Iterative autofocusing strategy for axial distance error correction in ptychography

The axial distance error can degrade the quality and resolution of the image reconstructed by ptychography. An iterative autofocusing method is proposed to correct the axial distance error. Based on the Fresnel integral theory, an axial distance error model is established to present the effect of the axial distance error on the recovered image. The information of the retrieved image is chosen to calculate the axial distance by autofocusing algorithm. The calculated distance is used to replace the axial distance and applied for the image reconstruction. When the calculated axial distance reaches the convergence, the distance can be accurately obtained that can be used to enhance the quality and resolution of the reconstructed image. Simulations and experiments have been conducted to verify the performance of the proposed method.     

Compressed sensing with linear-in-wavenumber sampling in spectral-domain optical coherence tomography

We propose a novel method called compressed sensing with linear-in-wavenumber sampling (k-linear CS) to retrieve an image for spectral-domain optical coherence tomography (SD-OCT). An array of points that is evenly spaced in wavenumber domain is sampled from an original interferogram by a preset k-linear mask. Then the compressed sensing based on l1 norm minimization is applied on these points to reconstruct an A-scan data. To get an OCT image, this method uses less than 20% of the total data as required in the typical process and gets rid of the spectral calibration with numerical interpolation in traditional CS-OCT. Therefore k-linear CS is favorable for high speed imaging. It is demonstrated that the k-linear CS has the same axial resolution performance with ～30 dB higher signal-to-noise ratio (SNR) as compared with the numerical interpolation. Imaging of bio-tissue by SD-OCT with k-linear CS is also demonstrated.     

等离子体图像诊断中带吸收校正的轴对称重建

在轴对称等离子体的图像诊断中,根据等离子体在某个方向的X射线强度图像可以重建出辐射系数的空间分布.由于X射线在等离子体的传播过程中存在一定的吸收,需要在重建过程中考虑吸收校正.本文在滤波反投影法(FBP)的基础上,结合X射线在等离子体中的吸收规律,提出了带吸收校正的FBP迭代算法.通过对钠等离子体辐射系数的轴对称重建模拟,发现该算法重建精度高,收敛性好,取得了很好的重建结果.     

基于图像信息熵的ptychography轴向距离误差校正

在轴向距离参与运算的ptychography算法中,轴向距离误差会使重建图像变模糊并降低图像的分辨率.本文基于菲涅耳衍射理论建立了轴向距离误差模型,根据不同轴向距离误差对重构图像清晰度的影响,提出用图像信息熵确定图像最清晰时的轴向距离,并重建出清晰的ptychography图像.比较了图像能量变化、Tamura系数和图像信息熵这三种图像清晰度评价函数在轴向距离误差校正过程中的分布情况,发现它们均具有单峰性,且峰值确定的轴向距离相同.图像信息熵相比其他两种图像清晰度评价函数具有更高的灵敏性.仿真以及实验均证明了基于图像信息熵的ptychography轴向误差校正的可行性.     

Sparsity-constrained SENSE reconstruction: An efficient implementation using a fast composite splitting algorithm

Parallel imaging and compressed sensing have been arguably the most successful and widely used techniques for fast magnetic resonance imaging (MRI). Recent studies have shown that the combination of these two techniques is useful for solving the inverse problem of recovering the image from highly under-sampled k-space data. In sparsity-enforced sensitivity encoding (SENSE) reconstruction, the optimization problem involves data fidelity (L2-norm) constraint and a number of L1-norm regularization terms (i.e. total variation or TV, and L1 norm). This makes the optimization problem difficult to solve due to the non-smooth nature of the regularization terms. In this paper, to effectively solve the sparsity-regularized SENSE reconstruction, we utilize a new optimization method, called fast composite splitting algorithm (FCSA), which was developed for compressed sensing MRI. By using a combination of variable splitting and operator splitting techniques, the FCSA algorithm decouples the large optimization problem into TV and L1 sub-problems, which are then, solved efficiently using existing fast methods. The operator splitting separates the smooth terms from the non-smooth terms, so that both terms are treated in an efficient manner. The final solution to the SENSE reconstruction is obtained by weighted solutions to the sub-problems through an iterative optimization procedure. The FCSA-based parallel MRI technique is tested on MR brain image reconstructions at various acceleration rates and with different sampling trajectories. The results indicate that, for sparsity-regularized SENSE reconstruction, the FCSA-based method is capable of achieving significant improvements in reconstruction accuracy when compared with the state-of-the-art reconstruction method.     

