2-D bandpass

Figure 2 shows a the wavelet transform of a 2-D seismic image. The 1-D decomposition algorithm was applied along each dimension. Wavelengths progress from DC in the upper left to Nyquist in the lower right. The impression is of replicated images on a warped checkerboard. This is similar to the results of Mallat (1989).

Figure 3 show successive pass bands of the reconstructed seismic image. The logarithmic scaling of basis wavelengths seems too coarse for precision filtering. Also there are annoying, but computationally correct, discontinuities in the bandpassed image due to the roughness of the half-cycle square-wave function. It is suspected that alternative wavelet families appear better.

 

Figure 3: Bandpass filtering of Figure 2a image. The pass separation is two octaves from Nyquist laterally and one octave vertically.