在上一篇文章中，我们根据测出的四组psnr与bit rate之间的关系，根据这个关系以及VCEG-M34的提议拟合出相对的曲线。
现在需要计算你所采用的方法对psnr和bit rate 的影响。那么就需要求对应相同的psnr时候，码流的变化，和对应相同的码流是对应的psnr的变化。对于后者，我们根据上篇文章拟合出来的公式即可获得。
对于前者，我们需要知道其反函数才能求出对应的值。
然而，对于符号表达的参数如何求其反函数呢？matalb提供了相应的解决方法。首先先需要下面这三个函数。
syms: 指定符号变量，如，syms x,t,y
sym(finverse(myfun(par0,para1)));
subs( )
下面通过举例来求得反函数计算：
%fmyfun.m
function y=fmyfun(para,snr)
syms bit
f=sym(finverse(myfun(para,bit))) ;
y=subs(f,'bit',snr);
function y=fmyfun(para,snr)
syms bit
f=sym(finverse(myfun(para,bit))) ;
y=subs(f,'bit',snr);
这样，就可以实现在已知snr的情况下，求得bit rate
下面给出一个应用例子：
SNR_org = [
%blue_sky.yuv
47.658,45.278,43.129,40.932;
%pedestrian_area.yuv
47.362,44.574,42.903,41.470;
%riverbed.yuv
46.845,43.768,41.320,39.330;
%rush_hour.yuv
47.000,44.486,43.223,42.086;
%station2.yuv
46.700,43.697,41.978,40.400;
%sunflower.yuv
47.156,45.147,43.680,41.922;
%tractor.yuv
46.903,43.875,41.375,39.215;
];
bit_org = [
%blue_sky.yuv
46552.18,19108.14,8675.51,4435.90;
%pedestrain_area.yuv
62321.42,24765.34,9946.34,5424.77;
%river_bed
125062.30,75294.25,44999.84,27501.96;
%rush_hour
60778.31,21838.84,8316.55,4418.00;
%station2
67541.70,20353.78,4219.07,1900.40;
%sunflower
40896.95,12166.38,5558.72,2951.06;
%tractor
97024.69,49946.76,23004.60,11202.05;
];
bit_org = bit_org/1000;
SNR_25candi_us = [
%blue_sky
47.655,45.270,43.122,40.918;
%pedestrain_area
47.356,44.569,42.902,41.467;
%riverbed
46.847,43.764,41.316,39.323;
%rush hour
46.997,44.479,43.212,42.076;
%station2
46.690,43.688,41.965,40.388;
%sunflower
47.142,45.130,43.670,41.917;
%tractor
46.894,43.855,41.355,39.198;
];
bit_25candi_us = [
%blue_sky
46785.35,19217.93,8763.00,4475.66
%pedestrain_area
62328.03,24823.76,9958.28,5435.45;
%riverbed
124661.84,75122.54,44870.01,27449.57;
%rush_hour
60824.93,21945.10,8330.94,4427.84;
%station2
67662.64,20556.07,4223.99,1892.38;
%sunflower
41094.02,12226.13,5552.23,2954.66;
%tractor
97280.39,50153.28,23102.80,11236.82;
];
bit_25candi_us = bit_25candi_us/1000;
av_snr = zeros(1,7);
av_bit = zeros(1,7);
for seq = 1:1:7
bit_T8x8off = bit_25candi_us(seq,:);
snr_T8x8off = SNR_25candi_us(seq,:);
[para_T8x8off,res]=lsqcurvefit(@myfun,ones(1,4),bit_T8x8off,snr_T8x8off);
bit_T8x8on = bit_org(seq,:);
snr_T8x8on = SNR_org(seq,:);
[para_T8x8on,res]=lsqcurvefit(@myfun,ones(1,4),bit_T8x8on,snr_T8x8on);
bit_min = max(bit_T8x8off(1),bit_T8x8on(1));
bit_max = min(bit_T8x8off(4),bit_T8x8on(4));
bit = bit_max:0.1:bit_min;
snr_off = myfun(para_T8x8off,bit);
snr_on = myfun(para_T8x8on, bit);
snr_min = max(snr_T8x8off(1),snr_T8x8on(1));
