Gerchberg迭代法在三维面形测量中的应用

在基于结构光照明的三维面形测量中,针对有孤立区域物体的条纹图像存在不规则缺陷的问题,提出先对其进行Gerchberg迭代,消除或减少条纹缺陷,获取较完善的迭代条纹,然后再利用傅里叶变换轮廓术(FTP)重建面形。设计了迭代流程,并分析了影响迭代精度的因素,解决了光学加工用具磨盘表面不完善条纹Gerchberg迭代过程中存在的问题,成功地重建了磨盘的三维面形。该工作为表面存在孤立区域的被测物体三维面形测量提供了可供参考的技术方案,也给可实时形变的应力盘三维面形动态测量奠定了基础。     

Securing color image by using phase-only encoding in Fresnel domains

We propose a novel color image hiding scheme with three channels of cascaded Fresnel domain phase-only filtering. The original color image is encoded into three phase masks by using the Gerchberg–Saxton iterative phase retrieval algorithm with another predefined phase key. The individual phase masks are placed in the inputs of the Fresnel domains of the red–green–blue channels and the phase key in the public channel, during the optical retrieval. The physical parameters in the optical system will be regarded as the additional keys for security enhancement. Numerical simulation is performed to test the validity of our scheme.     

用二元光学技术制作反射式相息图

采且Ｇｅｒｃｈｂｅｒｇ－Ｓａｘｔｏｎ（Ｇ－Ｓ）迭代算法，在物域和频域之间进行多次迭代，使频谱的振幅大致为常数，并对频谱的位相进行量化，用二元光学技术制成了８台阶反射式相息图（ｋｉｎｏｆｏｒｍ）再现时获得清晰的像，衍射效率较高。     

Optical color image hiding scheme by using Gerchberg–Saxton algorithm in fractional Fourier domain

We proposed an optical color image hiding algorithm based on Gerchberg–Saxton retrieval algorithm in fractional Fourier domain. The RGB components of the color image are converted into a scrambled image by using 3D Arnold transform before the hiding operation simultaneously and these changed images are regarded as the amplitude of fractional Fourier spectrum. Subsequently the unknown phase functions in fractional Fourier domain are calculated by the retrieval algorithm, in which the host RBG components are the part of amplitude of the input functions. The 3D Arnold transform is performed with different parameters to enhance the security of the hiding and extracting algorithm. Some numerical simulations are made to test the validity and capability of the proposed color hiding encryption algorithm.     

基于焦斑空间频谱控制的连续相位板设计

 改进了传统的盖斯贝格 撒克斯通（G-S）算法,其中包含：改善了初始相位的选取;远场振幅采用弱调制,迭代中进行解相、滤波,以保证设计的相位板连续;对目标焦斑的频谱控制,使焦斑能量在频谱上重新分配。结果表明：相对传统设计的连续相位板（CPP）,改进后的G-S算法可以控制CPP的加工单元大小,降低CPP的相位梯度,更好地控制焦斑轮廓,降低特定频带的调制。进一步分析表明,新方法设计的CPP与光谱色散匀滑技术耦合的效果更佳。     

A comparison of iterative Fourier transform algorithms for image quality estimation

