Hopfield neural network based algorithms for image restoration andreconstruction. I. Algorithms and simulations

In our previous work, the eliminating-highest error (EHE) criterion was proposed for the modified Hopfield (1982) neural network (MHNN) for image restoration and reconstruction. The performance of the MHNN is considerably improved by the EHE criterion as shown in many simulations. In inspiration of revealing the insight of the EHE criterion, in this paper, we first present a generalized updating rule (GUR) of the MHNN for gray image recovery. The stability properties of the GUR are given. It is shown that the neural threshold set up in this GUR is necessary and sufficient for energy decrease with probability one at each update. The new fastest-energy-descent (FED) criterion is then proposed parallel to the EHE criterion. While the EHE criterion is shown to achieve the highest probability of correct transition, the FED criterion achieves the largest amount of energy descent. In image restoration, the EHE and FED criteria are equivalent. A group of new algorithms based on the EHE and FED criteria is set up. A new measure, the correct transition rate (CTR), is proposed for the performance of iterative algorithms. Simulation results for gray image restoration show that the EHE (FED) based algorithms obtained the best visual quality and highest SNR of recovered images, took much smaller number of iterations, and had higher CTR. The CTR is shown to be a rational performance measure of iterative algorithms and predict quality of recovered images     

Superresolution algorithms for a modified Hopfield neural network

The authors describe the implementation of a superresolution (or spectral extrapolation) procedure on a neural network, based on the Hopfield (1982) model. They show the computational advantages and disadvantages of such an approach for different coding schemes and for networks consisting of very simple two-state elements as well as those made up of more complex nodes capable of representing a continuum. It is demonstrated that, with the appropriate hardware, there is a computational advantage in using the Hopfield architecture over some alternative methods for computing the same solution. The relationship between a particular mode of operation of the neural network and the regularized Gerchberg (1974) and Papoulis (1975) algorithm is also discussed     

基于混沌Hopfield神经网络视觉意义的图像加密算法

为解决传统加密方案得到的类噪声图像在传输过程中常常会因其视觉效果而受到攻击的问题,提出一种基于混沌Hopfield神经网络的具有视觉意义的双图像加密算法.对混沌Hopfield神经网络迭代生成随机数矩阵,与两幅压缩后的明文图像组合后进行离散余弦变换.通过生命游戏算法生成置乱矩阵来进行置乱.将置乱后的图像分为三部分,通过...     

Improvement on performance of modified Hopfield neural network forimage restoration

By analyzing the same inequality ||u*||(1)=/<(1/2)trace(T), the authors conclude that a severely blurred image is generally restored less accurately than a mildly blurred one by the modified Hopfield neural network. This conclusion is the opposite of the statement made in Paik and Katsaggelos (1992). The authors also propose an improved new algorithm. Simulation results show that the SNRs of the images restored by the algorithm are higher by 3 to 8 db than those restored by the algorithm in Paik and Katsaggelos and the streaks in the restored images are obviously suppressed by the algorithm.     

Majorization-minimization algorithms for wavelet-based image restoration.

Standard formulations of image/signal deconvolution under wavelet-based priors/regularizers lead to very high-dimensional optimization problems involving the following difficulties: the non-Gaussian (heavy-tailed) wavelet priors lead to objective functions which are nonquadratic, usually nondifferentiable, and sometimes even nonconvex; the presence of the convolution operator destroys the separability which underlies the simplicity of wavelet-based denoising. This paper presents a unified view of several recently proposed algorithms for handling this class of optimization problems, placing them in a common majorization-minimization (MM) framework. One of the classes of algorithms considered (when using quadratic bounds on nondifferentiable log-priors) shares the infamous "singularity issue" (SI) of "iteratively reweighted least squares" (IRLS) algorithms: the possibility of having to handle infinite weights, which may cause both numerical and convergence issues. In this paper, we prove several new results which strongly support the claim that the SI does not compromise the usefulness of this class of algorithms. Exploiting the unified MM perspective, we introduce a new algorithm, resulting from using l1 bounds for nonconvex regularizers; the experiments confirm the superior performance of this method, when compared to the one based on quadratic majorization. Finally, an experimental comparison of the several algorithms, reveals their relative merits for different standard types of scenarios.     

