Wavelet Ridgelet Curvelet Contourlet Ripplet

Ripplet: A New Transform for Image Processing

Jun Xu, Lei Yang and Dapeng Wu

Ripplet: A New Transform for Feature Extraction and Image Representation

Dr. Dapeng Oliver Wu

Department of Electrical and Computer Engineering, University of Florida

傅里叶变换 使 微分方程 变为 代数方程，便于运算；变到频率域 分清主次 用于 压缩。

越变 会产生 无穷多的频率

Fourier transform —— Gibbs phenomenon

Wavelet transform can resolve 1-D singularities, but it can not resolve 2-D singularities

Ridgelet [Candes and Donoho] Resolve 2D singularities along lines

Curvelet [Candes and Donoho] Resolve 2D singularities along curves

parabolic scaling，不同于rotated 2D wavelet（各向同性）。

Contourlet [Do and Vetterli] Resolve 2D singularities along curves

Ripplet: Blocks with arbitrary shape and size, not good at 纹理