The seislet transform has found successful applications in noise attenuation Fomel and Liu (2010); Chen et al. (2014b). However, the successful application of the seislet transform in iterative interpolation, especially in the industry, is not reported often. One of the drawbacks that impede the wide application of seislet based interpolation is the efficiency. The seislet transform itself does not slow down the efficiency too much. However, the slope estimation that is required by the seislet transform is much slower. The efficiency of seislet transform is about 2-4 times slower than the fast Fourier transform, and is about 4-8 times slower than the fast wavelet transform Fomel and Liu (2010). In order to accelerate the process, the slope estimation is commonly estimated every several iterations.
In Gan et al. (2015), the slope estimation is iterated every 5 iterations. Even though, the computational cost is still much heavier than the widely used Fourier transform. In this letter, the one-step slope estimation from velocity-slope transformation (shown in equation 4) can greatly improve the efficiency by reducing numerous cost in iterative slope estimation. According to the performance of the synthetic example in the letter, the more accurate slope can even make the finally reconstructed data more accurate. Thus, the utilization of velocity-slope transformation in seislet-based interpolation could be of a huge influence on promoting the wide application of seislet based interpolation approach in the industry.