The application of competitive Hopfield neural network to medical image segmentation

In this paper, a parallel and unsupervised approach using the competitive Hopfield neural network (CHNN) is proposed for medical image segmentation. It is a kind of Hopfield network which incorporates the winner-takes-all (WTA) learning mechanism. The image segmentation is conceptually formulated as a problem of pixel clustering based upon the global information of the gray level distribution. Thus, the energy function for minimization is defined as the mean of the squared distance measures of the gray levels within each class. The proposed network avoids the onerous procedure of determining values for the weighting factors in the energy function. In addition, its training scheme enables the network to learn rapidly and effectively. For an image of n gray levels and c interesting objects, the proposed CHNN would consist of n by c neurons and be independent of the image size. In both simulation studies and practical medical image segmentation, the CHNN method shows promising results in comparison with two well-known methods: the hard and the fuzzy c-means (FCM) methods.     

Wavelet-based neural network with fuzzy-logic adaptivity fornuclear image restoration

A novel wavelet-based neural network with fuzzy-logic adaptivity (WNNFA) is proposed for image restoration using a nuclear medicine gamma camera based on the measured system point spread function. The objective is to restore image degradation due to photon scattering and collimator photon penetration with the gamma camera and allow improved quantitative external measurements of radionuclides in vivo. The specific clinical model proposed is the imaging of bremsstrahlung radiation using ³² P and ⁹⁰Y. The theoretical basis for four-channel multiresolution wavelet decomposition of the nuclear image into different subimages is developed with the objective of isolating the signal from noise. A fuzzy rule is generated to train a membership function using least mean squares to obtain an optimal balance between image restoration and the stability of the neural network, while maintaining a linear response for the camera to radioactivity dose. A multichannel modified Hopfield neural network architecture is then proposed for multichannel image restoration using the dominant signal subimages     

一种基于神经网络的图像复原方法

提出了一种基于BP神经网络的图像复原算法.在分析图像模糊机制的基础上,为了降低输入维数,该方法采用滑动窗口操作来提取特征,同时为了加快训练速度和改善网络复原效果,首先对图像进行边缘提取,对图像内边缘区域和平坦区域分别采用滑动窗口获得训练集.利用BP神经网络的学习能力,通过训练,建立含有退化信息(高斯模糊)的模糊图像和清晰图像之间的映射关系模型,利用该模型对模糊图像进行复原,得到的复原图像在视觉上和定量分析上都获得了较好的效果.     

Image restoration using a modified Hopfield network

A modified Hopfield neural network model for regularized image restoration is presented. The proposed network allows negative autoconnections for each neuron. A set of algorithms using the proposed neural network model is presented, with various updating modes: sequential updates; n-simultaneous updates; and partially asynchronous updates. The sequential algorithm is shown to converge to a local minimum of the energy function after a finite number of iterations. Since an algorithm which updates all n neurons simultaneously is not guaranteed to converge, a modified algorithm is presented, which is called a greedy algorithm. Although the greedy algorithm is not guaranteed to converge to a local minimum, the l (1) norm of the residual at a fixed point is bounded. A partially asynchronous algorithm is presented, which allows a neuron to have a bounded time delay to communicate with other neurons. Such an algorithm can eliminate the synchronization overhead of synchronous algorithms.     

图像复原算法研究

研究了几种经典图像复原算法,在已知系统退化模型的情况下,对观测图像分别使用逆滤波、维纳滤波、有约束的最小二乘方滤波算法进行复原,在这几种算法的参数选取上得到了丰富的经验数据,并对实验结果进行了分析总结.     

基于神经网络和维纳滤波的半盲离焦图像复原

本文提出了一种基于小波神经网络和维纳(Wiener)滤波的半盲离焦图像复原算法,首先提取训练图像的小波域特点参数向量,将该参数用来训练小波神经网络,利用训练好的网络估计图像离焦模糊参数.由离焦模糊参数获得点扩展函数,然后用Wiener滤波完成图像的复原.实验结果表明:该方法能有效地估计离焦模糊参数和复原模糊图像.     

