Abstract

Images are often degraded during the data acquisition process. The degradation may involve blurring, information loss due to sampling, and various sources of noise. The purpose of image restoration is to estimate the original image from the degraded data. The present work sets forward a restoration technique for exponential dispersion noise based on Particle filtering (PF) using Hidden Markov Model. In order not to take observation information into account in general, the PF algorithm produced an incorrect sample from a discrete approximation distribution. To resolve this problem, we propose in the resampling stage of PF, samples which are generated from a continuous distribution rather than a discrete one based on Exponential Dispersion Models (EDM). An iterative approach, called the Expectation-Maximization (EM) algorithm, is used to find the maximum likelihood estimates of the relevant unknown parameters of the EDM. Moreover, under some conditions, the concavity of the conditional expected log-likelihood function is established in the maximization step of the EM algorithm. The proposed approach is rooted in ideas from statistics, control theory and signal processing. Experimental results are eventually displayed with simulation and satellite images, which demonstrate the good performance of the proposed approach.

摘要

在数据采集过程中，图像通常会退化。退化可能涉及模糊、由于采样导致的信息丢失以及各种噪声源。图像复原的目的是从退化的数据中估计出原始图像。本工作提出了一种基于使用隐马尔可夫模型的粒子滤波（PF）的指数色散噪声恢复技术。为了不考虑一般情况下的观察信息，PF 算法从离散近似分布中生成了不正确的样本。为了解决这个问题，我们建议在 PF 的重采样阶段，从连续分布而不是基于指数分散模型 (EDM) 的离散分布生成样本。一种称为期望最大化 (EM) 算法的迭代方法，用于找到 EDM 的相关未知参数的最大似然估计。此外，在某些条件下，条件期望对数似然函数的凹性是在 EM 算法的最大化步骤中建立的。所提出的方法植根于统计学、控制理论和信号处理的思想。实验结果最终通过仿真和卫星图像显示，证明了所提出方法的良好性能。