基于物理总能量目标函数的稀疏重建模型

欠采样条件下的稀疏重建模型往往直接取稀疏约束项或保真项作为求解的目标函数, 却从未阐述其中的物理演化规律. 针对此问题, 从物理运动的角度出发, 提出了一种基于物理总能量目标函数的稀疏重建模型. 首先, 建立了微粒在黏性介质中的运动模型, 模型中粒子的重力势能函数为松弛变换后的l₂-l₁ 范数; 其次, 基于该微粒的物理总能量建立了新的稀疏重建模型, 该重建模型在保留l₂-l₁ 模型稀疏约束和保真项的基础上, 增加了对相邻两次迭代结果偏差的约束, 避免因该偏差过大引起的震荡; 第三, 提出了针对该模型的梯度投影算法, 并证明了算法的收敛性, 算法在新模型目标函数下的梯度方向总是包含上一步迭代的物理惯性, 从而达到加速收敛和避免局部最优解的目的; 最后, 将该模型应用于标准灰度图像的稀疏重建以及精密电子组装中微焦点X射线缺陷检测. 实验结果表明, 该算法不仅保证了图像的重建质量, 收敛速度还得到了大幅提升. 在精密电子组装内部缺陷检测应用中, 该算法在微焦点X射线图像的边缘细节保留方面有明显的优势, 可更准确地识别缺陷, 满足工业应用快速性和准确性要求.     

用重谱检测天文迭代位移叠加法的收敛过程

在天文像复原“迭代位移叠加法”中，判定其迭代过程发展的方向和收敛结果是否正确是关键问题。根据斑点掩模法中目标重谱与目标像间的相互对应的性质，用目标重谱作为检验迭代结果的标准函数。用最小二乘法鉴别迭代过程的发展方向和收敛结果，因而可避免迭代过程的盲目性，并将得到正确复原像。     

Tikhonov-regularization-based projecting sparsity pursuit method for fluorescence molecular tomography reconstruction

For fluorescence molecular tomography(FMT),image quality could be improved by incorporating a sparsity constraint.The L1 norm regularization method has been proven better than the L2 norm,like Tikhonov regularization.However,the Tikhonov method was found capable of achieving a similar quality at a high iteration cost by adopting a zeroing strategy.By studying the reason,a Tikhonov-regularization-based projecting sparsity pursuit method was proposed that reduces the iterations significantly and achieves good image quality.It was proved in phantom experiments through time-domain FMT that the method could obtain higher accuracy and less oversparsity and is more applicable for heterogeneous-target reconstruction,compared with several regularization methods implemented in this Letter.     

An algorithm for computed tomography image reconstruction from limited-view projections

<正>With the development of the compressive sensing theory,the image reconstruction from the projections viewed in limited angles is one of the hot problems in the research of computed tomography technology.This paper develops an iterative algorithm for image reconstruction,which can fit most cases.This method gives an image reconstruction flow with the difference image vector,which is based on the concept that the difference image vector between the reconstructed and the reference image is sparse enough.Then the l_2-norm minimization method is used to reconstruct the difference vector to recover the image for flat subjects in limited angles.The algorithm has been tested with a thin planar phantom and a real object in limited-view projection data.Moreover,all the studies showed the satisfactory results in accuracy at a rather high reconstruction speed.     

基于声透镜的三维光声成像技术

基于声透镜的光声成像系统中, 由样品的光声压分布等效样品的吸收分布, 进行光声像重建, 但之前的这种等效是一种近似, 理论上并不准确. 本文阐述了声透镜三维光声成像的基本原理, 揭示了声透镜像面上光声压信号的时间分布与样品轴向吸收分布之间的关系; 提出用积分法和希尔伯特变换提取光声信号瞬时值法, 解调样品吸收系数分布并重建光声像; 实验上, 对不同样品分别用积分法和希尔伯特变换法获取样品的吸收系数, 重建光声像的横向和轴向分辨率均约为1 mm, 实现了真正的三维快速光声成像.     

