ON THE EXISTENCE OF INFINITELY MANY CRITICAL POINTS OF THE EVEN FUNCTIONAL integral from n=Q to (F(x,u,Du))+integral from n=■Q to (G(x,u))

In this paper we deal with the existence of infinitely many critical points of the even functional I(u)=integral from n=Q to (F(x,u,Du))+integral from n=(?)Q to (G(x,u)), u∈W^(1,p)(Ω),where G(x, u)=integral from n=o to u (g(x,t)dt), under the weak structure conditions on F(x, u, q) by the Mountain Pass Lemma.

DiriNet:An Estimation Network for Spectral Response Function and Point Spread Function

Hyper-and multi-spectral image fusion is an important technology to produce hyper-spectral and hyper-resolution images,which always depends on the spectral response function andthe point spread function.However,few works have been payed on the estimation of the two degra-dation functions.To learn the two functions from image pairs to be fused,we propose a Dirichletnetwork,where both functions are properly constrained.Specifically,the spatial response function isconstrained with positivity,while the Dirichlet distribution along with a total variation is imposedon the point spread function.To the best of our knowledge,the neural network and the Dirichlet regularization are exclusively investigated,for the first time,to estimate the degradation functions.Both image degradation and fusion experiments demonstrate the effectiveness and superiority of theproposed Dirichlet network.

Physics-constrained deep-inverse point spread function model:toward non-line-of-sight imaging reconstruction

Non-line-of-sight(NLOS)imaging has emerged as a prominent technique for reconstructing obscured objects from images that undergo multiple diffuse reflections.This imaging method has garnered significant attention in diverse domains,including remote sensing,rescue operations,and intelligent driving,due to its wide-ranging potential applications.Nevertheless,accurately modeling the incident light direction,which carries energy and is captured by the detector amidst random diffuse reflection directions,poses a considerable challenge.This challenge hinders the acquisition of precise forward and inverse physical models for NLOS imaging,which are crucial for achieving high-quality reconstructions.In this study,we propose a point spread function(PSF)model for the NLOS imaging system utilizing ray tracing with random angles.Furthermore,we introduce a reconstruction method,termed the physics-constrained inverse network(PCIN),which establishes an accurate PSF model and inverse physical model by leveraging the interplay between PSF constraints and the optimization of a convolutional neural network.The PCIN approach initializes the parameters randomly,guided by the constraints of the forward PSF model,thereby obviating the need for extensive training data sets,as required by traditional deep-learning methods.Through alternating iteration and gradient descent algorithms,we iteratively optimize the diffuse reflection angles in the PSF model and the neural network parameters.The results demonstrate that PCIN achieves efficient data utilization by not necessitating a large number of actual ground data groups.Moreover,the experimental findings confirm that the proposed method effectively restores the hidden object features with high accuracy.

Analysis of the optical quality by determining the modulation transfer function for anterior corneal surface in myopes

AIM: To describe the characteristics of modulation transfer function (MTF) of anterior corneal surface, and obtain the the normal reference range of MTF at different spatial frequencies and optical zones of the anterior corneal surface in myopes. METHODS: Four hundred eyes from 200 patients were examined under SIRIUS corneal topography system. Phoenis analysis software was applied to simulate the MTF curves of anterior corneal surface at vertical and horizontal meridians at the 3, 4, 5, 6, 7mm optical zones of cornea. The MTF values at spatial frequencies of 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55 and 60 cycles/degree (c/d) were selected. RESULTS: The MTF curve of anterior corneal surface decreased rapidly from low to intermediate frequency (0-15cpd) at various optical zones of cornea, the value decreased to 0 slowly at higher frequency (>15cpd). With the increase of the optical zones of cornea, MTF curve decreased gradually. 3) In the range of 3 mm- 6 mm optical zones of the cornea, the MTF values measured at horizontal meridian were greater than the corresponding values at horizontal meridian of each spatial frequency, the difference was statistically significant (P<0.05). At 7 mm optical zones of cornea, the MTF values measured at horizontal meridian were less than the corresponding values at vertical meridian at 10-60 spatial frequencies (cpd), and the difference was statistically significant in 25, 30, 35, 40, 45, 50 cpd(P<0.05). CONCLUSION: MTF can be used to describe the imaging quality of optical systems at anterior corneal surface objectively in detail.

