基于支撑先验与深度图像先验的无预训练磁共振图像重建方法

基于深度学习的磁共振成像(magnetic resonance imaging, MRI)方法需要大规模、高质量的病患数据样本集进行预训练.然而,由于病患隐私及设备等因素限制,获取大规模、高质量的磁共振数据集在实际临床应用中面临挑战.本文提出一种新的基于深度学习的欠采样磁共振图像重建方法,该方法无需预训练、不依赖训练数据集,而是充分利用待重建的目标MR图像的结构先验和支撑先验,并将其引入深度图像先验(deep image prior, DIP)框架,从而削减对训练数据集的依赖,提升学习效率.基于参考图像与目标图像的相似性,采用高分辨率参考图像作为深度网络输入,将结构先验信息引入网络;将参考图像在小波域中幅值大的系数索引集作为目标图像的已知支撑集,构造正则化约束项,将网络训练转化为网络参数的最优化求解过程.实验结果表明,本文方法可由欠采样k空间数据重建得到更精确的磁共振图像,且在保留组织特征、细节纹理方面具有明显优势.     

基于赋权连接图的增量式运动恢复结构算法北大核心CSCD

运动恢复结构算法(structure from motion, SfM)是一种通过计算图像匹配关系,恢复出相机位姿和目标三维结构的重建算法。提出一种基于赋权视角连接图的增量式运动恢复结构算法。首先建立基于图像对立体匹配质量的赋权连接图,量化了图像两两之间的匹配关系;其次在赋权连接图中边的权重的基础上,搜索度数感知的最佳初始种子对;最后根据已重建顶点的连通性构建下一张最佳图像候选集,设计了基于顶点度数与特征点分布的下一张最佳图像评价算法。在公开数据集上实验结果显示,本文算法在重建质量、相机校准率和点云生成数量的表现优于现有先进的运动恢复结构算法,相比基准对比算法,本文算法在不同数据集上平均重建耗时至少降低了19%,点云生成速率至少提升了21%。     

A Projection Proximal-Point Algorithm for ℓ1 Minimization

The problem of the minimization of least squares functionals with ?¹ penalties is considered in an infinite dimensional Hilbert space setting. Though there are several algorithms available in the finite dimensional setting there are only a few of them that come with a proper convergence analysis in the infinite dimensional setting.

In this work we provide an algorithm from a class that has not been considered for ?¹ minimization before, namely, a proximal-point method in combination with a projection step. We show that this idea gives a simple and easy-to-implement algorithm. We present experiments that indicate that the algorithm may perform better than other algorithms if we employ them without any special tricks. Hence, we may conclude that the projection proximal-point idea is a promising idea in the context of ?¹ minimization.     

Complexity results for reconstructing binary images with disjoint components from horizontal and vertical projections

The problem of reconstructing a special class of binary images from their horizontal and vertical projections is considered. We present a general framework for analyzing the worst case complexity of this task if the image consists of more than one pairwise disjoint component. Applying the presented technique we analyze the complexity of reconstructing canonical hv-convex binary images. We also present parameterized complexity results on general and so-called glued hv-convex images. Moreover, we study how our results are related to the reconstruction of permutation matrices from four projections.     

Computational inversion of electron micrographs using L2‐gradient flows—convergence analysis

A gradient flow‐based explicit finite element method (L2GF) for reconstructing the 3D density function from a set of 2D electron micrographs has been proposed in recently published papers. The experimental results showed that the proposed method was superior to the other classical algorithms, especially for the highly noisy data. However, convergence analysis of the L2GF method has not been conducted. In this paper, we present a complete analysis on the convergence of L2GF method for the case of using a more general form regularization term, which includes the Tikhonov‐type regularizer and modified or smoothed total variation regularizer as two special cases. We further prove that the L²‐gradient flow method is stable and robust. These results demonstrate that the iterative variational reconstruction method derived from the L²‐gradient flow approach is mathematically sound and effective and has desirable properties. Copyright © 2013 John Wiley & Sons, Ltd.     

Stable carbon isotopic composition of tree rings from a pine tree from Augustów Wilderness,Poland, as a temperature and local environment conditions indicator

Tree rings can be used as archives of climatic and environmental data with annual resolution. Tree rings widths, maximum late wood density and other parameters as stable composition in tree rings can be used for the reconstruction of past climatic and environmental changes. Stable carbon isotope ratios in tree rings may provide valuable information on past climatic conditions. ¹³C/¹²C ratios of plant organic matter can reflect corresponding ¹³C/¹²C ratio of atmospheric CO₂ during formation of the rings. Investigations of isotopic carbon composition in tree rings from in the ecologically clean the Augustów Wilderness region in the north-eastern part of Poland (22°58′E, 53°51′N) (nowadays a sanctuary) were undertaken. Series of δ¹³C in α-cellulose and in wholewood were acquired. Those measurements constituted a part of more complex investigations of carbon isotope composition in tree rings including the measurements of radiocarbon concentration and tree ring widths. This article presents preliminary results. It is argued that contrary to the tree ring widths and δ¹³C in wholewood that do not reveal significant correlation with temperature, the variation of δ¹³C in the latewood α-cellulose is correlated with combined July and August temperatures.     

MAP-regularized robust reconstruction for underwater imaging detection

In order to enhance the visual quality of underwater images, applications such as enhancement and restoration can be applied, but the resolution is still limited. Super-resolution reconstruction is a widely used technique for improving resolution beyond the limit of imaging system. With knowledge of the point spread function and techniques of regularization, the performance of reconstruction can be further enhanced. The presented effort proposed a robust image super-resolution reconstruction method under maximum a posteriori framework with regularization by the point spread function for underwater imaging detection. Objective image quality metrics are used to quantify the effectiveness of the reconstruction. Experimental results showed that the proposed method can effectively improve the resolution and quality of underwater imaging detection.     

An approach for sensing marine plankton using digital holographic imaging

The goal of this paper is to use digital holographic imaging for sensing marine plankton in recording sampling volume. The process stage of this approach includes: wavefront recording using in-line holographic recording set up and numerical reconstruction using Fresnel approximation and convolution algorithm. So, by capturing hologram of marine plankton and reconstructing hologram, the recorded optical field of marine plankton is retrieved. Digital holographic imaging is an extremely powerful technique for the study of marine plankton fields as it allows instantaneous, noninvasive, high-resolution recording of substantial volumes. Finally, this paper presents that it is possible for digital holographic imaging system to sense marine plankton according to laboratory results.     

Image fusion through local feature extraction by using multi-scale top-hat by reconstruction operators

The purpose of image fusion is to combine useful image features of different original images into the final fusion image, which will produce one useful result image for different applications. One of the main difficulties of image fusion is extracting useful image features of different original images. In some cases, useful image features are local image features of the whole image. To efficiently extract local image features and produce an efficient fusion result, an image fusion algorithm based on the extracted local image features by using multi-scale top-hat by reconstruction operators is proposed in this paper. Firstly, multi-scale local feature extraction using multi-scale top-hat by reconstruction operators is discussed. Then, based on the extracted multi-scale local features of different original images, the useful image features for image fusion are constructed. Finally, the constructed useful image features for image fusion are combined into the final fusion image. Experimental results on different types of images show that, the proposed algorithm performs well for image fusion.