数字脊波变换及图像的稀疏表示(英文)

Digital Ridgelet Transform and Image Representation

在二维或更高维空间中,小波不能有效地表达沿边缘间断的物体。脊波变换对连续空间中沿直线奇异的函数能够进行稀疏表达。理论上的吸引力促使人们将其从连续概念转化到数字实现。本文着重比较脊波变换的几种不同数字实现及对于小波的改进。实验结果说明,脊波在对具有直线边缘的图像逼近和去噪时的确比小波有效。

In dimensions two and higher, wavelets can not efficiently represent object with discontinuities along edges. The ridgelet transform[3] was introduced as a sparse expansion for functions on continuous spaces that are smooth away from discontinuities along lines. The conceptual attractiveness of this theoretical work drives people to convert it from continuum concepts to realization for digital data. Several digital ridgelet transforms are compared in this paper. Numerical results show that ridgelet transform is more effective than the wavelet transform in approximating and denoising images with straight edges.