PET image reconstruction with a system matrix containing point spread function derived from single photon incidence response

A point spread function（PSF） for the blurring component in positron emission tomography（PET） is studied. The PSF matrix is derived from the single photon incidence response function. A statistical iterative reconstruction（IR） method based on the system matrix containing the PSF is developed. More specifically, the gamma photon incidence upon a crystal array is simulated by Monte Carlo（MC） simulation, and then the single photon incidence response functions are calculated. Subsequently, the single photon incidence response functions are used to compute the coincidence blurring factor according to the physical process of PET coincidence detection. Through weighting the ordinary system matrix response by the coincidence blurring factors, the IR system matrix containing the PSF is finally established. By using this system matrix, the image is reconstructed by an ordered subset expectation maximization（OSEM） algorithm. The experimental results show that the proposed system matrix can substantially improve the image radial resolution, contrast,and noise property. Furthermore, the simulated single gamma-ray incidence response function depends only on the crystal configuration, so the method could be extended to any PET scanner with the same detector crystal configuration.

Study on the 3D Green＇s functions of the fluid and piezoelectric bimaterials

Because most piezoelectric devices have interfaces with fluid in engineering, it is valuable to study the coupled field between fluid and piezoelectric media. As the fundamental problem, the 3D Green＇s functions for point forces and point charge loaded in the fluid and piezoelectric bimaterials are studied in this paper. Based on the 3D general solutions expressed by harmonic functions, we constructed the suitable harmonic functions with undetermined constants at first. Then, the couple field in the fluid and piezoelectric bimaterials can be derived by substitution of harmonic functions into general solutions. These constants can be obtained by virtue of the compatibility, boundary, and equilibrium conditions. At last, the characteristics of the electromechanical coupled fields are shown by numerical results.

Reusing Test Cases Based on the Function Point

Reusing test cases from existing test case library is quite common in the software testing field. Testing practice tells us that there is a strong relationship between the granularity of a function unit under testing and that of the test case. A function unit with small granularity usually results in the test cases with the same small granularity. Therefore a test case defined as the function point,i. e.,the smallest size function unit,was provided for the first time.Though test cases with smaller granularity usually have better reusability,the cost of accurately reusing and integrating such test cases is also higher. In order to balance the test case reusability and the cost of test case reuse,a novel test case reuse model based on the function point was proposed in this paper. In this model,a reusable test case for specification-based testing was defined and some reuse strategies and three formal reuse methods were given. Finally,the complete automatic software process was realized by a reusing generation tool. The new method has improved reuse accuracy,while greatly enhances the software productivity.

Thin-film approximate point scattered function and its application to neutron radiography

A simpler and improved utility approximate point scattered function for thin-film converters currently used in neutron photographic devices is proposed as a correction method to produce clearer,more realistic images.The validity of the model was demonstrated through a simulation experiment.Based on the results,an error analysis was carried out,certain corrections were made to the original model,and the final model achieved a very low relative error in the simulation experiment.The model can also be optimized for quantitative neutron photographic analysis using iterative algorithms to obtain realistic neutron photographic images more quickly.At the end of the article,the model is extended to consider the case of energy spectrum hardening by introducing a temperature correction parameter.

Bistatic Synthetic Aperture Radar Point Spread Function Characteristic Analysis

Based on the point spread function （PSF） theory, the side-lobe extension direction of the impulse response in bistatic synthetic aperture radar （BSAR） is analyzed in detail; in addition, the corresponding autofocus in BSAR should be considered along iso-range direction, not the traditional azimuth resolution （AR） direction. The conclusion is verified by the computer simulation.

Existence of Positive Solutions for a Fourth-Order Three-Point BVP with Sign-Changing Green’s Function

In this article, by using a fixed point theorem, we study following fourth-order three-point BVP: where f ∈ C([0,1]×[0,+∞),[0,+∞)) α ∈ [0,6) and . The main point to emphasize is that although the corresponding Green’s function is changing signs, by applying the fixed point theorem, we can still obtain at least two positive solutions and degreased solutions under certain suitable conditions.

