【作者】 徐鑫；

【导师】 田逢春；

【作者基本信息】 重庆大学 ， 电路与系统， 2009， 博士

【摘要】 小波分析是继傅立叶分析之后又一经典的信号分析工具,被广泛应用于各种信号处理领域中。其中的二维多方向小波——多尺度几何分析是目前的研究热点,因为其多尺度,多方向的良好稀疏分解能力,在二维图像信号处理领域中被寄予厚望。在图像噪声抑制领域,目前有一系列的多尺度几何分析变换域处理方法,比如经典的阈值收缩降噪、层间相关性降噪等基于图像信息物理特性模型的处理方法,以及隐马尔可夫树模型、广义逆高斯模型等基于图像变换系数统计假设模型的处理方法。这些方法的特点是,经典的物理特性模型主要对能量、幅值进行考察,但这些物理性能并不一定与图像的几何特性很好地对应,常有过度扼杀图像信息的趋势;而统计假设模型与图像信息的物理对应关系还有待进一步研究,而且其中有较多的参数和先验条件设置,这限制了其在实践中的应用。总的说,寻找更符合实际图像信号几何或者视觉性能的系数模型和算法参数是目前多尺度几何分析域噪声抑制技术发展的研究热点之一。相干光图像处理系统基于傅立叶光学原理,用光来实现图像的数值计算处理,比如经典的4f光学系统(或者叫组件),它具有并行、处理量大的优势,是信息光学的一大发展方向。目前,相干光图像处理领域处于已经能构建出多种不同功能和针对性的系统,但性能还有待进一步提高的阶段。其一,目前的光电转换器件还大都是串行逐像素点处理形式,这限制了整个光路的并行处理能力的发挥,是相干光图像处理系统的瓶颈问题之一。其二,从图像质量角度讲,傅立叶透镜的低通特性给系统图像带来了一定的低通滤波效果,这要求处理图像时比其他场合更侧重保护图像细节信息;同时,在这类光程较近的相干光系统中,由于光源的强相干性,使得系统图像中除了常见的随机噪声外,还有特殊的低频相干噪声,这也限制了相干光图像处理系统的发展,同样需要解决。本文主要从信号处理角度出发,着眼于这类相干光系统中图像的噪声抑制技术的研究,其中对图像细节的保护和对低频段噪声的处理则是本文研究内容的特色。总之,研究多尺度几何分析技术用于相干光系统图像的噪声抑制中的应用,有具体的应用背景,既能发展多尺度几何分析噪声抑制技术,又能改善相干光图像系统质量,具有相应的理论和实用价值。本文的具体工作是:①噪声的方差估计是随机噪声分析中的重要问题之一,其基本思想是通过某种方法寻找含噪图像中的“纯”噪声子图像来估计原噪声方差。传统的方法是通过空频域采样,得到子噪声图像,然后直接对其估计方差,它在图像高频信息丰富的场合中常常会受到干扰。本文在Donoho提出的传统频域采样方法的基础上,提出一种基于图像二维小波变换系数层间相关性的新方法。其过程是:对第一级有效小波分解的斜向子块进行分析,利用小波变换系数的层间相关性,寻找其中的图像信息,并将其排除,得到更“纯”的子噪声块,将剩下的噪声系数重组并估计其方差,逼近原噪声参数。仿真实验和实际4f系统输出图像实验都符合理论分析,实验结果中该方法比传统方法的估计结果更准确,能提高准确度4%～6%,适合需要侧重保护图像细节信息的场合。参考实际系统图像数据,对4f相干光系统图像误差进行了分析,为噪声抑制提供先验知识。指出了其低通带宽背景下,随机噪声和低频相干噪声并存的误差特点;进而分析了其带限低通性能;分析了随机噪声的高斯零均值分布特性,并引入层间相关性方法估计噪声方差;分析了低频相干噪声的产生原因和它与点扩散函数以及SAR图像中的乘性相干斑的区别,并指出其固定位置,相同形式的分布特性,为后期校正提供了先验基础。②针对需要侧重保护图像细节的降噪处理场合,提出一种基于图像细节几何连续性模型的稀疏分解域图像去噪方法。在传统Donoho能量模型阈值收缩方法基础上,首先对稀疏分解的高频子带图像用一个衰减的阈值去除小幅值噪声点,以更多的保护图像细节并凸显剩下的大幅值噪声点的孤立性,再利用击中击不中原理,设定相应的结构元素,考察图像细节几何连续性和剩下的大幅值噪声点孤立性的区别以分离剩下的图像细节和噪声点,在实现去噪的同时更好地保护图像细节。常见图像和SAR图像的曲线波和非下采样轮廓波变换域仿真实验结果符合理论分析,该方法在去噪方面可以达到与传统方法相当的程度,同时在保护图像细节方面有更优的表现,视觉效果边缘更清晰,峰-峰信噪比有0.5~1db的提高,结构相似度指数有3%到5%的提高。在实际图像实验中,该方法实现过程简便,可以灵活选择模型的形状,而且模型与图像本身几何信息对应关系强,适合于需要侧重保护图像细节的降噪场合。4f系统输出图像存在带限低通、随机噪声和低频相干噪声并存的特点,这要求对其做复原处理时要比平常情况在细节保护方面的难度更大,而且不仅要处理常见的随机噪声,还要处理这类近距离相干光图像中的低频相干噪声。针对这些特点,本文提出一种处理方法:先利用系统的阶跃响应获取相干噪声的位置和形式的先验信息,然后对阶跃响应图像和待处理图像分别用同样过程和参数的、结合图像细节几何连续性模型的NSCT域去噪方法处理随机噪声,再利用4f系统线性特性将两幅去除随机噪声后的图像进行点除以去除相干噪声,完成降噪。实际实验中,该方案从峰-峰信噪比、结构相似度指数和视觉效果方面都有很好的复原效果,分别有5db和6%左右的提高,从视觉上看,该方法能很好地保护图像细节,符合系统的要求。与常用稀疏分解域高频子带降噪方法相比,该方法能更好地保护图像细节并同时处理随机和低频噪声。而且还突出体现了相干光图像处理系统并行处理图像的特色。③针对重复采集含随机噪声的固定目标图像场合,为降噪时更好地保护图像细节信息,设计了一种重复采集图像融合的降噪方法。该方法利用噪声在“时间”意义上的随机性,对重复采集的各图像同一位置上的像素点进行融合处理,进行降噪。具体流程是先对融合图像进行NSCT分解,在其高频子图中用各像素点的邻域方差模型描述其中的噪声情况,再按照“取小”原则调整该点的融合权值;在低频子图中,则用方差均值积考察噪声情况,调整融合权值,最后用重复采集图像的融合实现时域累计平均降噪。实验结果符合理论分析,能有效抑制随机噪声,并且在理论上是对图像无损的。将该方法引入4f系统图像降噪处理中,提出一种基于多谱点图像融合的相干光图像处理系统降噪方法。先利用系统中的数字采样器件的的信号复制功能,在同一次试验平台中获取多个谱点图像,其中各图像包含有相同的图像信息和同分布规律但不同数值形式的噪声信息。再对其做NSCT分解,高频子图中考察方差模型调整融合权值,以消除随机噪声;低频子图中针对相干噪声的特性,改为考察方差模型,并用多极权值融合,以削弱相干噪声。最终实现对图像无损前提下,既处理随机噪声又处理低频段相干噪声的目的。实验结果与理论分析吻合。该方法对噪声时间意义上的随机性的利用,突出的体现了4f系统空间换时间的思想;由于不在图像平面坐标上做运算,所以对图像理论上是无损的,这是其他单幅图像中的噪声抑制技术所没有的优点,可以说是对图像融合技术应用的一种扩展。更多还原

【Abstract】 Wavelet analysis is the most successful signal processing technology after Fourier analysis, and it has been applied in many areas. The multiscale geometric analysis is a new focus in recent years and has great potential in image processing because of its’multi-scales and multi-directions decomposition capability. In image denoising, there are many methods in multiscale geometric analysis transform domain, such as methods based on physics models such as the energy model and inter-scale correlation model and methods based on statistical models like the hidden Markov tree model and inverse Gaussian distributions model. But the methods based on physics models study the energy or values of images and noise coefficient which sometimes can not be consistent with the image detail well enough, so that they will damage the image detail. And the statistical models whose corresponding relation to image details still needing to be studied have many parameters and priori limitations for application. In brief, now denoising method in multiscale geometric analysis transform domain