Wavelets

Ive added some -vf uspp (PP by (mis)using the snow codec) based images to pp vs. spp filters, the reason for uspp=6 instead of higher values is that higher ones wake the OOM-killer :-) the reason for the lack of pp=ac/ha/va based samples is that they look identical to the pp=de/hb/vb

The default wavelet used by the snow codec in ffmpeg is a symmetric biorthogonal compact 9/7 wavelet with rational coefficients with properties very similar to the famous biorthoginal daubechies 9/7 wavelet, it was found by bruteforce search with the goal of having a simple lifting implemenattion and having many vanishing moments or almost vanishing moments, the daubechies wavelet has (4,4) our wavelet has (4,2) vanishing moments
The lifting coefficients are:

dau97 snow
-0.443506852 -15/32
-0.882911075 -4/5
0.052980118 1/16
1.586134342 3/2

The resulting wavelet and scaling functions look like:

One thing which is still annoying is the 4/5, while this can be approximated pretty well by a multiplication and a shift right but this tends to overflow so something like

x += x+x;
x += x>>4;
x += x>>8;
x >>= 2;

is needed, this one only differs from 4/5 by a factor of ~0.00001, alternatively the 4/5 can be merged into the unquantization step so that

\ | /|\ | /|\ | /|\ | /|\
 \|/ | \|/ | \|/ | \|/ |
  +  |  +  |  +  |  +  |   -15/32
 /|\ | /|\ | /|\ | /|\ |
/ | \|/ | \|/ | \|/ | \|/
  |  +  |  +  |  +  |  +   -4/5
\ | /|\ | /|\ | /|\ | /|\
 \|/ | \|/ | \|/ | \|/ |
  +  |  +  |  +  |  +  |   +1/16
 /|\ | /|\ | /|\ | /|\ |
/ | \|/ | \|/ | \|/ | \|/
  |  +  |  +  |  +  |  +   +3/2
is changed to
\ | /|\ | /|\ | /|\ | /|\
 \|/ | \|/ | \|/ | \|/ |
  +  |  +  |  +  |  +  |   -3/8
 /|\ | /|\ | /|\ | /|\ |
/ | \|/ | \|/ | \|/ | \|/
 (|  + (|  + (|  + (|  +   -1
\ + /|\ + /|\ + /|\ + /|\  +1/4
 \|/ | \|/ | \|/ | \|/ |
  +  |  +  |  +  |  +  |   +1/16
 /|\ | /|\ | /|\ | /|\ |
/ | \|/ | \|/ | \|/ | \|/
  |  +  |  +  |  +  |  +   +3/2

Now lets compare quality between the snow and daubechies 9/7 wavelets, this comparission has been done with JasPer with this change and tinypsnr (from ffmpeg) The used test image was the 256×256 lena grayscale image

Daubechies 9/7 wavelet Snows 9/7 wavelet
size PSNR
618 24.02
1283 27.32
3194 31.80
6503 36.82
13079 42.93
22945 47.14
size PSNR
622 24.03
1295 27.33
3212 31.82
6519 36.83
12981 42.87
22941 47.18