Image reconstruction in fluorescence molecular tomography involves seeking stable and meaningful solutions via the inversion of a highly under-determined and severely ill-posed linear mapping. An attractive scheme consists of minimizing a convex objective function that includes a quadratic error term added to a convex and nonsmooth sparsity-promoting regularizer. Choosing l₁-norm as a particular case of a vast class of nonsmooth convex regularizers, our paper proposes a low per-iteration complexity gradient-based first-order optimization algorithm for the l₁-regularized least squares inverse problem of image reconstruction. Our algorithm relies on a combination of two ideas applied to the nonsmooth convex objective function: Moreau–Yosida regularization and inertial dynamics-based acceleration. We also incorporate into our algorithm a gradient-based adaptive restart strategy to further enhance the practical performance. Extensive numerical experiments illustrate that in several representative test cases (covering different depths of small fluorescent inclusions, different noise levels and different separation distances between small fluorescent inclusions), our algorithm can significantly outperform three state-of-the-art algorithms in terms of CPU time taken by reconstruction, despite almost the same reconstructed images produced by each of the four algorithms.

将频域变密度减采样应用于无放大同轴全息图的压缩传感层析重建当中，旨在于从无放大同轴全息图的频域中提取少量信息，实现全息图频域少量数据的压缩传感层析重建。首先，理论介绍了三种变密度减采样法与全息图压缩传感重建相结合的原理，三种变密度减采样分别是射线分布、螺旋线分布以及指数分布变密度减采样；其次，分别开展了仿真实验和测试实验，分析了与压缩全息相结合的三种变密度减采样方法的重建质量。由实验可知：(1) 能够通过三种变密度减采样实现全息图频域少量数据的提取；(2) 随着采样率的增大，变密度减采样获得的全息图频域少量数据的压缩传感层析重建质量不断提高；(3) 在采样率小于50%的情况下，指数分布减采样具有比另外两种减采样方法获得更高的重建质量(例如低采样率15%，指数分布减采样比另外两种方法的效果更为明显)；(4)在采样率大于50%的情况下，三种减采样模式所获得数据的层析重建质量较高且基本相一致。

针对截断奇异值分解方法进行动态光散射反演存在的颗粒粒度信息丢失问题, 本文在分析自相关函数不同衰减时段粒度信息分布差异的基础上, 提出利用每一角度核矩阵与对应角度下粒度信息在自相关函数不同延迟时刻的分布构建扩展矩阵的扩展截断奇异值分解方法.该方法通过用自相关函数中每一延迟时刻的粒度信息, 调节同一时刻原核矩阵数据对信噪比的贡献, 进而保留了更多的有效奇异值, 减少了由于奇异值截断引起的信息丢失, 在保证抗噪性的基础上, 提高了自相关函数的信息利用率.在1×10－3噪声水平下, 对一组单峰宽分布(260 nm)和三组双峰颗粒分布(250/750 nm)、(270/800 nm)以及(306/974 nm)的模拟动态光散射数据, 进行了单角度、3角度和6角度反演.结果表明, 与截断奇异值分解方法相比, 采用扩展截断奇异值分解方法反演得到的峰值粒度误差和分布误差均明显减小.对306/974 nm颗粒体系的6角度实测数据的反演表明, 采用扩展截断奇异值分解法得到的颗粒峰值粒度误差由非扩展方法的0.032/0.016降至0.029/0.006, 且得到的峰值比更接近真实值.

Fluorescence molecular tomography (FMT) allows the detection and quantification of various biological processes in small animals in vivo, which expands the horizons of pre-clinical research and drug development. Efficient three-dimensional (3D) reconstruction algorithm is the key to accurate localization and quantification of fluorescent target in FMT. In this paper, 3D reconstruction of FMT is regarded as a sparse signal recovery problem and the compressive sampling matching pursuit (CoSaMP) algorithm is adopted to obtain greedy recovery of fluorescent signals. Moreover, to reduce the modeling error, the simplified spherical harmonics approximation to the radiative transfer equation (RTE), more specifically SP₃, is utilized to describe light propagation in biological tissues. The performance of the proposed reconstruction method is thoroughly evaluated by simulations on a 3D digital mouse model by comparing it with three representative greedy methods including orthogonal matching pursuit (OMP), stagewise OMP (StOMP), and regularized OMP (ROMP). The CoSaMP combined with SP₃ shows an improvement in reconstruction accuracy and exhibits distinct advantages over the comparative algorithms in multiple targets resolving. Stability analysis suggests that CoSaMP is robust to noise and performs stably with reduction of measurements. The feasibility and reconstruction accuracy of the proposed method are further validated by phantom experimental data.

采用两种常用的粒度反演方法——正则化和Chahine算法, 对90 nm与250 nm单峰分布、50 nm与200 nm双峰分布、100 nm与300 nm双峰分布的模拟动态光散射数据, 以及105 nm、300 nm标准颗粒的实测动态光散射数据进行了反演分析.结果表明: 噪声水平的高低是影响粒度分布反演准确性的关键因素之一, 反演结果的准确性随噪声水平的增加而降低, 噪声水平超过某一阈值后, 将无法得到有意义的反演结果; 不同反演方法具有不同的抗噪能力, 在低噪声水平下反演结果无显著差别, 随着噪声水平的增加, 反演结果表现出很大差异; 正则化方法通过正则参数的选择可以有效抑制噪声影响, 表现出强于Chahine算法的抗噪能力; 与Chahine算法相比, 正则化方法不需要假定初始分布, 因此, 在噪声较大的实验或生产过程中进行颗粒分布测量时, 宜采用正则化方法.

在动态光散射颗粒测量时, 为了从含噪的自相关函数数据中准确地反演出颗粒粒度分布, 对Tikhonov正则化算法进行改进, 将噪声作为一个独立的未知变量应用到正则化方程中进行粒度反演.在计算过程中, 相应增加方程中各系数矩阵的行数和列数, 对求解的粒度分布数值则仍取其原来方程的行数和列数, 从而达到对部分噪声的剔除作用.不同噪声水平下的颗粒粒度反演结果表明, 改进后的算法能够显著提高低信噪比动态光散射数据粒度反演结果的准确性, 适用于宽分布较大粒径的颗粒粒度反演.

自干涉非相干数字全息可记录和再现非相干光源照明下物光场信息。但基于目前理论的重建算法对待测光场的不同纵向深度层面进行聚焦重构时，聚焦面信息会受到离焦层面光场信息的干扰。基于压缩感知理论，根据自干涉非相干数字全息的光学记录与再现过程，建立与该物理过程相适应的传感矩阵，从理论上构建实现光场分层重构的数值重建算法框架。基于自干涉非相干数字全息光路，以多个不同纵向深度的LED 点光源构建物光场，分别进行计算机数值模拟及实验研究，并且深入讨论光场层面再现距离与各实验参数之间的关系，指出增大各光场层面再现距离间差距的方法。理论及实验研究结果表明该方法可重构不同纵向深度层面的三维物光场，并有效抑制离焦层面光场信息的干扰。

We successfully extend the standard Fibonacci zone plates with two on-axis foci to the generalized Fibonacci photon sieves (GFiPS) with multiple on-axis foci. We also propose the direct and inverse design methods based on the characteristic roots of the recursion relation of the generalized Fibonacci sequences. By switching the transparent and opaque zones, according to the generalized Fibonacci sequences, we not only realize adjustable multifocal distances but also fulfill the adjustable compression ratio of focal spots in different directions.