The contourlet transform  is considered as a true 2D representation of images. It uses a long strip base with directional and anisotropic support intervals that changes with the scale to approximate the image, making it more "sparse" than the wavelet base that lacks directionality when capturing the segmented quadratic continuous curve in the image. That is, the energy of the coefficients is more concentrated, and the expression of structures such as image edges is more effective.

 

The non-sub-sampled contourlet transform (NSCT)  provides better orientation decomposition properties than the contourlet transform. As shown in Figure 2.10, based on non-sub-sampled pyramid filter banks (NSPFB) and non-sub-sampled directional filter banks (non-sub-sampled directional filter banks, NSDFB), NSCT first decomposes the image It is a two-dimensional low-frequency sub-band and a two-dimensional band-pass sub-band, and then the band-pass sub-band is decomposed in multiple directions through the fan and quadrant filters in NSDFB; the low-pass sub-band uses NSPFB to continue to the next level of scale decomposition, so Repeatedly, obtain multi-layer decomposition. Because there is no sampling link in the tower decomposition process, spectral aliasing is eliminated, and the subband image with the same size as the source image is obtained after decomposition. Combined with many excellent properties of NSCT, this section discusses a thermal infrared image denoising method based on NSCT and combined with the aforementioned Self-Snake model.