Self-invertible 2D log-gabor wavelets
Self-invertible 2D log-gabor wavelets
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DOI：
10.1007/s11263-006-0026-8
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发表时间：
2007-11-01
影响因子：
19.5
通讯作者：
Sroubek, Filip
中科院分区：
文献类型：
--
作者：
Fischer, Sylvain;Sroubek, Filip
正交和双正交小波成为非常流行的图像处理工具，但表现出主要的缺点，即在方向上的分辨率差和缺乏平移不变性，由于子带之间的混叠。已经提出了专门解决这些缺点的替代多分辨率变换。这些变换通常是过完备的，因此在其设计中提供了很大的自由度。同时，它们的优化也是一项具有挑战性的任务。我们建议在这里的建设，允许准确的重建和加强优秀的数学性能的Gabor滤波器的对数Gabor小波变换。对已有的Gabor小波变换方案提出了两个主要改进：第一，用窄局部化方向滤波器覆盖最高频带;其次，滤波器的集合均匀地覆盖包括最高和最低频率的傅立叶域，并且因此在直接变换和逆变换两者中使用相同的滤波器来实现精确的重构（这意味着变换是自可逆的）。本变换不仅实现了重要的数学性质，它还尽可能多地遵循初级视觉皮层（V 1）的简单细胞的感受野特性和自然图像的统计学知识。与现有技术相比，log-Gabor小波表现出优异的能力，分离图像信息（例如，对比度边缘）从空间不相干的高斯噪声通过硬阈值，然后表示图像特征，通过一组减少的大幅度系数。这些特性使得变换成为处理自然图像的一个很有前途的工具。
Orthogonal and biorthogonal wavelets became very popular image processing tools but exhibit major drawbacks, namely a poor resolution in orientation and the lack of translation invariance due to aliasing between subbands. Alternative multiresolution transforms which specifically solve these drawbacks have been proposed. These transforms are generally overcomplete and consequently offer large degrees of freedom in their design. At the same time their optimization gets a challenging task. We propose here the construction of log-Gabor wavelet transforms which allow exact reconstruction and strengthen the excellent mathematical properties of the Gabor filters. Two major improvements on the previous Gabor wavelet schemes are proposed: first the highest frequency bands are covered by narrowly localized oriented filters. Secondly, the set of filters cover uniformly the Fourier domain including the highest and lowest frequencies and thus exact reconstruction is achieved using the same filters in both the direct and the inverse transforms (which means that the transform is self-invertible). The present transform not only achieves important mathematical properties, it also follows as much as possible the knowledge on the receptive field properties of the simple cells of the Primary Visual Cortex (V 1) and on the statistics of natural images. Compared to the state of the art, the log-Gabor wavelets show excellent ability to segregate the image information (e.g. the contrast edges) from spatially incoherent Gaussian noise by hard thresholding, and then to represent image features through a reduced set of large magnitude coefficients. Such characteristics make the transform a promising tool for processing natural images.