A comparison was established between two iterative Fourier transform algorithms (IFTAs), such as the original Gerchberg–Saxton (GS) and the mixed-region amplitude freedom (MRAF) algorithms, for the hologram reconstruction of different target images through the full reference image quality estimation (IQE) and pixel homogeneity in the Fourier plane presented theoretically and experimentally. The comparison was applied depending upon both algorithms based on a computer-generated hologram (CGH) implemented utilizing a reflective phase-modulated liquid-crystal spatial light modulator (LC-SLM) to obtain the digital kinoform holograms of the desired intensity distributions. These digital holograms were applied to reconstruct the intensity patterns for 852 nm, which represents a laser beam source. The theoretical and experimental results of the reconstructed patterns obtained using the MRAF algorithm were found to be smoother and better than the patterns obtained using the GS algorithm. Unmodulated light beam (dc term) is removed from the reconstructed patterns attributed to digital kinoform holograms of MRAF algorithm as an alternative to the theoretical and experimental results without using any additional optic equipment at the light path. Moreover, this paper discussed the full reference objective quality estimations, such as mean square error (MSE), peak signal-to-noise ratio (PSNR), structural content (SC), normalized absolute error (NAE), normalized cross correlation (NK), and homogeneity of pixels, through the contrast (Cont) and inverse difference moment (IDM) for numerical and experimental results. According to the two desired intensity distributions processed theoretically and experimentally, the results of MRAF algorithm were found to be in the highly accurate recovered phase, the quality of image was enhanced, and the dc term was decreased. Image quality estimation of full reference objective relay on the feedback algorithms experimental attestation has not been implemented yet.     

光学系统和电子显微系统中振幅和相位恢复问题的算法

由强度测量来恢复相位,是个很重要的问题之一,它普遍地出现在物理学的许多领域中。对于电子显微术中由双强度测量恢复相位的比较成功相有效的算法是1971年Gesrchbe-rg-Saxton提出的一套算法(GS),随后,不少学者又提出有效的修正的GS算法。由单强度测量来恢复相位问题,也有过讨论,可以利用解析函数特有性质或应用取样定理来实现相位恢复。但上述方法只适用于Fourier相位问题。1981年以来,本文作者根据一般光学变换理论公式,提出了一般变换下系统的振幅-相位恢复的更普遍的描述方式,并由严格的数学推导,给出确定振幅-相位的方程组,利用迭代算法,可以处理各种各样的振幅-相位问题。本文对上述诸种算法做了综合性评述,指出算法的优缺点。还举些有实际意义的例子,来说明算法的应用,理论计算与模拟实验结果也作了介绍。这是一个尚待进一步开发的有实用价值的研究领域。     

Optimization of ultra-fast interactions using laser pulse temporal shaping controlled by a deterministic algorithm

Femtosecond laser pulse temporal shaping techniques have led to important advances in different research fields like photochemistry, laser physics, non-linear optics, biology, or materials processing. This success is partly related to the use of optimal control algorithms. Due to the high dimensionality of the solution and control spaces, evolutionary algorithms are extensively applied and, among them, genetic ones have reached the status of a standard adaptive strategy. Still, their use is normally accompanied by a reduction of the problem complexity by different modalities of parameterization of the spectral phase. Exploiting Rabitz and co-authors’ ideas about the topology of quantum landscapes, in this work we analyze the optimization of two different problems under a deterministic approach, using a multiple one-dimensional search (MODS) algorithm. In the first case we explore the determination of the optimal phase mask required for generating arbitrary temporal pulse shapes and compare the performance of the MODS algorithm to the standard iterative Gerchberg–Saxton algorithm. Based on the good performance achieved, the same method has been applied for optimizing two-photon absorption starting from temporally broadened laser pulses, or from laser pulses temporally and spectrally distorted by non-linear absorption in air, obtaining similarly good results which confirm the validity of the deterministic search approach.     

Optical color image encryption based on the wavelength multiplexing using cascaded phase-only masks in Fresnel transform domain

A novel technique, based on a modified Gerchberg–Saxton algorithm (MGSA) in the Fresnel-transform (FrT) domain, is proposed to encode a color image into three phase-only functions (POFs) for three separated channels: red (R), green (G), and blue (B). The decomposed three RBG channels can avoid the interference of crosstalks efficiently. In proposed decryption process, a color image can be promptly reconstructed by summing of the three decrypted RGB images after the created three POFs which are decrypted one by one. In this paper, all the created three POFs and the system parameters of FrT can be used as the keys for increasing security that are also demonstrated. The computer application simulations to the partial color encryption and decryption are given to validate the feasibility of the proposed scheme.     

