Ridgelet transform, curvelet transform, contourlet transform, bandelet transform, wedgelet transform, beamlet transform, etc. are collectively referred to as X-let multiscale Geometric analysis tools, which enable efficient sparse representation of images. Taking the contourlet transform as an example, it can represent the edge contour of an image with a strip base that is sparser than the wavelet transform, and can generate more directional subbands at the same scale (compared to the discrete wavelet transform, which only has three detail subbands), so the expression of image components is finer than wavelet transform.

 

The multi-scale geometric analysis is used to realize image enhancement. Firstly, the image is decomposed in multi-scale and multi-direction, and then each sub-band coefficient is enhanced by an enhancement operator. Finally, the enhanced image is obtained by corresponding inverse transformation.