FIXED POINT WITH ORBITAL DIAMETRAL FUNCTION

A foremost general contraction condition is introduced to prove the existence of fixed points for a self-mapping in a somplete metric space whose orbital diametral functions are closed. This condition covers not only the Kannan type but also covers Reich, and Hardy and Roger's type contractive conditions. An example is given in its support.

A Knife-edge Input Point Spread Function Estimation Method for Document Images

In this paper the progress of document image Point Spread Function （PSF） estimation will be presented. At the beginning of the paper, an overview of PSF estimation methods will be introduced and the reason why knife-edge input PSF estimation method is chosen will be explained. Then in the next section, the knife-edge input PSF estimation method will be detailed. After that, a simulation experiment is performed in order to verify the implemented PSF estimation method. Based on the simulation experiment, in next section we propose a procedure that makes automatic PSF estimation possible. A real document image is firstly taken as an example to illustrate the procedure and then be restored with the estimated PSF and Lucy-Richardson deconvolution method, and its OCR accuracy before and after deconvolution will be compared. Finally, we conclude the paper with the outlook for the future work.

Research on ballistic missile laser SIMU error propagation mechanism

It is necessary that the laser inertial system is used to further improve the fire accuracy and quick reaction capability in the ballistic missile strapdown inertial navigation system. According to the guidance controlling method and the output and error model of ballistic missile laser SIMU, the mathematical model of error propagation mechanism is set up and any transfer environmental function of error coefficient that affects the fire accuracy is deduced. Also, the missile longitudinal/lateral impact point is calculated using MATLAB. These establish the technical foundation for further researching the dispersion characteristics of impact point and reducing the laser guidance error.

Broadband seismic illumination and resolution analyses based on staining algorithm

Seismic migration moves reflections to their true subsurface positions and yields seismic images of subsurface areas. However, due to limited acquisition aperture, complex overburden structure and target dipping angle, the migration often generates a distorted image of the actual subsurface structure. Seismic illumination and resolution analyses provide a quantitative description of how the above-mentioned factors distort the image. The point spread function （PSF） gives the resolution of the depth image and carries full information about the factors affecting the quality of the image. The staining algorithm establishes a correspondence between a certain structure and its relevant wavefield and reflected data. In this paper, we use the staining algorithm to calculate the PSFs, then use these PSFs for extracting the acquisition dip response and correcting the original depth image by deconvolution. We present relevant results of the SEG salt model. The staining algorithm provides an efficient tool for calculating the PSF and for conducting broadband seismic illumination and resolution analyses.

ROV Based Underwater Blurred Image Restoration

In this paper, we present a method of ROV based image processing to restore underwater blurry images from the theory of light and image transmission in the sea. Computer is used to simulate the maximum detection range of the ROV under different water body conditions. The receiving irradiance of the video camera at different detection ranges is also calculated. The ROV’s detection performance under different water body conditions is given by simulation. We restore the underwater blurry images using the Wiener filter based on the simulation. The Wiener filter is shown to be a simple useful method for underwater image restoration in the ROV underwater experiments. We also present examples of restored images of an underwater standard target taken by the video camera in these experiments.

Parameter recognition for defocus blur image using cepstrum analysis

Successful restoration of blurred images depends primarily on the knowledge about the degradationparameter.Defocus blur model in the frequency domain is characterized by concentric rings and the blurradius of the point spread function(PSF)can be identified conveniently in the frequency field for peopleby manual means rather than for computer.This paper introduces a practical method for computer to esti-mate the defocus blur parameter in cepstrum area.Fourier transform plays an intermediate role in the pathto cepstrum domain.We suggest a weighted adjustment operation in the frequency domain and then con-vert it to the cepstrum field to increase the accuracy of recognition.

