适用于尺寸为2的幂次方图像的离散ridgelet变换
doi: 10.3724/SP.J.1146.2005.00826
A New Digital Implementation of Ridgelet Transform for Images of Dyadic Length
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摘要: Ridgelet变换是继小波变换之后提出的一种新的多尺度变换，它能比小波变换更好地表达高维线性奇异性。Finite ridgelet是ridgelet变换的离散实现算法，具有和连续ridgelet变换一样精确的代数意义，并且算法复杂度低。但是finite ridgelet只适用于图像尺寸为PP(P为素数)的图像，这一点限制了它的应用范围。该文将finite ridgelet的算法进行改进，提出了一种可以适用于图像大小为NN ( N=2k, kZ)的离散ridgelet算法。该算法不仅推广了finite ridgelet的适用范围，而且简化了finite ridgelet的算法过程。Abstract: The ridgelet transform is a new directional multi-resolution transform，which is more suitable for describing signals with high dimensional singularities. Finite ridgelet transform is a discrete version of ridgelet transform, which is as numerically precise as the continuous ridgelet transform and has low computational complexity. However, finite ridgelet transform is only suitable for images of prime-pixels length, which is a limitation of its application in image processing. In this paper, an improved finite ridgelet algorithm which is suitable for images of dyadic length is proposed. This method not only expands the application of finite ridgelet, but also simplifies the algorithm.
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