Fast and accurate generation method of PSF-based system matrix for PET reconstruction

This work investigates the positional single photon incidence response(P-SPIR) to provide an accurate point spread function(PSF)-contained system matrix and its incorporation within the image reconstruction framework.Based on the Geant4 Application for Emission Tomography(GATE) simulation,P-SPIR theory takes both incidence angle and incidence position of the gamma photon into account during crystal subdivision,instead of only taking the former into account,as in single photon incidence response(SPIR).The response distribution obtained in this fashion was validated using Monte Carlo simulations.In addition,two-block penetration and normalization of the response probability are introduced to improve the accuracy of the PSF.With the incorporation of the PSF,the homogenization model is then analyzed to calculate the spread distribution of each line-of-response(LOR).A primate PET scanner,Eplus-260,developed by the Institute of High Energy Physics,Chinese Academy of Sciences(IHEP),was employed to evaluate the proposed method.The reconstructed images indicate that the P-SPIR method can effectively mitigate the depth-of-interaction(DOI) effect,especially at the peripheral area of field-of-view(FOV).Furthermore,the method can be applied to PET scanners with any other structures and list-mode data format with high flexibility and efficiency.     

Centric scan SPRITE magnetic resonance imaging: optimization of SNR, resolution, and relaxation time mapping

Two strategies for the optimization of centric scan SPRITE (single point ramped imaging with T1 enhancement) magnetic resonance imaging techniques are presented. Point spread functions (PSF) for the centric scan SPRITE methodologies are numerically simulated, and the blurring manifested in a centric scan SPRITE image through PSF convolution is characterized. Optimal choices of imaging parameters and k-space sampling scheme are predicted to obtain maximum signal-to-noise ratio (SNR) while maintaining acceptable image resolution. The point spread function simulation predictions are verified experimentally. The acquisition of multiple FID points following each RF excitation is described and the use of the Chirp z-Transform algorithm for the scaling of field of view (FOV) of the reconstructed images is illustrated. Effective recombination of the rescaled images for SNR improvement and T*2 mapping is demonstrated.     

Application of multi-frame approach in single-frame blind deconvolution

A new single-frame blind deconvolution algorithm for the linear shift-invariant imaging system is presented. The algorithm processes the partial images segmented from one single degraded image by multi-frame approach to recover the point spread function (PSF). Then a deconvolution method is employed to restore the whole image with the recovered PSF. In addition, in order to improve the fidelity and resolution of the recovered PSF, the coprimeness of the partial images is utilized. Results of simulated and real atmospheric turbulence degraded images using the algorithm are reported.     

Estimation of the ocular point spread function by retina modeling

Retinal imaging often suffers from blurring aberrations. With knowledge of the blurring point spread function (PSF), better images can be reconstructed by deconvolution techniques. We demonstrate a method to enhance the contrast of retinal cells by estimating the ocular PSF. This is done by finding the cells' positions and their intensity distributions and using these as a model for the image. The feasibility of this method is demonstrated by Wiener deconvolution both for adaptively and nonadaptively corrected images.     

Phase-encoding strategies for optimal spatial resolution and T1 accuracy in 3D Look-Locker imaging

The Look-Locker (LL) imaging method provides an accurate and efficient approach for mapping the spin-lattice relaxation time, T(1). However, the same recovery of signal during LL image acquisition required to estimate T(1) also results in unwanted modulation of k-space. This is particularly problematic with 3D LL imaging as the number of phase-encoding steps during the recovery interval (e.g., 16) increases in an effort to reduce imaging times. This modulation of k-space has the effect of introducing a point spread function (PSF), which can lead to either image blurring (if the earlier tip angles are assigned to the centre of k-space) or edge enhancement (if the earlier tip angles are assigned to the edges of k-space), thus corrupting T(1) estimation, particularly for small objects. In this study, the PSF and its effect on the acquired images for four different interleaved phase-encode schemes (centric-in, centric-out, sequential and hybrid-sequential) are simulated for a range of T(1), tip angle and 3D LL acquisition parameters expected in practice. It is shown by simulation and confirmed experimentally in phantoms that a hybrid sequential phase-encoding scheme reduces image blurring while maintaining T(1) accuracy ( approximately 2%) and precision (2%) over a range of object sizes down to 2 pixels (2 mm).     

