ETF with better effect are realized.

Phase space reconstruction of chaotic dynamical system based on wavelet decomposition

In view of the disadvantages of the traditional phase space reconstruction method, this paper presents the method of phase space reconstruction based on the wavelet decomposition and indicates that the wavelet decomposition of chaotic dynamical system is essentially a projection of chaotic attractor on the axes of space opened by the wavelet filter vectors, which corresponds to the time-delayed embedding method of phase space reconstruction proposed by Packard and Takens. The experimental results show that, the structure of dynamical trajectory of chaotic system on the wavelet space is much similar to the original system, and the nonlinear invariants such as correlation dimension, Lyapunov exponent and Kolmogorov entropy are still reserved. It demonstrates that wavelet decomposition is effective for characterizing chaotic dynamical system.

Degradation Process of Coated Tinplate by Phase Space Reconstruction Theory

The degradation process of organosol coated tinplate in beverage was investigated by electrochemical noise (EN) technique combined with morphology characterization.EN data were analyzed using phase space reconstruction theory.With the correlation dimensions obtained from the phase space reconstruction,the chaotic behavior of EN was quantitatively evaluated.The results show that both electrochemical potential noise (EPN) and electrochemical current noise (ECN) have chaotic properties.The correlation dimensions of EPN increase with corrosion extent,while those of ECN seem nearly unchanged.The increased correlation dimensions of EPN during the degradation process are associated with the increased susceptibility to local corrosion.

Transverse phase space reconstruction study in Shanghai soft X-ray FEL facility

Phase space is one of the most important parameters used to describe beam properties. Computer tomography, as a method for reconstructing phase space and measuring beam emittance, has been used in many accelerators over the past few decades. In this paper, we demonstrate a transverse phase space reconstruction study in the Shanghai soft X-ray free electron laser facility. First,we discuss the basic principles of phase space reconstruction and the advantage of reconstructing beam distribution in normalized phase space. Then, the phase space reconstruction results by different computer tomography methods based on the maximum entropy(MENT) algorithm and the filtered back projection algorithm in normalized phase space are presented. The simulation results indicate that,with proper configuration of the phase advance between adjacent screens, the MENT algorithm is feasible and has good efficiency. The beam emittance and Twiss parameters are also calculated using the reconstructed phase space.

Research on the Signal Reconstruction of the Phased Array Structural Health Monitoring Based Using the Basis Pursuit Algorithm

The signal processing problem has become increasingly complex and demand high acquisition system,this paper proposes a new method to reconstruct the structure phased array structural health monitoring signal.The method is derived from the compressive sensing theory and the signal is reconstructed by using the basis pursuit algorithm to process the ultrasonic phased array signals.According to the principles of the compressive sensing and signal processing method,non-sparse ultrasonic signals are converted to sparse signals by using sparse transform.The sparse coefficients are obtained by sparse decomposition of the original signal,and then the observation matrix is constructed according to the corresponding sparse coefficients.Finally,the original signal is reconstructed by using basis pursuit algorithm,and error analysis is carried on.Experimental research analysis shows that the signal reconstruction method can reduce the signal complexity and required the space efficiently.

Study on resource quantity of surface water based on phase space reconstruction and neural network

Proposed a new method to disclose the complicated non-linearity structure of the water-resource system, introducing chaos theory into the hydrology and water resources field, and combined with the chaos theory and artificial neural networks. Training data construction and networks structure were determined by the phase space reconstruction, and establishing nonlinear relationship of phase points with neural networks, the forecasting model of the resource quantity of the surface water was brought forward. The keystone of the way and the detailed arithmetic of the network training were given. The example shows that the model has highly forecasting precision.

Analysis of dynamic of two-phase flow in small channel based on phase space reconstruction combined with data reduction sub-frequency band wavelet

A new method of nonlinear analysis is established by combining phase space reconstruction and data reduction sub-frequency band wavelet. This method is applied to two types of chaotic dynamic systems(Lorenz and Rssler) to examine the anti-noise ability for complex systems. Results show that the nonlinear dynamic system analysis method resists noise and reveals the internal dynamics of a weak signal from noise pollution. On this basis, the vertical upward gas–liquid two-phase flow in a 2 mm × 0.81 mm small rectangular channel is investigated. The frequency and energy distributions of the main oscillation mode are revealed by analyzing the time–frequency spectra of the pressure signals of different flow patterns. The positive power spectral density of singular-value frequency entropy and the damping ratio are extracted to characterize the evolution of flow patterns and achieve accurate recognition of different vertical upward gas–liquid flow patterns(bubbly flow:100%, slug flow: 92%, churn flow: 96%, annular flow: 100%). The proposed analysis method will enrich the dynamics theory of multi-phase flow in small channel.