Least squares weighted twin support vector machines with local information

A least squares version of the recently proposed weighted twin support vector machine with local information(WLTSVM) for binary classification is formulated. This formulation leads to an extremely simple and fast algorithm, called least squares weighted twin support vector machine with local information(LSWLTSVM), for generating binary classifiers based on two non-parallel hyperplanes. Two modified primal problems of WLTSVM are attempted to solve, instead of two dual problems usually solved. The solution of the two modified problems reduces to solving just two systems of linear equations as opposed to solving two quadratic programming problems along with two systems of linear equations in WLTSVM. Moreover, two extra modifications were proposed in LSWLTSVM to improve the generalization capability. One is that a hot kernel function, not the simple-minded definition in WLTSVM, is used to define the weight matrix of adjacency graph, which ensures that the underlying similarity information between any pair of data points in the same class can be fully reflected. The other is that the weight for each point in the contrary class is considered in constructing equality constraints, which makes LSWLTSVM less sensitive to noise points than WLTSVM. Experimental results indicate that LSWLTSVM has comparable classification accuracy to that of WLTSVM but with remarkably less computational time.

Lattice QCD Calculation of ππ Scattering Length

We study s-wave pion-pion scattering length in lattice QCD for pion masses ranging from 330 MeV to 466 MeV. In the ＂Asqtad＂ improved staggered fermion formulation, we measure full ππ four-point correlators for isospin I = 0 and 2 channels, and use chiral perturbation theory at next-to-leading order to extrapolate our simulation results. Extrapolating to the physical pion mass yields scattering lengths as mna01=2 = -0.041 6（2） and mna01= 0.186（2） for isospin I = 2 and 0 channels, respectively. Our lattice simulation for ππ scattering length in I = 0 channel is an exploratory study, where we include the disconnected contribution, and our preliminary result is near to its experimental value. These simulations are carried out with MILC 2 ＋ 1 flavor gauge configurations at lattice spacing a ≈0.15 fm.

Reduced aliasing artifacts using shaking projection k-space sampling trajectory

Radial imaging techniques, such as projection-reconstruction （PR）, are used in magnetic resonance imaging （MRI） for dynamic imaging, angiography, and short-T2 imaging. They are less sensitive to flow and motion artifacts, and support fast imaging with short echo times. However, aliasing and streaking artifacts are two main sources which degrade radial imaging quality. For a given fixed number of k-space projections, data distributions along radial and angular directions will influence the level of aliasing and streaking artifacts. Conventional radial k-space sampling trajectory introduces an aliasing artifact at the first principal ring of point spread function （PSF）. In this paper, a shaking projection （SP） k-space sampling trajectory was proposed to reduce aliasing artifacts in MR images. SP sampling trajectory shifts the projection alternately along the k-space center, which separates k-space data in the azimuthal direction. Simulations based on conventional and SP sampling trajectories were compared with the same number projections. A significant reduction of aliasing artifacts was observed using the SP sampling trajectory. These two trajectories were also compared with different sampling frequencies. ASP trajectory has the same aliasing character when using half sampling frequency （or half data） for reconstruction. SNR comparisons with different white noise levels show that these two trajectories have the same SNR character. In conclusion, the SP trajectory can reduce the aliasing artifact without decreasing SNR and also provide a way for undersampling recon- struction. Furthermore, this method can be applied to three-dimensional （3D） hybrid or spherical radial k-space sampling for a more efficient reduction of aliasing artifacts.

Single exposure passive three-dimensional information reconstruction based on an ordinary imaging system

Existing three-dimensional(3D) imaging technologies have issues such as requiring active illumination, multiple exposures, or coding modulation. We propose a passive single 3D imaging method based on an ordinary imaging system.Using the point spread function of the imaging system to realize the non-coding measurement on the target, the full-focus images and depth information of the 3D target can be extracted from a single two-dimensional(2D) image through the compressed sensing algorithm. Simulation and experiments show that this approach can complete passive 3D imaging based on an ordinary imaging system without any coding operations. This method can achieve millimeter-level vertical resolution under single exposure conditions and has the potential for real-time dynamic 3D imaging. It improves the efficiency of 3D information detection, reduces the complexity of the imaging system, and may be of considerable value to the field of computer vision and other related applications.