系统中基于快速扫描光学延迟线的色散补偿

分析了光学相干层析成像(Optical Coherence Temography,OCT)系统中色散失配对系统纵向分辨率的影响,详细阐述了快速扫描光学延迟线(Rapid Scanning Optical Delay Line,RSOD)的色散性质,提出并采用基于RSOD的色散补偿方法,实验验证了这种色散补偿方法能够实现OCT系统的纵向分辨率接近于理论值,并因此得到了高质量的OCT图像.     

迭代重加权时域平面波叠加法的非稳态声场重建

提出了迭代重加权时域平面波叠加法,并应用于非稳态声场重建。该方法首先通过时域离散卷积得到全息面时域声压与虚源面时域波数谱离散状态公式;然后根据稀疏表示和迭代重加权,得到残差范数与加权解范数最小化问题表达式;最后将每一对波数下虚源面时域波数谱与时域传播核卷积叠加得到重建面上的时域声压。为了验证该方法的有效性,给出了激励板声源的仿真验证,并在半消声室内进行了实验验证。讨论了一些参数对该方法的影响,并通过与基于Tikhonov正则化的时域平面波叠加法比较,突出该方法的重建优势。仿真和实验结果表明,该方法对非稳态声场重建具有很好的效果,并且重建精度高。     

利用积分方程法的各向异性地层频率测深三维模拟

应用一种新的积分方程算法对各向异性地层频率域电磁测深三维问题进行正演模拟.利用范数小于或等于1的修正Green算子得到各向异性地层中的新积分方程,由于满足压缩映射条件,该积分方程在任意参数条件下总是迭代收敛的.提出一种应用迭代法求解新积分方程的迭代初值优化选择方法,并通过具体算例对比说明该方法可使频率域电磁测深三维模拟的计算效率得到有效提高.最后应用所述算法对层状各向异性大地轴向频率测深视电阻率响应进行三维数值模拟,考察分析地层的各向异性对视电阻率响应特征的影响,得到一些重要结论.     

An iterative method based on 1D subspace for projective reconstruction

Heyden et al. introduced an iterative factorization method for projective reconstruction from image sequences. In their formulation, the projective structure and motion are computed by using an iterative factorization based on 4D subspace. In this paper, the problem is reformulated based on fact that the x, y, and z coordinates of each feature in projective space are known from their projection. The projective reconstruction, i.e., the relative depths w and the 3D motion, is obtained by a simple iterative factorization based on 1D subspace. This allows the use of very fast algorithms even when using a large number of features and large number of frames. The experiments with both simulate and real data show that the method presented in the paper is efficient and has good convergency.     

单幅同轴全息图两步迭代收缩重建

利用压缩传感理论中的两步迭代收缩重建算法,开展单幅同轴全息图重建实验研究,实现单幅同轴全息图共轭重建像的消除并克服数字全息技术在轴向聚焦平面识别能力的不足。以数字图像和标准分辨率板为记录物体,比较分析了基于两步迭代收缩算法和菲涅尔近似衍射重建算法的重建质量;以两根裸光纤为实验样本,分析了两步迭代收缩重建算法对记录物体轴向不同焦平面的识别能力。实验结果表明两步迭代收缩重建算法可得到清晰度高于68.73%的重建信息,同时对直径为125 m的两根光纤在9 mm的轴向间距条件下,显示出了比全息菲涅尔近似算法更好的聚焦平面识别能力。这一轴向聚焦识别能力有助于数字全息技术应用于功能材料梯度参数或功能涂层光学器件涂层厚度检测。     

阵列式康普顿相机GEANT4模拟与图像重建及优化

出于对放射性核素各种应用和安全的考虑,需要性能良好的康普顿相机。通过蒙特卡罗方法模拟了双层阵列式康普顿相机,散射探测器材料为Si,吸收探测器材料为CZT（碲锌镉）。利用反投影图像重建算法进行了图像重建,采用极大似然法对重建结果进行优化,有效地提高了重建图像的分辨率。当放射源与探测器距离100 mm时,经过10次极大似然法迭代计算,位置分辨率与角分辨率分别达到5.1 mm与7.3。检验了极大似然法对于康普顿相机放射源图像重建的优化作用。     

