Image reconstruction from an efficient number of moment-based projections

This paper presents a new technique for computed tomography that is based on moment reconstruction. The proposed technique employs the Fourier and Haar coefficients for spectral and spatial moment-based image analyses, respectively. It provides a new approach to the problem of tomographic image reconstruction, where an X-ray image is obtained from a set of line projections. The experimental evaluation includes reconstructions of standard tomographic images in the presence of blur, caused by uniform linear motions. The results lead to the conclusion that the proposed method is more selective, efficient and robust. Another issue considered is the noise associated with normal transmission.     

Incorporating mutation scheme into krill herd algorithm for global numerical optimization

Recently, Gandomi and Alavi proposed a robust meta-heuristic optimization algorithm, called Krill Herd (KH), for global optimization. To improve the performance of the KH algorithm, harmony search (HS) is applied to mutate between krill during the process of krill updating instead of physical diffusion used in KH. A novel hybrid meta-heuristic optimization approach HS/KH is proposed to solve global numerical optimization problem. HS/KH combines the exploration of harmony search (HS) with the exploitation of KH effectively, and hence, it can generate the promising candidate solutions. The detailed implementation procedure for this improved meta-heuristic method is also described. Fourteen standard benchmark functions are applied to verify the effects of these improvements, and it is demonstrated that, in most cases, the performance of this hybrid meta-heuristic method (HS/KH) is superior to, or at least highly competitive with, the standard KH and other population-based optimization methods, such as ACO, BBO, DE, ES, GA, HS, KH, PSO, and SGA. The effect of the HS/FA parameters is also analyzed.     

Fine-tuning Deep Belief Networks using Harmony Search

In this paper, we deal with the problem of Deep Belief Networks (DBNs) parameters fine-tuning by means of a fast meta-heuristic approach named Harmony Search (HS). Although such deep learning-based technique has been widely used in the last years, more detailed studies about how to set its parameters may not be observed in the literature. We have shown we can obtain more accurate results comparing HS against with several of its variants, a random search and two variants of the well-known Hyperopt library. The experimental results were carried out in two public datasets considering the task of binary image reconstruction, three DBN learning algorithms and three layers.     

改进二进制和声搜索算法求解多维背包问题

和声搜索（HS）是一种已广泛应用于连续优化问题的元启发式方法。针对典型的组合优化问题——多维背包问题（MKP）,提出一种改进二进制和声搜索（IBHS）算法。算法通过伯努利随机过程生成二进制群体,在候选和声生成算子中,引入动态自适应参数,通过算法参数的自适应调整来协调算法的全局搜索和局部搜索,并提出一种新的更有效的衡量商品多维加权价值密度的方法用于二进制个体修正和优化;引入精英局部搜索机制进行协同寻优,提高IBHS的收敛速度。通过求解10组不同规模的典型多维背包算例和与贪心二进制狮群优化（GBLSO）算法、改进的差分演化（MBDE）算法以及二进制修正和声（BMHS）算法的对比分析,实验结果表明,所提算法在求解MKP时有具有良好的收敛效率、较高的寻优精度和很好的鲁棒性。     

A memetic approach to discrete tomography from noisy projections

Discrete tomography deals with the reconstruction of images from very few projections, which is, in the general case, an NP-hard problem. This paper describes a new memetic reconstruction algorithm. It generates a set of initial images by network flows, related to two of the input projections, and lets them evolve towards a possible solution, by using crossover and mutation. Switch and compactness operators improve the quality of the reconstructed images during each generation, while the selection of the best images addresses the evolution to an optimal result. One of the most important issues in discrete tomography is known as the stability problem and it is tackled here, in the case of noisy projections, along four directions. Extensive experiments have been carried out to evaluate the robustness of the new methodology. A comparison with the output of two other evolutionary algorithms and a generalized version of a deterministic method shows the effectiveness of our new algorithm.     

Image Reconstruction from Sparse Projections Using S-Transform

Sparse projections are an effective way to reduce the exposure to radiation during X-ray CT imaging. However, reconstruction of images from sparse projection data is challenging. This paper introduces a new sparse transform, referred to as S-transform, and proposes an accurate image reconstruction method based on the transform. The S-transform effectively converts the ill-posed reconstruction problem into a well-defined one by representing the image using a small set of transform coefficients. An algorithm is proposed that efficiently estimates the S-transform coefficients from the sparse projections, thus allowing the image to be accurately reconstructed using the inverse S-transform. The experimental results on both simulated and real images have consistently shown that, compared to the popular total variation (TV) method, the proposed method achieves comparable results when the projections is sparse, and substantially improves the quality of the reconstructed image when the number of the projections is relatively high. Therefore, the use of the proposed reconstruction algorithm may permit reduction of the radiation exposure without trade-off in imaging performance.     