still needs to be studied, and the key problem is to find more suitable denoising models and optimize the parameters and algorithms.Coherent optic image processing systems such as the 4f optic system which is based on the Fourier optic theory calculate the image data by optic way. It is a potential subject in information optics for its advantage of parallel processing. Now, researchers can construct many systems for different applications which are sometimes not precise enough. Firstly, current photoelectricity switch devices still process image pixels serially which limit the parallel processing of the whole system. Furthermore, in view of the quality of output images, many problems should be studied. The low-pass band of Furieour lens limits the band width of the output images which require more attention on protection of the useful details when enhancing the noised images. And in such near field coherent optical system, because of the coherent character of lasar, there is not only random noise, but also some low frequency coherent noise in the output images. These make the denoising in coherent system images a diffirent work to the current denoising processing in digital images. This thesis will focus on the second problem——noise reduction, and the protection of the image details and removing of the low frequency noise are excellency of the thesis.Research on the image denoising methods in multiscale geometric analysis area is the work based on advancing signal processing theory and focusing on practically application. It can expand the image denoising technology in multiscale geometric analysis area and also improve the quality of the practical coherent optic image system. It is significant both in theory and practice.The main works of this thesis are:①Variance estimation is an important problem in random noise analysis. The basic idea is to get a sub-image which includes“pure”noise to estimate the variance of the original noise. The traditional method is to obtain the sub-image by sampling the noisy image in spatial or frequency domain, then calculate its variance to replace that of the original noise. It has some limitation when the image has plenty of high frequency details. Based on the traditional frequency sampling method, a new method is proposed. Firstly, choose the first effective oblique high sub-image in 2-D wavelet transform domain as the sub-noise image. Then wipe off the useful image information in it by using the inter-scale correlation to get more“pure”noise sub-image and estimate its variance. Simulation experiments of the real 4f system consistent with the theoretical analysis. The experiment results show that the new method is about 4%～6% more accurate than the traditional method. It is more suitable for the images outputting from a low-pass bandwidth system or images full of details.To get the pre-knowledge for post-correction, according to the real system images, the system error of the 4f coherent optic system is analyzed. The coexistence of low pass error, additional random noise and low frequency coherent noise is indicated. The calculation of low-pass error is deduced; the zero mean Gaussian distribution of random noise is analyzed and its’variance is estimated by the method based on the inter-scale correlation; the original of low frequency coherent noise is indicated, its feature differ from the point-spread function and coherent speckle noise in SAR images is analyzed, and its distribution of stable location and figuration is pointed out. These provide the basis of post-correction.