High resolution image reconstruction method for a double-plane PET system with changeable spacing

Breast-dedicated positron emission tomography(PET) imaging techniques have been developed in recent years. Their capacities to detect millimeter-sized breast tumors have been the subject of many studies. Some of them have been confirmed with good results in clinical applications. With regard to biopsy application, a double-plane detector arrangement is practicable, as it offers the convenience of breast immobilization. However, the serious blurring effect of the double-plane PET, with changeable spacing for different breast sizes, should be studied. We investigated a high resolution reconstruction method applicable for a double-plane PET. The distance between the detector planes is changeable. Geometric and blurring components were calculated in real-time for different detector distances, and accurate geometric sensitivity was obtained with a new tube area model. Resolution recovery was achieved by estimating blurring effects derived from simulated single gamma response information. The results showed that the new geometric modeling gave a more finite and smooth sensitivity weight in the double-plane PET.The blurring component yielded contrast recovery levels that could not be reached without blurring modeling, and improved visual recovery of the smallest spheres and better delineation of the structures in the reconstructed images were achieved with the blurring component. Statistical noise had lower variance at the voxel level with blurring modeling at matched resolution, compared to without blurring modeling. In distance-changeable double-plane PET,finite resolution modeling during reconstruction achieved resolution recovery, without noise amplification.     

多波段相关光子光谱分布与时间相关性测量实验研究

基于相关光子的定标技术能够实现“无标准传递”绝对定标,研究相关光子的光谱辐射特性及时间相关特性对遥感器在宽波段的辐射定标具有重要意义。为满足光电探测器在宽谱段量子效率定标需求,基于相关光子的定标技术有必要从单一波段向更多波段扩展。根据自发参量下转换所满足的相位匹配条件,推导出相关光子在晶体内的非共线角计算公式,通过数值模拟相关光子光谱辐射角度分布规律,优化晶体相位匹配角,使得自发参量下转换产生的相关光子具有宽光谱分布,并且相关光子辐射角度与光谱波长能够一一对应。根据光谱分布数值模拟结果,建立了多波段相关光子的光谱分布和时间相关性测量实验系统,利用该系统测量了四对相关光子的光谱分布、符合计数、相关时间以及偏振特性。其中,测量的光谱分布范围为633~808 nm,最大光谱分布测量偏差为1.51 mm,光谱分布实验测量结果与数值模拟结果符合一致;测量了四对相关光子对的相关时间,最小相关时间为0.32 ns,并在实验中观察到了“符合三峰”现象;相关光子单光子计数及符合计数与泵浦光的偏振方向呈正弦函数关系。实验研究表明,相关光子对具有可见光~近红外宽波段分布、时间相关及偏振特性。论文研究结果在国内外尚属首次报道,该研究结果有望应用于光电探测器在多波段的辐射定标。     

X光能点、放大倍率及针孔尺寸对空间分辨的影响

X光针孔成像是惯性约束聚变(ICF)研究中重要的诊断方法,对其点扩散函数的计算可用于图像重建和系统空间分辨的判断。对菲涅耳衍射公式进行了化简,分析了X光能点、针孔尺寸及放大倍率对针孔点扩散函数的影响。实验在保证成像能获得足够高信噪比的条件下,通过模拟获得在最佳空间分辨时所要的针孔大小、放大倍率和X光能点等参数。在流体力学不稳定性的静态样品定标实验中,通过模拟获得了针孔的调制传递函数(MTF),结合实验测量的结果反推获得分幅相机本身的MTF值。同时采用测刀边函数的方法获得了分幅相机本身的刀边函数,进而得到相机在各空间频率下的MTF值。两种方法得到的分幅相机MTF值一致,验证了通过菲涅耳衍射模拟X光针孔成像的可行性。     

定量中子数字成像散射校正的蒙特卡罗模拟

 中子数字成像过程中,散射中子可降低像质致使提取样品的定量信息变得困难。针对该情况,分析了中子微光成像系统图像散射降质的原理,采用点扩展函数的叠加来表征散射中子引起图像降质的过程,借助于蒙特卡罗方法（MC）对点扩展函数进行模拟和建模,将点扩展函数描述为样品厚度以及样品到探测器距离为参量的解析函数,研究了点扩展函数的计算方法。研究结果表明,借助于MC方法构建系统的点扩展函数之解析函数,并利用该函数对中子图像进行散射校正,是一种行之有效的定量中子数字成像散射校正方法。     