利用加权预测的图像迭代盲解卷积

为解决大气湍流造成的图像退化问题,本文鉴于现有的盲解卷积算法收敛性不稳定,计算量大等特点,提出了一种基于加权预测的迭代盲解卷积算法。对目前性能优秀的用迭代实现盲解卷积的L-R算法进行优化,在每次迭代结束后通过加权方法求出预测值,根据预测值计算方向加速算子,从而大大提高算法的收敛速度。实验表明：该算法不仅可对模糊退化图像进行很好的复原,同时与L-R算法相比收敛速度提高约43.8倍,其迭代速度快的特点决定了算法具有较高的工程实用价值。     

Optical multiple-image encryption based on phase encoding algorithm in the Fresnel transform domain

A novel method of the optical multiple-image encryption based on the modified Gerchberg–Saxton algorithm (MGSA) is presented. This proposed method with an architecture of two adjacent phase only functions (POFs) in the Fresnel transform (FrT) domain that can extremely increase capacity of system for completely avoiding the crosstalk between the decrypted images. Each encrypted target image is separately encoded into a POF by using the MGSA which is with constraining the encrypted target image. Each created POF is then added to a prescribed fixed POF composed of a proposed MGSA-based phase encoding algorithm. Not only the wavelength and multiple-position parameters in the FrT domain as keys to increase system security, the created POFs are also served mutually as the encryption keys to decrypt target image based on cascading two POFs scheme. Compared with prior methods [23], [24], the main advantages of this proposed encryption system is that it does not need any transformative lenses and that makes it very efficient and easy to implement optically. Simulation results show that this proposed encryption system can successfully achieve the multiple-image encryption with multiple-position keys, which is more advantageous in security than previous work [24] for its decryption process with only two POFs keys to accomplish this task.     

基于实时帧迭代反向投影算法的图像序列超分辨率处理

提出一种实时帧迭代反向投影算法实现对图像序列的超分辨率处理。通过建立虚拟全景图像及其迭代权阵,实现迭代反向投影的逐帧处理,从而可实时地对视频图像序列作超分辨率处理。另外还采用了基于光流计算的分层迭代图像配准、双线性插值模拟采样、阈值先验约束、坐标系同步变换等技术来提高算法的有效性。通过对仿真和实际视频序列的处理对算法进行了验证。     

利用加权预测的图像迭代盲解卷积

为解决大气湍流造成的图像退化问题,本文鉴于现有的盲解卷积算法收敛性不稳定,计算量大等特点,提出了一种基于加权预测的迭代盲解卷积算法。对目前性能优秀的用迭代实现盲解卷积的L-R算法进行优化,在每次迭代结束后通过加权方法求出预测值,根据预测值计算方向加速算子,从而大大提高算法的收敛速度。实验表明:该算法不仅可对模糊退化图像进行很好的复原,同时与L-R算法相比收敛速度提高约43.8倍,其迭代速度快的特点决定了算法具有较高的工程实用价值。     

基于递推最小二乘的红外焦平面非均匀校正算法

根据递推最小二乘和图像配准原理,提出了基于递推最小二乘的红外焦平面非均匀校正算法（简称ILS算法）,有效降低算法的时间和空间复杂度,使噪音图像的校正处理能够实时完成.ILS算法具有噪音参量估计准确度高、收敛速度快和计算复杂度低等优点.给出了算法的推导并用仿真数据对算法的有效性进行验证.     

Image double encryption based on iteration Fourier and chaos system

According to the digital image encryption, a double encryption algorithm based on the iterative Fourier transform and chaotic transform is proposed. It uses iterative Fourier transform to encrypt image for the first time, then processes the encrypted image through the chaos replacement, which can change image pure phase distribution to realize double encryption. The simulated result shows that the algorithm can effectively resist the attacks of statistical analysis, and has higher encryption effect and safety which is very sensitive to secret key.     