Classification of power quality combined disturbances based on phase space reconstruction and support vector machines

Power Quality (PQ) combined disturbances become common along with ubiquity of voltage flickers and harmonics. This paper presents a novel approach to classify the different patterns of PQ combined disturbances. The classification system consists of two parts, namely the feature extraction and the automatic recognition. In the feature extraction stage, Phase Space Reconstruction (PSR), a time series analysis tool, is utilized to construct disturbance signal trajectories. For these trajectories, several indices are proposed to form the feature vectors. Support Vector Machines (SVMs) are then implemented to recognize the different patterns and to evaluate the efficiencies. The types of disturbances discussed include a combination of short-term dis-turbances (voltage sags, swells) and long-term disturbances (flickers, harmonics), as well as their homologous single ones. The feasibilities of the proposed approach are verified by simulation with thousands of PQ events. Comparison studies based on Wavelet Transform (WT) and Artificial Neural Network (ANN) are also reported to show its advantages.

A Phase Space Reconstruction Based Approach to Throughput Prediction in Semiconductor Wafer Fabrication System

In order to manage and control semiconductor wafer fabrication system (SWFS) more effectively,the daily throughput prediction data of wafer fab are often used in the planning and scheduling of SWFS.In this paper,an artificial neural network (ANN) prediction method based on phase space reconstruction (PSR) and ant colony optimization (ACO) is presented,in which the phase space reconstruction theory is used to reconstruct the daily throughput time series,the ANN is used to construct the daily throughput prediction model,and the ACO is used to train the connection weight and bias values of the neural network prediction model.Testing with factory operation data and comparing with the traditional method show that the proposed methodology is effective.

SELECTION OF PROPER EMBEDDING DIMENSION IN PHASE SPACE RECONSTRUCTION OF SPEECH SIGNALS

In phase space reconstruction of time series, the selection of embedding dimension is important. Based on the idea of checking the behavior of near neighbors in the reconstruction dimension, a new method to determine proper minimum embedding dimension is constructed. This method has a sound theoretical basis and can lead to good result. It can indicate the noise level in the data to be reconstructed, and estimate the reconstruction quality. It is applied to speech signal reconstruction and the generic embedding dimension of speech signals is deduced.

Design of Perfect Reconstruction Cosine Modulated Filter Bank with Linear Phase

We propose the quadratic constrained formulas for the design of linear phase cosine modulated paraunitary filter banks given in references . Using these formulae, we can, directly, optimize the prototype filter coefficients in a quadratic form. A design example is also given to demonstrate these formulae in this paper.

A method for phase reconstruction in optical three-dimensional shape measurement

In optical three-dimensional shape measurement, a method of improving the measurement precision for phase reconstruction without phase unwrapping is analyzed in detail. Intensities of any five consecutive pixels that lie in the x-axis direction of the phase domain are given. Partial derivatives of the phase function in the x- and y-axis directions are obtained with a phase-shifting mechanism, the origin of which is analysed. Furthermore, to avoid phase unwrapping in the phase reconstruction, we derive the gradient of the phase function and perform a two-dimensional integral along the x- and y-axis directions. The reconstructed phase can be obtained directly by performing numerical integration, and thus it is of great convenience for phase reconstruction. Finally, the results of numerical simulations and practical experiments verify the correctness of the proposed method.

PARAMETERS DETERMINATION METHOD OF PHASE-SPACE RECONSTRUCTION BASED ON DIFFERENTIAL ENTROPY RATIO AND RBF NEURAL NETWORK

Phase space reconstruction is the first step of recognizing the chaotic time series.On the basis of differential entropy ratio method,the embedding dimension opt m and time delay t are optimal for the state space reconstruction could be determined.But they are not the optimal parameters accepted for prediction.This study proposes an improved method based on the differential entropy ratio and Radial Basis Function(RBF)neural network to estimate the embedding dimension m and the time delay t,which have both optimal characteristics of the state space reconstruction and the prediction.Simulating experiments of Lorenz system and Doffing system show that the original phase space could be reconstructed from the time series effectively,and both the prediction accuracy and prediction length are improved greatly.