基于Gate与Matlab的PET电子学仿真系统研究

正电子发射断层成像PET （Positron Emission Tomography）是一套庞大、复杂而又极其精密的大型医疗设备,由成千上万个探测单元及相应的信号采集通道组成,其复杂的采集逻辑直接导致系统前期研发迭代次数多、硬件调试困难,且时间与资金成本投入高。本文通过研究PET系统整体结构及前端电子采集模块的功能,设计出基于Gate仿真软件（Geant4 application for tomographic emission）和MATLAB （matrixlaboratory,Mathworks Inc.）数据处理包的PET电子学仿真架构,利用数字化单事件重建DiSER （digitalsingle-event-reconstruction）模型将Gate仿真得到的湮灭事件的能量、时间信息进行综合,转换为光子脉冲信号并由模数转换器ADC （analog-to-digital converter）进行量化,量化数据输入到现场可编程门阵列FPGA （field programmable gate array）和MATLAB协仿真模块中,验证FPGA硬件采集算法的可行性。待各模块的湮灭事件采集完毕,将多模块数据进一步综合输入到FPGA符合处理模块中,完成PET系统符合单元的功能验证。最后,将设计的算法在基于飞行时间技术的TOF （time-of flight）-PET样机上进行了测试,验证了设计的有效性和正确性。该系统仿真平台可应用于PET系统整个研发周期,其搭建思路也可灵活、有效地拓展到其他领域的系统建模与验证之中。     

中子针孔成像点扩展函数模拟研究

应用Geant4系统对中子针孔成像的点扩展函数进行了模拟研究.建立了点扩展函数的数学模型,并将其分布图像与能量沉积数据的分布图像作了比较,可看出点扩展函数与能量沉积数据吻合得较好.研究结果表明,在一定偏移量范围内,拟合得到的点扩展函数更好,能得到较好的图像分辨率.通过对不同入射能量在一定偏移量入射下的点扩展函数讨论认为,入射能量增大虽然会增强图像的对比度,但会降低分辨率.     

Single frame blind image deconvolution by non-negative sparse matrix factorization

Novel approach to single frame multichannel blind image deconvolution has been formulated recently as non-negative matrix factorization problem with sparseness constraints imposed on the unknown mixing vector that accounts for the case of non-sparse source image. Unlike most of the blind image deconvolution algorithms, the novel approach assumed no a priori knowledge about the blurring kernel and original image. Our contributions in this paper are: (i) we have formulated generalized non-negative matrix factorization approach to blind image deconvolution with sparseness constraints imposed on either unknown mixing vector or unknown source image; (ii) the criteria are established to distinguish whether unknown source image was sparse or not as well as to estimate appropriate sparseness constraint from degraded image itself, thus making the proposed approach completely unsupervised; (iii) an extensive experimental performance evaluation of the non-negative matrix factorization algorithm is presented on the images degraded by the blur caused by the photon sieve, out-of-focus blur with sparse and non-sparse images and blur caused by atmospheric turbulence. The algorithm is compared with the state-of-the-art single frame blind image deconvolution algorithms such as blind Richardson-Lucy algorithm and single frame multichannel independent component analysis based algorithm and non-blind image restoration algorithms such as multiplicative algebraic restoration technique and Van-Cittert algorithms. It has been experimentally demonstrated that proposed algorithm outperforms mentioned non-blind and blind image deconvolution methods.     

Random phase mask in a filamentation regime: application to the localization of point sources

We present a optical system with an extended point-spread function (PSF) for the localization of point sources in the visible and IR spectral ranges with a subpixel precision. This compact system involves a random phase mask (RPM) as its unique component. It exhibits original properties, because this RPM is used in a particular regime, called the "filamentation regime," before the speckle region. The localization is performed by calculating the phase correlation between the PSF and the image obtained under off-axis illumination. Numerical simulations are presented to assess the basic optical properties of this RPM in the filamentation regime.     

谱域光学相干层析系统中基于解卷积方法的像质优化

谱域光学相干层析（spectral domain optical coherence tomography, 简记为SD-OCT）系统的轴向点扩散函数（point spread function, 简记为PSF）并不具备空不变特性,无法直接应用于解卷积运算.为实现SD-OCT系统成像质量基于解卷积算法的优化,本文采用数值校正后的轴向扫描信号和轴向有效PSF来实施基于Lucy-Richardson算法的解卷积运算,进而实现了SD-OCT系统中图像质量尤其是轴向分辨率的改善.本文理论分析了SD-OCT系统中导致轴向有效PSF随成像深度增大而下降和图像模糊的因素,阐述了利用解卷积算法实现图像质量优化的过程,基于建立的SD-OCT系统实施了不同成像深度位置处PSF的标定,并利用离散轴向位置处PSF的峰值拟合了轴向有效PSF的调制函数.利用调制函数对所有轴向扫描信号进行数值校正,然后根据轴向有效PSF进行解卷积算法.典型样品的解卷积图像重建结果表明,提出的解卷积方法能有效提高系统的轴向分辨率,同时有效抑制系统灵敏度随成像深度增大而下降的趋势. 关键词： 谱域光学相干层析 Lucy-Richardson解卷积 有效点扩散函数     