Fast Estimation of Scatter Components Using the Ordered Subset Expectation Maximization Algorithm for Scatter Compensation

In this work we propose a method for scatter compensation in single photon emission computed tomography imaging, by which we can estimate the scatter components in projections in high speed with good accuracy. The method is that we first estimate the scatter components in projections based on scatter response kernels by one time of ordered subsets expectation maximization iterative reconstruction, and then subtract the estimated scatter components from the projections and complete reconstruction by filtered back-projection method. The principle is that the image corresponding to the scatter components in projections consists largely of low-frequency components of an activity distribution; these low-frequency components will converge faster than the high ones in iterative reconstruction. Therefore, we can estimate the low-frequency component image before the image converges with the high-frequency ones, and obtain the scatter components by re-projecting the low-frequency component image with scatter response kernels. The effects of the proposed method were compared with the dual- and triple-energy window methods using experimental measurements. The results show that good accuracy in estimated scatter components, good uniformity of scatter compensation at the center and the side of an object, and good noise property can be acquired by this method.     

天文斑点成像技术中的噪声影响分析

为进一步说明天文像复原新方法-迭代位移叠加法的性质，对探测器的附加噪声在斑点干涉术、斑点掩模法和迭代位移叠加法中的影响分别进行了分析。结果表明：在斑点掩模法中，复杂的噪声高阶矩统计被引入了重谱的噪声偏差，因此对噪声极为敏感，使数据处理更加复杂化；与斑点掩模法相比，迭代位移叠加法仅涉及对噪声的一阶矩统计平均，所以此新方法的特点是对噪声不敏感，具有图像复原处理过程简单快捷的优越性。     

Birefringence imaging of human skin by polarization-sensitive spectral interferometric optical coherence tomography

We have developed a spectral interferometric optical coherence tomography (OCT) system with polarization sensitivity that is able to measure a two-dimensional tomographic image by means of one-dimensional mechanical scanning. Our system, which has an axial resolution of 32 mum , calculates the distribution of each element of the Müller matrix of a measured object from 16 OCT images. The OCT system successfully reveals the birefringent nature of human skin tissue.     

Smoothly Clipped Absolute Deviation (SCAD) regularization for compressed sensing MRI Using an augmented Lagrangian scheme

PurposeCompressed sensing (CS) provides a promising framework for MR image reconstruction from highly undersampled data, thus reducing data acquisition time. In this context, sparsity-promoting regularization techniques exploit the prior knowledge that MR images are sparse or compressible in a given transform domain. In this work, a new regularization technique was introduced by iterative linearization of the non-convex smoothly clipped absolute deviation (SCAD) norm with the aim of reducing the sampling rate even lower than it is required by the conventional l₁ norm while approaching an l₀ norm.Materials and MethodsThe CS-MR image reconstruction was formulated as an equality-constrained optimization problem using a variable splitting technique and solved using an augmented Lagrangian (AL) method developed to accelerate the optimization of constrained problems. The performance of the resulting SCAD-based algorithm was evaluated for discrete gradients and wavelet sparsifying transforms and compared with its l₁-based counterpart using phantom and clinical studies. The k-spaces of the datasets were retrospectively undersampled using different sampling trajectories. In the AL framework, the CS-MRI problem was decomposed into two simpler sub-problems, wherein the linearization of the SCAD norm resulted in an adaptively weighted soft thresholding rule with a sparsity enhancing effect.ResultsIt was demonstrated that the proposed regularization technique adaptively assigns lower weights on the thresholding of gradient fields and wavelet coefficients, and as such, is more efficient in reducing aliasing artifacts arising from k-space undersampling, when compared to its l₁-based counterpart.ConclusionThe SCAD regularization improves the performance of l₁-based regularization technique, especially at reduced sampling rates, and thus might be a good candidate for some applications in CS-MRI.