Modified harmony search optimization for constrained design problems

Constrained optimization is a major real-world problem. Constrained optimization problems consist of an objective function subjected to both linear and nonlinear constraints. Here a constraint handling procedure based on the fitness priority-based ranking method (FPBRM) is proposed. It is embedded into a harmony search (HS) algorithm that allows it to satisfy constraints. The HS algorithm is conceptualized using the musical process of searching for a perfect state of harmony. Here, the original heuristic HS was improved by combining both improved and global-best methods along with the FPBRM. The resulting modified harmony search (MHS) was then compared with the original HS technique and other optimization methods for several test problems.     

New neural network algorithm for image reconstruction from fan-beam projections

Neural networks have some applications in computerized tomography, in particular to reconstruct an image from projections. The presented paper describes a new practical approach to the reconstruction problem using a Hopfield-type neural network. The methodology of this reconstruction algorithm resembles a transformation formula—the so-called ρ-filtered layergram method. The method proposed in this work is adapted for discrete fan beam projections, already used in practice. Performed computer simulations show that the neural network reconstruction algorithm designed to work in this way outperforms conventional methods in obtained image quality, and in perspective of hardware implementation in the speed of the reconstruction process.     

用线性神经网络映射光学过程层析成像的逆问题

过程层析成像 (Process tomography)的逆问题也称为成像算法 ,它不仅需要反映被测物质与激励场的相互作用原理 ,而且应与传感器的空间阵列结构相匹配 .成像算法的性能好坏 (包括图象质量和每帧计算需时 )是过程层析成像技术能否应用于工业过程监控系统的关键问题之一 .为了得到性能良好的重建图象 ,提出了一种线性神经网络图象重建算法 .该算法首先通过建立光学层析成像的正问题和逆问题的线性化模型来求解正问题 ,以得出图象和投影的关系模式对 ,然后将其用于训练和构造线性神经网络 ;最后使用训练好的线性神经网络来映射光学层析成像的逆问题 .实验表明 ,该方法具有较高的图象质量和极高的成像实时性 ,是一种性能良好的图象重建算法     

定步长压缩感知锥束CT重建算法

针对锥束CT成像系统中投影数据不完全的图像重建问题,提出了一种定步长压缩感知锥束CT重建算法。首先将锥束CT重建问题归结为投影数据均方误差作为数据保真项、全变分作为正则项的无约束优化问题,分析目标函数的Lipschitz连续性;然后近似计算Lipschitz常数,求出梯度下降步长,利用梯度下降法进行重建;最后对CT投影数据采用联合代数重建算法更新重建图像。在每次迭代过程中调整梯度下降步长,提高重建算法的收敛速度。Shepp-Logan模型的无噪声实验结果表明,该算法的重建图像信噪比分别比联合代数重建算法、自适应最速下降-凸集投影算法、BB梯度投影算法的重建图像信噪比高出13.7728dB、12.8205dB、7.3580dB。仿真试验表明该重建算法提高了收敛速度,同时减少了重建图像的相对误差,极大提高了用少量投影数据重建的图像质量。     

基于混合搜索的含逻辑“与”“或”的RM优化算法

相对于标准约束优化问题,广义约束优化问题（或称析取优化问题）的等式或不等式约束条件中不仅包含逻辑“与”关系,还含有逻辑“或”关系.单调速率（RM）优化问题是广义约束优化问题的一个重要应用.目前RM优化问题已有的解法包括函数变换、混合整数规划、线性规划搜索等算法.随着任务数的增多,这些算法的求解时间较长.提出一种基于线性规划的深度广度混合搜索算法（LPHS）,将广义约束优化问题拆分成若干子问题,建立线性规划搜索树,合理选择搜索顺序,利用动态剪枝算法减小子问题的规模,最终求得最优解.实验结果表明,LPHS算法比其他方法有明显的效率提升.研究成果与计算机基础理论中的可满足性模理论的研究相结合,有助于提高可满足性模理论问题的求解效率,促进该理论在程序验证、符号执行等领域的进一步应用.     

