关键词: 方向性小波 Ridgelet变换 非线性逼近 去噪

Abstract:

The directional wavelet theory provides a novel sparse representation method for image processing, and it can capture geometrical image structures mor e efficiently. Beginning with the characteristics of basis, the paper compares the differences between directional wavelets and traditional wavelets when approximating geometrical edges in an image. Several important theories of the field proposed in recent years are summarized, and the ridgelet transfo rm is taken as an example to explain the basic principle of the directional wavelet theory. Numerical experiments demonstrate the nonlinear approximation performance and denoising effect of directional wavelets and traditional wavelets. Finally, the paper points out the further research directions.

Key words: （directional wavelet, Ridgelet transform, nonlinear approximation, denoising）