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.

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.

Point spread functions for a small gamma camera with pinhole collimator

A set of point spread functions (PSF) has been obtained by means of Monte-Carlo simulation for asmall gamma camera with a pinhole collimator of various hole diameters. The FOV (field of view) of the camera isexpended from 45 mm to 70 mm in diameter. The position dependence of the variances of PSF is presented, and theacceptance for the 140 kev gamma rays is explored. A phantom of 70 mm in diameter was experimentally imaged inthe camera with effective FOV of only 45 mm in diameter.

Plasmon point spread functions： How do we model plasmon-mediated emission processes？

A major challenge with studying plasmon-mediated emission events is the small size of plasmonic nanoparticles relative to the wavelength of light. Objects smaller than roughly half the wavelength of light will appear as diffraction-limited spots in far-field optical images, presenting a significant experimental challenge for studying plasmonic processes on the nanoscale. Super-resolution imaging has recently been applied to plasmonic nanosystems and allows plasmon-mediated emission to be resolved on the order of ~5 nm. In super-resolution imaging, a diffraction-limited spot is fit to some model function in order to calculate the position of the emission centroid, which represents the loca- tion of the emitter. However, the accuracy of the centroid position strongly depends on how well the fitting function describes the data. This Perspective discusses the commonly used two-dimensional Gaussian fitting function applied to super-resolution imaging of plasmon-mediated emission, then introduces an alternative model based on dipole point spread flmctions. The two fitting models are compared and contrasted for super-resolution imaging of nanoparticle scattering/luminescence, surface-enhanced Raman scattering, and surface-enhanced fluorescence.

Point spread function modeling and image restoration for cone-beam CT

X-ray cone-beam computed tomography （CT） has such notable features as high efficiency and precision, and is widely used in the fields of medical imaging and industrial non-destructive testing, but the inherent imaging degradation reduces the quality of CT images. Aimed at the problems of projection image degradation and restoration in cone-beam CT, a point spread function （PSF） modeling method is proposed first. The general PSF model of cone- beam CT is established, and based on it, the PSF under arbitrary scanning conditions can be calculated directly for projection image restoration without the additional measurement, which greatly improved the application convenience of cone-beam CT. Secondly, a projection image restoration algorithm based on pre-filtering and pre-segmentation is proposed, which can make the edge contours in projection images and slice images clearer after restoration, and control the noise in the equivalent level to the original images. Finally, the experiments verified the feasibility and effectiveness of the proposed methods.

Effects of mask-alignment error on point spread function for multi-level Fresnel diffractive lenses

The full aperture complex amplitude transmittance function of a multi-level diffraction lens with mask- alignment errors was derived based on scalar diffraction theory. The point spread function （PSF） was calculated by the Kirchhoff diffraction integral. It is found that the radius of the Airy disk increases with the increase of the error in the direction of misalignment, and the image center shifts along the direction of misalignment. A fourlevel diffractive lens with a diameter of 80 mm was fabricated, and its PSF and diffraction efficiency of ＋1st order were calculated and measured. The distribution of PSF is consistent with the calculated results, and the tested diffraction efficiency is slightly smaller than the calculated value; the relative error is 5.71%.

Resolution enhancement of optical scanning holography with a spiral modulated point spread function

In optical scanning holography, one pupil produces a spherical wave and another produces a plane wave. They interfere with each other and result in a fringe pattern for scanning a three-dimensional object. The resolution of the hologram reconstruction is affected by the point spread function(PSF) of the optical system. In this paper, we modulate the PSF by a spiral phase plate, which significantly enhances the lateral and depth resolution. We explain the theory for such resolution enhancement and show simulation results to verify the efficacy of the approach.

