Dept. de Engenharia Electrotecnica e de Comput., Inst. Superior Tecnico, Lisbon.
IEEE Trans Image Process. 1994;3(6):789-801. doi: 10.1109/83.336248.
Sequential and parallel image restoration algorithms and their implementations on neural networks are proposed. For images degraded by linear blur and contaminated by additive white Gaussian noise, maximum a posteriori (MAP) estimation and regularization theory lead to the same high dimension convex optimization problem. The commonly adopted strategy (in using neural networks for image restoration) is to map the objective function of the optimization problem into the energy of a predefined network, taking advantage of its energy minimization properties. Departing from this approach, we propose neural implementations of iterative minimization algorithms which are first proved to converge. The developed schemes are based on modified Hopfield (1985) networks of graded elements, with both sequential and parallel updating schedules. An algorithm supported on a fully standard Hopfield network (binary elements and zero autoconnections) is also considered. Robustness with respect to finite numerical precision is studied, and examples with real images are presented.
提出了一种基于神经网络的序贯和并行图像恢复算法及其实现方法。对于由线性模糊和加性高斯白噪声污染的图像，最大后验（MAP）估计和正则化理论导致相同的高维凸优化问题。在使用神经网络进行图像恢复时，常用的策略是将优化问题的目标函数映射到预定义网络的能量中，利用其能量最小化特性。从这个方法出发，我们提出了迭代最小化算法的神经实现，这些算法首先被证明是收敛的。所开发的方案基于改进的 Hopfield（1985）分级元素网络，具有序贯和并行更新方案。还考虑了基于全标准 Hopfield 网络（二进制元素和零自连接）的算法。研究了对有限数值精度的稳健性，并给出了真实图像的例子。
