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小波域反卷积问题研究
其他题名Deconvolution in Wavelet Domain
曹学光
学位类型工学博士
导师彭思龙
2005-11-03
学位授予单位中国科学院研究生院
学位授予地点中国科学院自动化研究所
学位专业模式识别与智能系统
关键词反卷积 规整化 贝叶斯理论 隐马尔可夫树模型 Kalman滤波 Bivariate模型 Deconvolution Regularization Bayesian Theory Hidden Markov Tree Model Kalman Filtering Bivariate Model
摘要由于测量过程或其他技术条件的限制,观测到的信号(例如二维图像信号)往往都是降质的(例如模糊的观测图像)。反卷积的目的就是从观测到的降质信号中尽量恢复出原来未失真的信号。由于信号的降质过程往往表现为一个低通滤波过程,因而反卷积问题是一个典型的病态问题。需要通过规整化技术获取一个关于原始信号的合适稳定的估计。到目前为止,已经有许多的反卷积算法为人们所熟知,包括频率域方法,空间域方法,以及小波域等其他变换域的方法。小波域反卷积方法较之其他非小波域方法,有很多明显的优点。其中最重要的一点就是在小波域中,信号的突变点(例如图像的边缘)能够几乎完整地被保持。这是由于小波变换的时频局部性以及其他一些性质,使得基于小波变换的去噪和复原算法能够比较准确地反映信号的局部结果和性质。小波变换用于反卷积主要有两类方法:一类是小波收缩阈值;另一类则是为小波系数指定某种先验分布形式,在Bayesian反卷积理论的框架下求得原始图像的一个最大后验概率(MAP)估计。本课题分别从这两个方面研究了在小波域中图像的反卷积问题,主要有以下工作。 在深入分析频域上图像信号的降晰退化模型以及小波重构在各个尺度上的表现形式的基础上,建立了Kalman滤波的观测方程,尺度之间的状态转移方程。将最低分辨率上得到的复原结果作为多尺度Kalman滤波状态变量的初始值,然后在分解后的各个低频子带上预测矫正复原,最后得到最高分辨率上的频域复原结果,再经过傅立叶逆变换就可以得到最终的反卷积复原结果。 将Bivariate模型引入到小波域图像反卷积中,以Bivariate概率分布函数作为自然图像小波系数向量的先验模型。从图像复原的贝叶斯理论出发,提出基于Bivariate概率分布函数非抽取小波域的图像复原算法,取得了不错的效果。 由于复小波拥有移不变性和多方向选择性,且隐马尔可夫树(HMT)模型比较准确地刻画了信号小波系数的统计分布形式,所以提出了基于二元树复小波变换(DT-CWT)的复小波域隐马尔可夫树(HMT)模型的图像反卷积算法。该算法提出一种简单可行的快速算法来估计HMT模型参数。该算法较好地再现了各种边缘信息,其复原结果较之一些传统的复原方法有不同程度的提高,其运行效率较之传统的HMT模型参数估计方法有比较明显的提高。
其他摘要The observed signal (e.g. image) is often degraded (e.g. blurred image) due to the constraints of the observation and other technical conditions. The aim of deconvolution is to restore the observed to the undistorted as exact as possible. Generally speaking, the process of degrading is a process of low-pass filtering, so the deconvolution is a classical ill-conditioned problem and must be regularized to make a stable estimation of the original signal. There have been many methods of deconvolution including based on frequency-domain, space-domain, wavelet-domain and other transformation-domain. Wavelet-domain deconvolution algorithms have same outstanding advantages over other non-wavelet-domain methods. The most important one is that the singularities of signal (e.g. the edges of image) can almost be preserved during the processing in wavelet domain thanks to the time-frequency locality and other characteristics of wavelet transformation. Two classes of methods can be summarized for deconvolution in wavelet domain, one is wavelet shrinkage and the other one is MAP estimation based on Bayesian deconvolution theory. The wavelet-domain deconvolution methods in the two classes are studied in this paper including the following. An image restoration algorithm based on Kalman filtering in multi-scale space is proposed for effectively restoring blurred image. We first build the observation equation of Kalman filtering in frequency domain through the de-blurring models in each scale and the state transformation equation from the wavelet reconstruction processes in frequency domain. The Fourier Transformation of the restoration result in the lowest resolution can be regarded as the original state vector for Kalman filtering, and then process predictions and rectifications on every low-frequency sub-band until to the scale (the finest resolution). Applying the inverse Fourier Transformation on the last result can get the final restored signal. The non-Gaussian bivariate distributions can represent accurately the dependencies between the coefficients and their parents, and work well in de-noising. In this paper, the bivariate distributions model is introduced into un-decimated wavelet domain image restoration. We discuss this restoration algorithm from the view of adaptive regularization. Because complex wavelets can provide both shift invariance and good directional selectivity, and the wavelet-doamin hidden Markov tree (HMT) model can represents exactly the distributions of the wavelet coefficients, a linear image restoration algorithm based on the wavelet-domain HMT model, and a feasible, fast method to estimate the model parameters adaptively are proposed. The restoration algorithm models the prior distribution of the real-world image by wavelet-domain HMT model and converts the restoration problem to a constrained optimization one which can be solved through the steepest descend method.
馆藏号XWLW952
其他标识符200218014603192
语种中文
文献类型学位论文
条目标识符http://ir.ia.ac.cn/handle/173211/5881
专题毕业生_博士学位论文
推荐引用方式
GB/T 7714
曹学光. 小波域反卷积问题研究[D]. 中国科学院自动化研究所. 中国科学院研究生院,2005.
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