Closed flying-gwx closed 5 months ago
The forward and inverse wavelet transform, when starting with spherical harmonic coefficients and going back to spherical harmonic coefficients, should indeed reach numerical precision. However, the spherical harmonic transforms with Healpix are highly approximate, so you'll see a large overall error if comparing signals before and after a wavelet transform in pixel space. One way to improve Healpix accuracy is to iterate the Healpix spherical harmonic transforms.
Note also that we're in the process of re-writing ssht, so3 and s2let in JAX to support GPU acceleration and automatic differentiation. This is still a work in progress but the corresponding s2fft and s2wav codes are already public.
Thanks for your reply. My statement may not be clear and let me explain my problem.
The forward and inverse spherical harmonic transform with Healpix, which starting with spherical harmonic coefficients and going back to spherical harmonic coefficients, do not reach numerical precision in spherical harmonic space. The error of 4.6795 is actually in spherical harmonic space and it is too large comparing with the paper(alound 10-6 in spherical harmonic space).
I totally understand the Healpix can result in error comparing signals before and after a wavelet transform in pixel space. However, the error is too large even in spherical harmonic space.
Hello, I want to use s2let in Healpix sampling scheme. I build the s2let with Healpix_3.82(for lib).
Here is the code in s2let_hpxtest.m I used:
Here is the output:
I read the s2let paper, the error sholud be less than 10^-6 for max(|flm - flm_rec|). My error is too large(4.6795).
s2let_hpx_alm2map
ors2let_transform_axisym_analysis_hpx
, is there any thing I missed?