3D Data Denoising and Inpainting with low redundancy 3D Fast Curvelets

 

1/ Concept

3D Fast curvelets are implemented as a tiling of Fourier space as shown in Figure 1, and provide atoms which are plate-like, and oscillating in the normal direction. These atoms are localized in space, scale and orientation, and provide a good approximation of surfaces in a 3-D volume. Figure 2 shows a 3-D fast curvelet atom and its Fourier transform.

The main difference between the original implementation of 3D fast curvelets (L. Ying et al) and the proposed ones is the change of the radial filters. Figure 3 shows the 1D filters and the effect on a 2D paving for both Curvelab and the proposed implementation.

Fig. 1 - Tiling of the Fourier space

Fig. 2 - 3D curvelet atom and its Fourier transform

Fig. 3 - 1D filters and their impact on the 2D paving for both Curvelab (left) and the proposed method