Zerotree Coding Toolbox (v1.21)
Image compression based on wavelets, using zerotrees of wavelet coefficients. Uses Wavelet and Quality Assessment toolboxes. The SPIHT binaries required for function spspiht.m can be downloaded from the SPIHT image compression homepage, see below.
Functions
This toolbox consists of the following functions:
- dead_zone_q - Quantisation with a central dead-zone around zero
- ezw - EZW (Embedded Zerotree Wavelet) image compression
- pdf_opt - Optimisation (pdf) of reconstructed values of quantised wavelet coefficients
- spiht_stream_dec - Performs decoding of the bitstream produced by spiht_wpackets.m
- spiht_wpackets - SPIHT image compression using Wavelet Packets (WP) decomposition
- spspiht - Script for batch execution of DOS SPIHT binaries
Useful links:
- SPIHT image compression homepage - DOS SPIHT binaries required for function spspiht.m are available at this address.
- Agnieszka Miguel, teaching notes - An excellent step-by-step tutorial on EZW and SPIHT algorithms.
SPIHT algorithm flow-chart:
Examples
spiht_wpackets (with dyadic DWT, as in original SPIHT):
>> [Arec,bitstream,PSNR]=spiht_wpackets('Lena512.png',[0.1 1],'CDF_9x7',6);
6 decompositions, 0 packet depth, CDF_9x7 wavelet, highest bitrate 1.000000 bpp
Image transformed in 1.05 seconds
Maximum magnitudes computed in 0.56 seconds
SPIHT algorithm...
1. bitrate - 0.099995 bpp
No. output bits - 26216(3277 bytes; 3 excess bits)-> 0.100006 bpp
MSE (Mean Squared Error)= 68.231052
PSNR (Peak SNR)= 29.790983 dB
2. bitrate - 0.999996 bpp
No. output bits - 262144(32768 bytes; 1 excess bits)-> 1.000000 bpp
MSE (Mean Squared Error)= 6.535866
PSNR (Peak SNR)= 39.977772 dB
...LIS (checking children) loop out - completed in 14.47 seconds
Statistics collected during encoding ('bpc' stands for 'bits per significant coefficient') :
LIP loop LIS loop Total significant
pass(start bit) bits/coeffs. bits/coeffs. coeffs.(LSP start bit)
1.( 52) 65/1 =65.00 bpc 64/0 = Inf bpc 1( 181)
2.( 181) 81/18 = 4.50 bpc 89/5 =17.80 bpc 24( 351)
3.( 352) 67/12 = 5.58 bpc 246/32 = 7.69 bpc 68( 665)
4.( 689) 150/39 = 3.85 bpc 749/111 = 6.75 bpc 218( 1588)
5.( 1656) 362/80 = 4.53 bpc 1650/235 = 7.02 bpc 533( 3668)
6.( 3886) 927/237 = 3.91 bpc 4549/624 = 7.29 bpc 1394( 9362)
7.( 9895) 2512/621 = 4.05 bpc 9202/1334 = 6.90 bpc 3349( 21609)
8.( 23003) 5424/1489 = 3.64 bpc 17931/2677 = 6.70 bpc 7515( 46358)
9.( 49707) 10719/2998 = 3.58 bpc 33035/5101 = 6.48 bpc 15614( 93461)
10.( 100976) 20709/5739 = 3.61 bpc 68089/10551 = 6.45 bpc 31904( 189774)
11.( 205388) 45154/12562 = 3.59 bpc 11602/2519 = 4.61 bpc 46985( 0)
Total:
147206/23189 = 3.62 bpc 86170/23189 = 6.35 bpc 46985
pdf_opt:
The following example uses functions from Wavelet and Quality Assessment Toolboxes. It demonstrates that using the pdf-optimised reconstruction of quantised wavelet coefficients a meagre improvement of ~0.02 dB can be expected on high bit-rates.
>> D=dwt_dyadic_decomp('Lena256.png','CDF_9x7',6);
>> qstep = 4; %quantisation step is 4
>> Dq = dead_zone_q(D,qstep);
>> Drec_opt = pdf_opt(Dq,qstep);
>> iq_measures(idwt_dyadic_recon(Dq,'CDF_9x7',6),'Lena256.png',1,1);
MSE (Mean Squared Error)= 2.556086
PSNR (Peak SNR)= 44.055048 dB
>> iq_measures(idwt_dyadic_recon(Drec_opt,'CDF_9x7',6),'Lena256.png',1,1);
MSE (Mean Squared Error)= 2.544909
PSNR (Peak SNR)= 44.074081 dB
spspiht:
>> [Arec,bitstream,PSNR]=spspiht('Lena512.png',[0.1 1],'fast');
Number of bits = 262160(32770 bytes, 1.0001 bpp)
1. bitrate - 0.1000 bpp
MSE (Mean Squared Error)= 67.644821
PSNR (Peak SNR)= 29.828458 dB
2. bitrate - 1.0000 bpp
MSE (Mean Squared Error)= 6.532291
PSNR (Peak SNR)= 39.980148 dB
Total execution time - 0.84 seconds
ezw:
>> ezw('ezw_testdata1.mat',2,2,'CDF_9x7');
Image ezw_testdata1.mat, 2 decompositions, CDF9_7 wavelet, bitrate 2.000000 bpp
Example matrix:
55 42 24 -28 6 16 0 3 1 8 1 8
31 48 22 29 2 6 0 2 -8 2 -8 2
25 -21 26 20 6 18 2 7 -9 4 -9 4
1 0 29 18 16 10 5 3 1 2 1 2
17 2 7 -16 6 3 -4 6 1 0 7 0
13 -9 16 15 1 7 7 9 7 0 7 0
-18 0 1 2 6 -3 5 5 -7 8 -7 8
10 2 0 8 -1 9 5 9 6 3 6 3
1. pass
p z z z z z t t t t t t t t t t t t t t t t t t
1
2. pass
z p z z z z t t t t t t p t t t t t t t t t t t t t t t
100
3. pass
z z z z p z z t t z t t z n t z t t p t t t t t n p p t t p t t t n t t t t t t t t
EZW algorithm executed in 0.047000 seconds
Number of output bits: 192
MSE (Mean Squared Error)= 60.529236
PSNR (Peak SNR)= 30.311152 dB