谱域光学相干层析系统中基于解卷积方法的像质优化

谱域光学相干层析（spectral domain optical coherence tomography, 简记为SD-OCT）系统的轴向点扩散函数（point spread function, 简记为PSF）并不具备空不变特性,无法直接应用于解卷积运算.为实现SD-OCT系统成像质量基于解卷积算法的优化,本文采用数值校正后的轴向扫描信号和轴向有效PSF来实施基于Lucy-Richardson算法的解卷积运算,进而实现了SD-OCT系统中图像质量尤其是轴向分辨率的改善.本文理论分析了SD-OCT系统中导致轴向有效PSF随成像深度增大而下降和图像模糊的因素,阐述了利用解卷积算法实现图像质量优化的过程,基于建立的SD-OCT系统实施了不同成像深度位置处PSF的标定,并利用离散轴向位置处PSF的峰值拟合了轴向有效PSF的调制函数.利用调制函数对所有轴向扫描信号进行数值校正,然后根据轴向有效PSF进行解卷积算法.典型样品的解卷积图像重建结果表明,提出的解卷积方法能有效提高系统的轴向分辨率,同时有效抑制系统灵敏度随成像深度增大而下降的趋势.     

纠缠光子法绝对定标光电探测器量子效率的研究

为了应对国际上“坎德拉”新定义的动向,开展了利用纠缠光子法测量光电探测器量子效率的研究,并建立了测量装置。装置采用351.1 nm连续激光抽运BBO晶体产生纠缠光子场,然后通过双通道门控计数器组成的符合测量系统在702.2 nm和788.7 nm两个波长点对光电倍增管的量子效率进行了测量。同时对单光子脉冲信号获取、噪声抑制及提取、符合时间特性、偶然符合、暗背景计数和器件透过率等影响测量结果的关键因素进行了实验分析并给出了修正分量,最终在两个波长点量子效率测量不确定度小于0.7%。     

Image restoration of skin scattering and optical blurring for finger vein recognition

Finger vein recognition has been adopted due to its high recognition rate and the invisibility of vein in visible light. However, because a finger vein pattern is not distinctive due to light scattering in the skin layer, the localization of a finger vein pattern region using an image processing algorithm is a difficult procedure. Also, optical blurring increases these difficulties. We propose a new finger vein image restoration method to deal with skin scattering and optical blurring. Our research is novel in three ways compared to previous studies. Firstly, the amount of optical blurring of a finger vein image is measured based on the average gradient of the orthogonal profile of a finger edge. Secondly, the accurate point spread function (PSF) of optical blurring is adaptively determined based on the orthogonal profile of a finger edge. Thirdly, using a constrained least square (CLS) filter and optimized parameters in terms of the lowest error of finger vein recognition, the restoration of a skin scattered and optically blurred finger vein pattern was performed. Experimental results show that the equal error rate (EER) of finger vein recognition with restoration was reduced by as much as 3.14% (5.05-1.91%) compared to the EER without restoration.     

An improved image deconvolution approach using local constraint

Conventional deblurring approaches such as the Richardson–Lucy (RL) algorithm will introduce strong noise and ringing artifacts, though the point spread function (PSF) is known. Since it is difficult to estimate an accurate PSF in real imaging system, the results of those algorithms will be worse. A spatial weight matrix (SWM) is adopted as local constraint, which is incorporated into image statistical prior to improve the RL approach. Experiments show that our approach can make a good balance between preserving image details and suppressing ringing artifacts and noise.     

编码孔径成像系统中的点扩散函数

在X光编码孔径成像系统中，系统的点扩散函数决定成像系统的成像质量。由于系统的点扩散函数可用来求解系统的传递函数，并可由此制作实现图像重构的滤波器，因此点扩散函数的精确程度直接影响重构过程中图像的质量。本文以标量衍射理论为基础，从理论上推导出了衍射效应条件下编码孔径中圆环的点扩散函数，并将它用于制作光学系统的滤波器。最后利用Wiener滤波函数对编码重叠像的频谱分布进行滤波处理，再经过逆傅里叶变换得到了重构图像。     

Imaging resolution analysis in limited-view Laser Radar reflective tomography

In many applications of Laser radar reflective tomography, anisotropic resolution of images reconstructed from an incomplete set of reflective projections will degrade imaging quality. In this paper, we present the theoretical point spread function (PSF) of imaging system over full views for reflective tomography. The corresponding imaging resolution of the PSF was determined by Rayleigh's criterion, here the most common algorithm of filtered backprojection was used for image reconstruction. The theoretical imaging resolution was derived approximately from the range resolution resolved by the laser pulse. The simulated horizontal imaging resolutions of an ideal diffused single point target in different limited-views were compared with the theoretical value. Experimental reconstructed images from limit-view projections of letter “E” illustrated the effects of anisotropic resolution.