Phase Error Compensation of Three-Dimensional Reconstruction Combined with Hilbert Transform

Nonlinear response is an important factor affecting the accuracy of three-dimensional image measurement based on the fringe structured light method.A phase compensation algorithm combined with a Hilbert transform is proposed to reduce the phase error caused by the nonlinear response of a digital projector in the three-dimensional measurement system of fringe structured light.According to the analysis of the influence of Gamma distortion on the phase calculation,the algorithm establishes the relationship model between phase error and harmonic coefficient,introduces phase shift to the signal,and keeps the signal amplitude constant while filtering out the DC component.The phase error is converted to the transform domain,and compared with the numeric value in the space domain.The algorithm is combined with a spiral phase function to optimize the Hilbert transform,so as to eliminate external noise,enhance the image quality,and get an accurate phase value.Experimental results show that the proposed method can effectively improve the accuracy and speed of phase measurement.By performing phase error compensation for free-form surface objects,the phase error is reduced by about 26%,and about 27%of the image reconstruction time is saved,which further demonstrates the feasibility and effectiveness of the method.

Phase Reconstruction and Microstructure Evolution of Magnesia-carbon Refractories at High Temperatures in Nitrogen

Magnesia-carbon refractories were prepared using fused magnesia,flake graphite and metal aluminum powder as starting materials,phenolic resin as the binder,heat-treating at 1300-1600℃in nitrogen atmosphere.The phase reconstruction and the microstructure evolution of the obtained magnesia-carbon refractories were analyzed.The formation mechanisms of magnesia crystals with different morphologies by chemical vapor deposition were revealed.The results show that at 1300-1500℃,the non-oxides within the specimens are aluminum carbide(Al_(4)C_(3)),aluminum nitride(AlN)and magnesium aluminum nitride(Mg_(3)Al_(n)N_(n+2),n=2 or 3);at 1600℃,the diffraction characteristic peak intensity of Al_(4)C_(3) and AlN decreases sharply,and sharp diffraction characteristic peaks of nitrogen aluminum carbide(Al_(7)C_(3)N_(3))appear.Mg(g)is produced by the aluminothermic reduction and carbothermal reduction of magnesia.On the surface of the specimens,Mg(g)reacts with oxygen to form MgO whiskers.Inside the specimens,Mg(g)and O_(2)(g)undergo a CVD chemical deposition reaction to form cubic MgO crystals.There is a phase relationship between flake AlN and flake Mg3AlnNn+2,and they are so associated with each other that the morphology is difficult to distinguish.

Application of phase space reconstruction and v-SVR algorithm in predicting displacement of underground engineering surrounding rock

A new method for predicting the trend of displacement evolution of surroundingrock was presented in this paper.According to the nonlinear characteristics of displace-ment time series of underground engineering surrounding rock,based on phase spacereconstruction theory and the powerful nonlinear mapping ability of support vector ma-chines,the information offered by the time series datum sets was fully exploited and thenon-linearity of the displacement evolution system of surrounding rock was well described.The example suggests that the methods based on phase space reconstruction and modi-fied v-SVR algorithm are very accurate,and the study can help to build the displacementforecast system to analyze the stability of underground engineering surrounding rock.

A high precision phase reconstruction algorithm for multi-laser guide stars adaptive optics

Adaptive optics（AO） systems are widespread and considered as an essential part of any large aperture telescope for obtaining a high resolution imaging at present.To enlarge the imaging field of view（FOV）,multi-laser guide stars（LGSs） are currently being investigated and used for the large aperture optical telescopes.LGS measurement is necessary and pivotal to obtain the cumulative phase distortion along a target in the multi-LGSs AO system.We propose a high precision phase reconstruction algorithm to estimate the phase for a target with an uncertain turbulence profile based on the interpolation.By comparing with the conventional average method,the proposed method reduces the root mean square（RMS） error from 130 nm to 85 nm with a 30% reduction for narrow FOV.We confirm that such phase reconstruction algorithm is validated for both narrow field AO and wide field AO.