Numerical study of point spread function of a fast neutron radiography system based on scintillating-fiber array

For a scintillating-fiber array fast-neutron radiography system,a point-spread-function computing model was introduced,and the simulation code was developed. The results of calculation show that fast-neutron radiographs vary with the size of fast neutron sources,the size of fiber cross-section and the imaging geometry. The results suggest that the following qualifications are helpful for a good point spread function: The cross-section of scintillating fibers not greater than 200 μm×200 μm,the size of neutron source as small as a few millimeters,the distance between the source and the scintillating fiber array greater than 1 m,and inspected samples placed as close as possible to the array. The results give suggestions not only to experiment considerations but also to the estimation of spatial resolution for a specific system.

A phase model for point spread function estimation in ground-based astronomy

In ground-based astronomy,images of objects in outer space are acquired via ground-based telescopes.However,the imaging system is generally interfered by atmospheric turbulence and hence images so acquired are blurred with unknown point spread function(PSF).To restore the observed images,aberration of the wavefront at the telescope’s aperture,i.e.,the phase,is utilized to derive the PSF.However,the phase is not readily available.Instead,its gradients can be collected by wavefront sensors.Thus the usual approach is to use regularization methods to reconstruct high-resolution phase gradients and then use them to recover the phase in high accuracy.Here,we develop a model that reconstructs the phase directly.The proposed model uses the tight frame regularization and it can be solved efciently by the Douglas-Rachford alternating direction method of multipliers whose convergence has been well established.Numerical results illustrate that our new model is efcient and gives more accurate estimation for the PSF.

基于边缘约束与范数比值的图像盲复原

针对现有的研究方法对运动所引起的模糊图像进行复原时效果欠佳的问题,提出一种基于边缘约束与范数比值的图像盲复原算法.该算法首先对退化图像的边缘进行约束,得到图像的强边缘结构,提高了点扩散函数估计的准确率;然后对要估计的清晰图像构造范数比值的稀疏惩罚约束项,并将得到的强边缘信息与构造的范数比值惩罚约束项进行结合用于指引点扩散函数的复原;在对点扩散函数进行复原时,由粗到细多尺度交替迭代估计点扩散函数,使得迭代出的最大尺度更加精确;最后对图像进行非盲解卷积求解,使其复原.该算法将退化图像的边缘信息与构造的范数比值惩罚约束项进行结合指导点扩散函数的复原,可以抑制图像在复原过程中产生的大量伪迹.实验结果表明,该算法对恢复图像边缘细节具有很好的效果,可以得到优质的复原图像.

类THAAD导引头气动光学效应计算研究

针对类美国末段高空域防御(Terminal High Altitude Area Defense,THAAD)系统的红外导引头外形,开展了气动光学效应计算分析,并将其用于飞行器设计。利用国家数值风洞工程高速流场计算软件NNW-HyFLOW,考虑热化学非平衡效应和材料传热耦合效应,对导引头典型状态的流场进行了模拟,获得了流场的密度、温度、压力等参数和窗口的温度场参数。基于流场参数,利用HyFLOW气动光学传输效应计算功能,开展了红外光学传输成像计算;利用HyFLOW气动光学辐射效应计算模块,开展了流场和光学窗口的热辐射计算。计算结果表明,类THAAD导引头在30 km以上飞行时,流场和光学窗口基本不会影响目标信号的光学传输成像,但流场和窗口的热辐射效应会对导引头识别目标造成影响。不过随着飞行高度的升高,这种影响会减小。

计算成像技术中的点扩散函数工程

围绕光学成像中点扩散函数(Point spread function,PSF)在计算成像中的新内涵与应用,介绍了传统光学成像中PSF的概念以及PSF在光学系统设计中关键作用,并简要说明了几种利用PSF恢复图像算法以及图像评价指标。在此基础上以计算成像框架下信息传递的视角重新审视了PSF的内涵,从狭义、广义光学系统两个方面对计算成像领域中的相关研究进行了归纳总结,最后展望了PSF工程技术的应用前景及发展趋势。