②To remove the noise and protect the image detail better, a geometric continuity based method is proposed. Different with the classic Donoho threshold shrink denoising method in sparse decomposition domain, it adopts a smaller threshold to remove the small amplitude noise to protect the image detail more and protrude the isolation of remnant big amplitude noise, then it uses the hit-or-miss option and corresponding structure element to identify the continuity of image texture to remove the large amplitude isolated noise from the consecutive image detail in the high-frequency sub-band images. Eventually the noise is removed while the image detail is protected. Experiments of routine images and SAR images in curvelet and NSCT domain answer to the theory. Experiment results show that the method can reach the same degree with classic methods in denoising, and is better than classic threshold shrink method in protecting image detail in view of vision and numerical judgment standard (about 0.5~1db of PSNR and 3%~5% of SSIM). It is more suitable for the situation which needs to protect image details extraordinarily.Limited frequency band, random noise and coherent noise feature the conventional 4f information optics system images. The features demand protecting details better when restore those images. Besides, not only the random noise, but also the coherent fringes in low frequency domain should be removed. According to these characters, a new method is proposed to restore 4f system images. Firstly, prior knowledge of the coherent noise is obtained from the step response image of the 4f system. Then the step response and pending image are processed to remove the high frequency random noise in NSCT domain by the method based on geometric continuity with the same parameters. Lastly, based on the linear character of the 4f system, the pixel value of step response image is used from point to point to remove the coherent noise. Experimental results show that the method can restore the image and protect its detail well in view of PSNR (5 dB improved), SSIN (6% improved) and vision. Compared with the current denoising methods in sparse decomposition domain, this method can protect image details better and remove the low frequency noise, furthermore, the use of the step response image reflects the advantage of parallel processing of the 4f system.③For the situation that repeatedly capturing the same object with random noise, to remove the noise and protect image details well, a denoising method based on the fusion of images captured repeatedly is proposed. Taking the random characteristic of noise, it fuses the pixels at the same location of different images to reduce the noise in the way similar to the weighted averaging method. Firstly, the images are decomposed into sub-images in the NSCT domain. In high frequency sub-images, the variance model in neighborhood of corresponding pixels of different images is used to describe the noise density and to modify the fusion weight. In low frequency sub-images, the product of variance to the mean in neighborhood is studied to modify the fusion weight. Lastly, the noise is reduced by the fusion with the similar ideas of the weighted average denoising method, and it is perfect harmless to the image details in theory.By this way, a method based on fusion of multi-spectrum images is proposed. Firstly the multi-spectrum images of experiment based on the image copying character of spatial light modulators are collected. These images contain the same useful image information and noise with similar distribution but different values. Then these images are decomposed into the NSCT domain. The variance in neighborhood is compared to modify the fusion weights in high frequency sub-images so as to remove the random noise. In low frequency sub-image, the neighborhood variance is also studied to modify the multi-level fusion weights to weaken the coherent noise. Lastly, the multi-spectrum images are fused to reduce the random and coherent noise without image distortion. The experiments answer to the theory. The use of the random characteristic of noise in the averaging on time incarnates the idea of exchanging the time domain with space domain. Because it dose not make any calculation on single image plane, it well not change the structure of the image, for which the other denoising methods can not do. It expands the application of image fusion technologies.更多还原