方向性数字图像表示及去噪算法研究
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摘要
在目前的信号表示方法中小波变换法已被广泛接受,然而小波在高维(例如二维)应用中表现出了局限性。这是因为小波仅对零维奇异值的目标函数是最优基,在一维或更高维奇异性上,不是最优基。因此能够克服小波上述缺点的具有方向性的图像表示方法就成为人们寻求的目标。在近几年对方向性图像表示方法的研究中,脊波、曲波、Contourlet变换方法由于具有固定的变换形式和灵活的方向选择性而逐渐成为各种方向性图像表示中的佼佼者。
本文首先对这些变换方法进行详细地研究和讨论,包括原理、构造方法、性能、应用领域等。在此基础上,开发了简化计算的小波基矢量构造方法,并将其应用于改进的有限域脊波变换;在对Contourlet方向滤波器的研究中,结合全相位数字滤波,通过构造方向模板以及图像扭转和风扇滤波迭代的方法,得到了两种新型的方向滤波器组。这两种全相位方向滤波器组不对图像下采样,保留了图像方向的细节信息,具有更好的方向选择性能且在恢复时,不需要重建滤波,方法简单;在对Contourlet变换的分级研究中,建立了一种全相位分级方法,由于全相位子带分解的优异性能,使得这种分级方法优于拉普拉斯金字塔分级方法。将全相位分级方法同全相位方向滤波器相结合,形成了一种新型的全相位Contourlet离散变换。
本文研究了方向性表示方法在图像去噪中的应用。首先,总结了各种图像去噪的方法,重点介绍了小波去噪的各种算法。通过比较各种图像表示方法的图像去噪效果,得到了有意义的结论,即本文提出的改进有限域脊波变换方法适用于具有直线特征的图像去噪,而全相位Contourlet在对自然图像,尤其是细节较多图像去噪上性能优异。
Among the present image representations, wavelet transformation has been adopted widely. However, in high dimensions (such as two dimensions), wavelets expose an inherent limitation. It is because wavelets are optimal bases in catching zero-dimension singularities but not for one-dimension or higher dimensions singularities. This disappointing behavior indicates that more powerful directional image representations are necessary in higher dimensions. In recent researches about directional image representations, Ridgelet, Curvelet and Contourlet gradually are accepted for their fixed transforms and flexible directional image expansions.
In this dissertaion, firstly the above transformation methods are studied in detail, including theories, construction methods, performances, application fields and so on. During the process of research, this dissertation has developed wavelet base vectors to simplify the computation and has proposed the improved finite ridgelet; Then based on the directional filter bank of Contourlet and All phase digital filters, tow construction methods of the novel all phase directional filter banks (APDFB) are acquired respectively by constructing directional templates or by rotating images and iterating fan filters. Not considering subsample, these two filter banks retain more image details and better direction selectivity. As to the image reconstruction, the original image can be obtained only by adding all directional images and reconstruction filter is unnecessary; Furthermore, an all phase multiscale decomposition method is proposed to substitute the Laplacian pyramid applied in the original Contourlet. To combine it with APDFB, a novel all phase Contourlet discrete transform is accomplished.
Finally this dissertaion summarizes all sorts of image denoising methods and provides the results and comparisons of all denoising methods. The conclusion is that improved finite ridgelet transform adapts to denoise images with linear singularitiesand All phase Contourlet has excellent performances in denoising natural images especially those with more details.
本文首先对这些变换方法进行详细地研究和讨论,包括原理、构造方法、性能、应用领域等。在此基础上,开发了简化计算的小波基矢量构造方法,并将其应用于改进的有限域脊波变换;在对Contourlet方向滤波器的研究中,结合全相位数字滤波,通过构造方向模板以及图像扭转和风扇滤波迭代的方法,得到了两种新型的方向滤波器组。这两种全相位方向滤波器组不对图像下采样,保留了图像方向的细节信息,具有更好的方向选择性能且在恢复时,不需要重建滤波,方法简单;在对Contourlet变换的分级研究中,建立了一种全相位分级方法,由于全相位子带分解的优异性能,使得这种分级方法优于拉普拉斯金字塔分级方法。将全相位分级方法同全相位方向滤波器相结合,形成了一种新型的全相位Contourlet离散变换。
本文研究了方向性表示方法在图像去噪中的应用。首先,总结了各种图像去噪的方法,重点介绍了小波去噪的各种算法。通过比较各种图像表示方法的图像去噪效果,得到了有意义的结论,即本文提出的改进有限域脊波变换方法适用于具有直线特征的图像去噪,而全相位Contourlet在对自然图像,尤其是细节较多图像去噪上性能优异。
Among the present image representations, wavelet transformation has been adopted widely. However, in high dimensions (such as two dimensions), wavelets expose an inherent limitation. It is because wavelets are optimal bases in catching zero-dimension singularities but not for one-dimension or higher dimensions singularities. This disappointing behavior indicates that more powerful directional image representations are necessary in higher dimensions. In recent researches about directional image representations, Ridgelet, Curvelet and Contourlet gradually are accepted for their fixed transforms and flexible directional image expansions.
In this dissertaion, firstly the above transformation methods are studied in detail, including theories, construction methods, performances, application fields and so on. During the process of research, this dissertation has developed wavelet base vectors to simplify the computation and has proposed the improved finite ridgelet; Then based on the directional filter bank of Contourlet and All phase digital filters, tow construction methods of the novel all phase directional filter banks (APDFB) are acquired respectively by constructing directional templates or by rotating images and iterating fan filters. Not considering subsample, these two filter banks retain more image details and better direction selectivity. As to the image reconstruction, the original image can be obtained only by adding all directional images and reconstruction filter is unnecessary; Furthermore, an all phase multiscale decomposition method is proposed to substitute the Laplacian pyramid applied in the original Contourlet. To combine it with APDFB, a novel all phase Contourlet discrete transform is accomplished.
Finally this dissertaion summarizes all sorts of image denoising methods and provides the results and comparisons of all denoising methods. The conclusion is that improved finite ridgelet transform adapts to denoise images with linear singularitiesand All phase Contourlet has excellent performances in denoising natural images especially those with more details.
引文
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