新一代帕洛马天文台光谱仪的虚拟刀口欠采样像质测量方法

天文光谱仪的成像质量可用点扩散函数或线扩散函数来表征,但其相对于光谱仪探测器通常为欠采样,很难直接测量。在新一代帕洛马天文台光谱仪的像质测试中引入虚拟刀口法进行光源物面扫描,并应用虚拟刀口法开展欠采样光谱仪像质及光源尺度测量,通过模拟和实验研究,对比分析过采样经典直边刀口法和过采样直接测量方法,验证了虚拟刀口法具有良好的测量精度。在693 nm处,直边刀口法测得光谱仪过采样线扩散函数的半高全宽为7.05μm,虚拟刀口法测量欠采样线扩散函数的半高全宽为7.14μm,测量误差为1.3%。在0.3"视场的光源尺度下,虚拟刀口法测得689、693、701 nm欠采样线扩散函数的半高全宽分别为24.2、27.7、30.8μm,以过采样直接测量结果为参考,其测量准确度分别为98.3%,93.9%和88.8%。实验结果表明,探测器成像严重欠采样时,采用光源物面扫描的虚拟刀口法可准确测量光谱仪的成像质量,该方法结合色散系数还可实现光谱仪分辨率的测量,相关研究工作可为天文光谱仪像质的直接测量提供借鉴。

用于三维单颗粒示踪的多焦面双螺旋点扩散函数显微研究

双螺旋点扩散函数(double-helix point spread function,DH-PSF)显微可实现纳米尺度的三维单颗粒示踪(three-dimensional single particle tracking,3D SPT),被广泛应用于生命科学等领域,但DH-PSF显微的成像景深和定位精度有限,限制了其在活体厚样品中的应用.为了解决此问题,本文提出了一种基于轴向分光棱镜的多焦面DH-PSF显微(z-splitter prism-based multifocus DH-PSF microscopy,ZPMDM)方法和系统,通过将基于轴向分光棱镜的多焦面显微与DH-PSF相结合,在无需扫描的情况下提高DH-PSF显微的轴向定位范围和定位精度,解决完整活细胞内3D SPT的大景深探测难题.通过系统标定,ZPMDM中3个通道的平均三维定位精度分别为σ_(L(x,y,z))=(4.4 nm,4.6 nm,10.5 nm),σ_(M(x,y,z))=(4.3 nm,4.2 nm,8.2 nm),以及σ_(R(x,y,z))=(4.8 nm,4.4 nm,10.3 nm),DH-PSF的有效景深扩展至6μm,实现了大景深范围内的甘油-水混合溶液中的荧光微球示踪,并初步研究了活巨噬细胞的吞噬现象,进一步验证了该方法的有效性,对于3D SPT的发展和应用具有重要意义.

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.

考虑点扩散函数效应的光谱遥感图像超分辨率制图

由于硬件设备的限制和土地覆盖类别的多样性,采集得到的光谱遥感图像的空间分辨率有时较为粗糙,导致大量混合像元产生,严重影响了土地覆盖类型空间分布的制图精度。超分辨率制图技术可以有效地处理光谱遥感图像中的混合像元,获得准确的地物类别分布信息。在遥感大数据背景下,来自同一卫星采集同一区域的多位移图像可以作为辅助数据改进超分辨率制图结果。然而,目前多位移图像插值超分辨率制图方法很少有效地考虑点扩散函数效应影响,导致制图结果精度降低。为了解决这一问题,本文提出了一种考虑点扩散函数效应的多位移光谱遥感图像超分辨率制图方法,改善土地覆盖类别制图结果。在所提出的方法中,首先,对多位移图像进行光谱解混,以生成粗糙丰度图像。然后,在考虑点扩散函数效应的情况下,对粗糙丰度图像先采用面到点克里格法,然后进行理想方波滤波,得到改善的粗糙丰度图像。接下来,通过插值对改善的粗糙丰度图像进行上采样以获得上采样丰度图像,并对上采样的所有丰度图像进行整合以获得精细丰度图像。最后,根据精细丰度图像提供的类别比例信息,使用类别分配方法将类别标签分配给亚像元,以获得理想的制图结果。实验结果表明,通过减少点扩散函数效应影响,所提出的方法展示出最佳性能表现,例如在美国华盛顿特区数据集实验结果的总体精度分别达到77.63%和Kappa系数达到0.7263。