snr_max = min(snr_T8x8off(4),snr_T8x8on(4));
snr = snr_max:0.1:snr_min;
bit_off = fmyfun(para_T8x8off,snr);
bit_on = fmyfun(para_T8x8on, snr);
er_snr = snr_on - snr_off;
er_bit = (bit_on - bit_off)./bit_on;
av_snr(1,seq) = sum(er_snr)/(size(er_snr,2));
av_bit(1,seq) = sum(er_bit)/(size(er_bit,2));
%blue_sky.yuv
47.658,45.278,43.129,40.932;
%pedestrian_area.yuv
47.362,44.574,42.903,41.470;
%riverbed.yuv
46.845,43.768,41.320,39.330;
%rush_hour.yuv
47.000,44.486,43.223,42.086;
%station2.yuv
46.700,43.697,41.978,40.400;
%sunflower.yuv
47.156,45.147,43.680,41.922;
%tractor.yuv
46.903,43.875,41.375,39.215;
];
bit_org = [
%blue_sky.yuv
46552.18,19108.14,8675.51,4435.90;
%pedestrain_area.yuv
62321.42,24765.34,9946.34,5424.77;
%river_bed
125062.30,75294.25,44999.84,27501.96;
%rush_hour
60778.31,21838.84,8316.55,4418.00;
%station2
67541.70,20353.78,4219.07,1900.40;
%sunflower
40896.95,12166.38,5558.72,2951.06;
%tractor
97024.69,49946.76,23004.60,11202.05;
];
bit_org = bit_org/1000;
SNR_25candi_us = [
%blue_sky
47.655,45.270,43.122,40.918;
%pedestrain_area
47.356,44.569,42.902,41.467;
%riverbed
46.847,43.764,41.316,39.323;
%rush hour
46.997,44.479,43.212,42.076;
%station2
46.690,43.688,41.965,40.388;
%sunflower
47.142,45.130,43.670,41.917;
%tractor
46.894,43.855,41.355,39.198;
];
bit_25candi_us = [
%blue_sky
46785.35,19217.93,8763.00,4475.66
%pedestrain_area
62328.03,24823.76,9958.28,5435.45;
%riverbed
124661.84,75122.54,44870.01,27449.57;
%rush_hour
60824.93,21945.10,8330.94,4427.84;
%station2
67662.64,20556.07,4223.99,1892.38;
%sunflower
41094.02,12226.13,5552.23,2954.66;
%tractor
97280.39,50153.28,23102.80,11236.82;
];
bit_25candi_us = bit_25candi_us/1000;
av_snr = zeros(1,7);
av_bit = zeros(1,7);
for seq = 1:1:7
bit_T8x8off = bit_25candi_us(seq,:);
snr_T8x8off = SNR_25candi_us(seq,:);
[para_T8x8off,res]=lsqcurvefit(@myfun,ones(1,4),bit_T8x8off,snr_T8x8off);
bit_T8x8on = bit_org(seq,:);
snr_T8x8on = SNR_org(seq,:);
[para_T8x8on,res]=lsqcurvefit(@myfun,ones(1,4),bit_T8x8on,snr_T8x8on);
bit_min = max(bit_T8x8off(1),bit_T8x8on(1));
bit_max = min(bit_T8x8off(4),bit_T8x8on(4));
bit = bit_max:0.1:bit_min;
snr_off = myfun(para_T8x8off,bit);
snr_on = myfun(para_T8x8on, bit);
snr_min = max(snr_T8x8off(1),snr_T8x8on(1));
snr_max = min(snr_T8x8off(4),snr_T8x8on(4));
snr = snr_max:0.1:snr_min;
bit_off = fmyfun(para_T8x8off,snr);
bit_on = fmyfun(para_T8x8on, snr);
er_snr = snr_on - snr_off;
er_bit = (bit_on - bit_off)./bit_on;
av_snr(1,seq) = sum(er_snr)/(size(er_snr,2));
av_bit(1,seq) = sum(er_bit)/(size(er_bit,2));
end