VARIANCE-BASED HARMONY SEARCH ALGORITHM FOR UNIMODAL AND MULTIMODAL OPTIMIZATION PROBLEMS WITH APPLICATION TO CLUSTERING

This article presents a novel variance-based harmony search algorithm (VHS) for solving optimization problems. VHS incorporates the concepts borrowed from the invasive weed optimization technique to improve the performance of the harmony search algorithm (HS). This eliminates the main problem of constant parameter setting in the algorithm proposed recently and named as explorative HS. It uses the variance of a current population as well as presents a solution vector to improvise the harmony memory. In addition, the dynamic pitch adjustment operator is used to avoid solution oscillation. The proposed algorithm is evaluated on 14 standard benchmark functions of various characteristics. The performance of the proposed algorithm is investigated and compared with classical HS, an improved version of HS, the global best HS, self-adaptive HS, explorative HS, and the recently proposed state-of-art gravitational search algorithm. Experimental results reveal that the proposed algorithm outperforms the above-mentioned approaches. The effects of scalability, noise, harmony memory size, and harmony memory consideration rate have also been investigated with the proposed algorithm. The proposed algorithm is then employed for a data clustering problem. Four real-life datasets selected from the UCI machine learning repository have been used. The results indicate that the VHS-based clustering outperforms the existing well-known clustering algorithms.     

基于 GPU 加速技术的 C 形臂 Cone Beam CT 三维 图像快速重建方法

平板探测器技术的发展使得锥形束计算机断层扫描技术(Cone Beam Computerized Tomography,CBCT)成为一种重要的成像技术,有着十分广泛的应用.基于C形臂的CBCT,除了具有CBCT的技术优势外,还特别适合在影像引导介入手术中应用.然而,如何在满足手术实时性要求的同时获得高分辨率高质量的三维断层图像,仍是个十分具有挑战性的课题.文章提出一种基于GPU加速技术的C形臂CBCT三维图像快速重建方法:在算法层面应用GPU并行加速技术对重建算法进行优化,在系统层面通过设计分布式系统和延迟隐藏机制,大大提升了由二维投影图像重建三维体数据的效率.在保持重建精度的前提下,优化后的GPU加速的FDK算法极大地提升了重建过程的计算效率.延迟隐藏机制进一步提升了系统的运行效率.在使用90帧投影时,系统效率提升了26%,重建延迟加速了2.1倍;当使用120帧投影时,系统效率提升39%,重建延迟加速达到3.3倍.     

Multi-objective GA optimization of fuzzy penalty for image reconstruction from projections in X-ray tomography

This paper concerns X-ray tomography image reconstruction of an object function from few projections in Computed Tomography (CT). The problem is so ill-posed that no classical method can give satisfactory result. We have investigated a new combined method for penalized-likelihood image reconstruction that combines the fuzzy penalty function (FP) and GA (genetic algorithm) optimization. The proposed algorithm does not suffer from the same problem as that of ML EM (maximum likelihood expectation maximization) algorithm, and it converges rapidly to a low noisy solution even if the iteration number is high, and gives global estimation not a local one like in classical algorithm such as gradient, to the problem of determining object parameters. The method was tested and validated on datasets of synthetic and real image.     

Medical image reconstruction using a multi-objective genetic local search algorithm

Image reconstruction from projections is a key problem in medical image analysis. In this paper, we cast image reconstruction from projections as a multi-objective problem. It is essential to choose some proper objective functions of the problem. We choose the square error, smoothness of the reconstructed image, and the maximum entropy as our objective functions of the problem. Then we introduce a hybrid algorithm comprising of multi-objective genetic and local search algorithms to reconstruct the image. Our algorithm has remarkable global performance. Our experiments show that we can get different results when we give different weights to different objective functions. We can also control the noise by giving different weights on different objective function. At the same time, we can adjust the parameter to let it have good local performance. Though the computation demands of the hybrid algorithm tends to be larger because of the random search of the GA, it is really a common feature of the global optimization method. Our results show that the hybrid algorithm is a more effective than the conventional method. We think our method is very promising for the medical imaging field.     