基于点扩散函数的图像学高分辨率技术

常规基于一维假设的高分辨率处理技术如反褶积、反Q滤波方法等,针对水平构造或者小倾角构造有较好的处理效果,但在面向高陡构造或者断裂等复杂构造时处理效果不佳。而偏移成像结果可以看作是点扩散函数(PSF)与真实反射系数褶积的结果,高维空间条件下的高分辨率处理技术实际上是此正演问题的一个反问题,即基于成像结果进行反射系数反演。为此,提出了一种基于点扩散函数的高分辨率处理技术,首先基于点扩散函数的计算原理,推导出了基于高频近似条件下的快速求解算法,并在高维空间褶积理论的指导下结合图像学反演算法研发了纯数据驱动的点扩散函数提取技术,最后采用高维空间反褶积算法求得高分辨率成像结果,实现地震频带的有效拓宽和成像分辨率的提升。模型数据和实际数据测试结果表明,该算法可在不损失低频的前提下有效扩宽高频,且具有在计算效率与常规高分辨率算法基本相当的条件下有效提高不同展布方位地质体分辨率的优势。

基于动态规划旅行时场的海森矩阵计算方法及其应用

地震波反演成像是经典偏移成像在最小二乘反演框架下的延伸,其核心在于消除偏移成像系统中海森矩阵的影响,得到更高分辨率的成像结果。海森矩阵规模巨大,对其的高效计算可有力推动地震波反演成像方法的进步。本文首先从一次反射波的偏移和反演成像的对比出发,推导出海森矩阵的表达及其简化形式,通过分析表达式,指出旅行时场是海森矩阵计算的关键问题。接着,提出利用点扩散函数(PSF,Point Spread Function)来近似表达海森矩阵,并引入动态规划旅行时计算,获取了旅行时场表征的PSF,从而实现对一阶海森矩阵的高效表达,并分析计算所得的PSF性态,对比计算效率。最后,基于传统偏移成像结果,利用计算得到的PSF进行了成像校正,对计算得到的近似海森矩阵的有效性进行了测试和应用。数值实验表明,基于动态规划旅行时场可以高效稳定地计算近似海森矩阵。通过对比海森矩阵分辨率校正前后的成像结果,验证了本文发展的高效近似海森矩阵计算方法的有效性和应用潜力。

Analyzing the Effect of the Intra-Pixel Position of Small PSFs for Optimizing the PL of Optical Subpixel Localization

Subpixel localization techniques for estimating the positions of point-like images captured by pixelated image sensors have been widely used in diverse optical measurement fields.With unavoidable imaging noise,there is a precision limit(PL)when estimating the target positions on image sensors,which depends on the detected photon count,noise,point spread function(PSF)radius,and PSF’s intra-pixel position.Previous studies have clearly reported the effects of the first three parameters on the PL but have neglected the intra-pixel position information.Here,we develop a localization PL analysis framework for revealing the effect of the intra-pixel position of small PSFs.To accurately estimate the PL in practical applications,we provide effective PSF(e PSF)modeling approaches and apply the Cramér–Rao lower bound.Based on the characteristics of small PSFs,we first derive simplified equations for finding the best PL and the best intra-pixel region for an arbitrary small PSF;we then verify these equations on real PSFs.Next,we use the typical Gaussian PSF to perform a further analysis and find that the final optimum of the PL is achieved at the pixel boundaries when the Gaussian radius is as small as possible,indicating that the optimum is ultimately limited by light diffraction.Finally,we apply the maximum likelihood method.Its combination with e PSF modeling allows us to successfully reach the PL in experiments,making the above theoretical analysis effective.This work provides a new perspective on combining image sensor position control with PSF engineering to make full use of information theory,thereby paving the way for thoroughly understanding and achieving the final optimum of the PL in optical localization.