Hopfield神经网络的存贮容量

我们把理论推导与数值模拟相结合得出一个较好的误差函数近似解析式。应用该解析式分析了Ｈｏｐｆｉｅｌｄ神经网络绝对存同容量，得到了一更严格的结果。     

Object recognition using multilayer Hopfield neural network

An object recognition approach based on concurrent coarse-and-fine matching using a multilayer Hopfield neural network is presented. The proposed network consists of several cascaded single-layer Hopfield networks, each encoding object features at a distinct resolution, with bidirectional interconnections linking adjacent layers. The interconnection weights between nodes associating adjacent layers are structured to favor node pairs for which model translation and rotation, when viewed at the two corresponding resolutions, are consistent. This interlayer feedback feature of the algorithm reinforces the usual intralayer matching process in the conventional single-layer Hopfield network in order to compute the most consistent model-object match across several resolution levels. The performance of the algorithm is demonstrated for test images containing single objects, and multiple occluded objects. These results are compared with recognition results obtained using a single-layer Hopfield network.     

Block truncation coding using Hopfield neural network

The authors extend the analysis of the block truncation coding (BTC) algorithm using a Hopfield neural network (HNN). They show that its performance is suboptimum (in the mean square error sense) and that alternative (non-neural network) BTC algorithms are available with virtually the same performance.<>     

基于Hopfield神经网络模型的加密解密原理分析

本文介绍一种基于Hopfield神经网络模型的加密解密专用芯片设计方案,采用传统的弱金匙(Weak Key)和半弱金匙(Semi-weak Key)的加密方法会降低安全性,而在本文中所采用的Hopfield神经网络模型却能避免出现此弱点,本文还针对加密解密步骤做了具体的分析,加密和解密安全性和有效性大幅度提升.     

Systolic array algorithm for the Hopfield neural network guaranteeing convergence

It has been frequently reported that the Hopfield neural network operating in discrete-time and parallel update mode will not converge to a stable state, which inhibits the parallel execution of the model. The authors propose a systolic array algorithm for the parallel simulation of the Hopfield neural network which guarantees the convergence of the network and achieves linear speedup as the number of processors is increased.<>     

A positively self-feedbacked Hopfield neural network architecture for crossbar switching

We propose a positively self-feedbacked Hopfield neural network architecture for efficiently solving crossbar switch problem. A binary Hopfield neural network architecture with additional positive self-feedbacks and its collective computational properties are studied. It is proved theoretically and confirmed by simulating the randomly generated Hopfield neural network with positive self-feedbacks that the emergent collective properties of the original Hopfield neural network also are present in this network architecture. The network architecture is applied to crossbar switching and results of computer simulations are presented and used to illustrate the computation power of the network architecture. The simulation results show that the Hopfield neural network architecture with positive self-feedbacks is much better than the previous works including the original Hopfield neural network architecture, Troudet's architecture and maximum neural network for crossbar switching in terms of both the computation time and the solution quality.     

Multiobjective neural network for image reconstruction

The authors propose a multiobjective neural network model and algorithm for image reconstruction from projections. This model combines the Hopfield model and multiobjective decision making approach. A weighted sum optimisation based neural network algorithm is developed. The dynamic process of the net is based on minimisation of a weighted sum energy function and Euler's iteration and this algorithm is applied to image reconstruction from computer-generated noisy projections and Siemens Somaton DR scanner data, respectively. Reconstructions based on this method are shown to be superior to those based on conventional iterative reconstruction algorithms such as MART (multiplicate algebraic reconstruction technique) and convolution from the point of view of accuracy of reconstruction. Computer simulation using the multiobjective method shows a significant improvement in image quality and convergence behaviour over conventional algorithms     

Technique for multi-focus image fusion based on fuzzy-adaptive pulse-coupled neural network

Multi-focus image fusion technique can solve the problem that not all the targets in an image are clear in case of imaging in the same scene. In this paper, a novel multi-focus image fusion technique is presented, which is developed by using the nonsubsampled contourlet transform (NSCT) and a proposed fuzzy logic based adaptive pulse-coupled neural network (PCNN) model. In our method, sum-modified Laplacian (SML) is calculated as the motivation for PCNN neurons in NSCT domain. Since the linking strength plays an important role in PCNN, we propose an adaptively fuzzy way to determine it by computing each coefficient’s importance relative to the surrounding coefficients. Combined with human visual perception characteristics, the fuzzy membership value is employed to automatically achieve the degree of importance of each coefficient, which is utilized as the linking strength in PCNN model. Experimental results on simulated and real multi-focus images show that the proposed technique has a superior performance to series of exist fusion methods.