Noise-Robust Image Reconstruction Based on Minimizing Extended Class of Power-Divergence Measures

The problem of tomographic image reconstruction can be reduced to an optimization problem of finding unknown pixel values subject to minimizing the difference between the measured and forward projections. Iterative image reconstruction algorithms provide significant improvements over transform methods in computed tomography. In this paper, we present an extended class of power-divergence measures (PDMs), which includes a large set of distance and relative entropy measures, and propose an iterative reconstruction algorithm based on the extended PDM (EPDM) as an objective function for the optimization strategy. For this purpose, we introduce a system of nonlinear differential equations whose Lyapunov function is equivalent to the EPDM. Then, we derive an iterative formula by multiplicative discretization of the continuous-time system. Since the parameterized EPDM family includes the Kullback–Leibler divergence, the resulting iterative algorithm is a natural extension of the maximum-likelihood expectation-maximization (MLEM) method. We conducted image reconstruction experiments using noisy projection data and found that the proposed algorithm outperformed MLEM and could reconstruct high-quality images that were robust to measured noise by properly selecting parameters.     

基于多项式外推的Richardson-Lucy算法加速研究

提出一种新的可加速Richardson-Lucy(R-L)图像迭代恢复算法的方法.该方法基于阻尼R-L算法,通过存储阻尼R-L算法的前若干次(n次)迭代运算结果,利用多项式外推法分析这前n次迭代运算结果,并用一个多项式函数近似描述各结果之间的关系.通过该多项式的外推,预测以后的迭代结果,从而减少迭代运算的次数,取得了较好的加速效果.该方法可以实现几乎没有图像失真的复原,并能应用于其他类型的算法.     

基于模糊松弛迭代的分层图像增强算法

映射函数的研究是图像增强技术的关键,模糊松弛技术利用模糊函数建立其映射函数,通过设置该算法的模糊松弛参数可以达到对图像可控增强处理的目的。为了实现针对不同层次的图像内容实现可控式模糊增强,提出了多层次交互迭代的模糊松弛图像增强算法。通过分析各子层图像的直方图,分别设定各子层的模糊松弛参数,并建立对应的模糊松弛映射函数;分别对各子层图像进行可控迭代增强,选择合适的迭代次数作为终止条件。给出的实验结果证明了该算法能够取得较好的增强效果。     

An adaptive super-resolution method based on regional pixel information and ringing artifacts suppression

Multi-frame image super-resolution (SR) aims to utilize information from a set of low-resolution (LR) images to compose a high-resolution (HR) one. In this paper, a novel multi-frame image super-resolution algorithm is proposed based on regional pixel information and ringing artifacts suppression. Firstly, a new regularization term which adopts Regional Adaptive Weight Coefficients (RAWC) is produced to keep edges and flat regions. After detailed analysis, an iterative process is given for image reconstruction. Then an adaptive term according to the local variance of iterative correction image is designed to evaluate the ringing artifacts. Finally, the original iteration is updated by adding the restraint term for better visual effects and lower noise of reconstructive HR image. Thorough experimental results show the proposed algorithm is effective for SR reconstruction and ringing artifacts suppression.     

一种电磁干扰源成像多分辨率分区算法

在利用抛物反射面对电磁干扰源成像过程中,由于系统衍射受限导致干扰源成像模糊,分辨率低,难以分辨,由于不同频率不同区域干扰源所成图像分辨率不同,具有分区域多分辨率的特征,采用已有超分辨算法难以提高分辨率。利用Mean Shift算法,在原有算法基础上改进使其能够适应多分辨率的电磁干扰源成像,在图像分割的基础上对多分辨率图像进行分块抽离,并采用基于L_R迭代的盲反卷积算法分别对各区域进行分辨率的提高,仿真结果表明算法能够适应对干扰源的多分辨率电磁成像并提高分辨率。