A Network Flow Algorithm for Reconstructing Binary Images from Continuous X-rays

Tomography is a powerful technique to obtain accurate images of the interior of an object in a nondestructive way. Conventional reconstruction algorithms, such as filtered backprojection, require many projections to obtain high quality reconstructions. If the object of interest is known in advance to consist of only a few different materials, corresponding to known image intensities, the use of this prior knowledge in the reconstruction procedure can dramatically reduce the number of required projections. In previous work we proposed a network flow algorithm for reconstructing a binary image defined on a lattice from its projections. In this paper we propose a new algorithm for the reconstruction of binary images that do not have an intrinsic lattice structure and are defined on a continuous domain, from a small number of their projections. Our algorithm relies on the fact that the problem of reconstructing an image from only two projections can be formulated as a network flow problem in a graph. We derive this formulation for parallel beam and fan beam tomography and show how it can be used to compute binary reconstructions from more than two projections. Our algorithm is capable of computing high quality reconstructions from very few projections. We evaluate its performance on both simulated and real experimental projection data and compare it to other reconstruction algorithms.

一种用于视频超分辨率重建的块匹配图像配准方法

图像配准是超分辨率重建中的一个关键问题, 直接影响超分辨率重建图像的质量. 本文在自适应十字搜索(Adaptive rood pattern search, ARPS)块匹配算法的基础上, 根据小波域中各图像之间的相关性, 提出一种分层块匹配算法---基于小波变换的改进的自适应十字模式搜索算法(Improved adaptive rood pattern search algorithm based on wavelet transform, W-IARPS), 该方法在小波变换域完成匹配宏块的搜索, 有效地减少了匹配点的搜索个数, 且配准图像的峰值信噪比相比全搜索算法下降不到0.l dB, 保持了较高的配准精度. 最后采用凸集投影(Projections onto convex sets, POCS)算法对配准后的图像进行超分辨率重建, 取得了较好的视觉效果. 实验结果表明, 该方法具有较高的配准精度和重建效果, 算法稳健可靠.     

Hybrid Ultrasonic Computed Tomography

Ultrasonic computed tomography can provide valuable information on tissue properties. However, the large number of projections required to obtain a high-resolution image renders it impractical for routine clinical use. B-scan imaging, on the other hand is very rapid, but mainly provides information on tissue morphology. An algorithm which fuses information from a compound B-scan image and a limited view speed of sound (SOS) tomographic reconstruction of an object is presented here. The algorithm is iterative and is based on the two-dimensional Taylor series expansion. The algorithm diminishes artifacts caused by tomographic reconstruction from too few projections and produces an image which depicts both tissue morphology and acoustic properties (SOS). Consequently, quantitative images can be acquired in a much shorter time than required by conventional tomography. This method may potentially find application in ultrasonic breast screening.     

A new meta-heuristic algorithm for continuous engineering optimization: harmony search theory and practice

Most engineering optimization algorithms are based on numerical linear and nonlinear programming methods that require substantial gradient information and usually seek to improve the solution in the neighborhood of a starting point. These algorithms, however, reveal a limited approach to complicated real-world optimization problems. If there is more than one local optimum in the problem, the result may depend on the selection of an initial point, and the obtained optimal solution may not necessarily be the global optimum. This paper describes a new harmony search (HS) meta-heuristic algorithm-based approach for engineering optimization problems with continuous design variables. This recently developed HS algorithm is conceptualized using the musical process of searching for a perfect state of harmony. It uses a stochastic random search instead of a gradient search so that derivative information is unnecessary. Various engineering optimization problems, including mathematical function minimization and structural engineering optimization problems, are presented to demonstrate the effectiveness and robustness of the HS algorithm. The results indicate that the proposed approach is a powerful search and optimization technique that may yield better solutions to engineering problems than those obtained using current algorithms.     

A mathematical programming approach to the construction of BIBDs

A balanced incomplete block design (BIBD) is instrumental in design of experiments. This is usually constructed by algebraic methods such as finite algebra or difference sets. However, in algebraic approaches, no unified method exists, and each BIBD has been constructed in some ad hoc ways. On the other hand, computer-based methods apply the same algorithm to all BIBDs; hence, these are unified approaches. Although various meta-heuristic algorithms have been tried, the success of these methods has been rather limited. This article presents an alternative approach to this problem that formulates the problem as a nonlinear mixed integer programming problem. We develop a branch-and-bound algorithm to solve this, and a tabu search algorithm to overcome some weakness in the former algorithm. We compare the performance of these algorithms against some previously developed algorithms, and demonstrate that our algorithms are competitive to these methods.