function smallExpWavelet( FILE_NAME, line )
% 读bmp
Gray_image = imread( FILE_NAME );
% 得到图像高度
height = size( Gray_image, 1 );
% 得到图像宽度, 即一行信号长度
N = size( Gray_image, 2 );
% 得到第line行灰度信号
sig = zeros( 1, N );
for i = 1:N
sig( 1, i ) = double( Gray_image( line, i ) );
end
x = 0:1/511:1;
plot( x , sig );
figure;
% 对第sig信号用非正交二次样条小波进行二进小波变换
level = log( N )/log( 2 ); % 分解级数
d = zeros( level, N ); % 小波各级系数
% 分析滤波器h
sqrt2 = sqrt( 2.0 );
h = zeros( 1, 4 );
h( 1, 1) = 0.125*sqrt2;
h( 1, 2 ) = 0.375*sqrt2;
h( 1, 3 ) = 0.375*sqrt2;
h( 1, 4 ) = 0.125*sqrt2;
zero_h = 2;
% 分析滤波器g
g = zeros( 1, 2 );
g( 1, 1 ) = 1.0*sqrt2;
g( 1, 2 ) = -1.0*sqrt2;
zero_g = 1;
%综合滤波器h_w
h_w = zeros( 1, 4 );
h_w( 1, 1 ) = 0.125*sqrt2;
h_w( 1, 2 ) = 0.375*sqrt2;
h_w( 1, 3 ) = 0.375*sqrt2;
h_w( 1, 4 ) = 0.125*sqrt2;
zero_hw = 2;
% 综合滤波器g_w
g_w = zeros( 1, 6 );
g_w( 1, 1 ) = 0.015625*sqrt2;
g_w( 1, 2 ) = 0.109375*sqrt2;
g_w( 1, 3 ) = 0.34375*sqrt2;
g_w( 1, 4 ) = -0.34375*sqrt2;
g_w( 1, 5 ) = -0.109375*sqrt2;
g_w( 1, 6 ) = -0.015625*sqrt2;
zero_gw = 3;
a_last = sig;
% 离散二进小波变换
for i=1:level
[ a_now, d_now ] = BinaryWavelet( a_last, i-1, h, zero_h, g, zero_g );
a_last = a_now;
d( i, : ) = d_now;
end
% 画出离散二进小波变换结果
for i=1:level
d_now = d( i, : );
subplot(level,1,i);
plot(x, d_now);
title = sprintf( '2^%d', i-1 );
ylabel(title);
end
figure;
%求模极大
d_MM = zeros( level, N );
for i=1:level
for j=2:N-1
if ( abs( d( i, j ) ) >=abs( d( i, j-1 ) ) ) & ( abs( d( i, j ) ) >abs( d( i, j+1 ) ) ) & (abs( d( i, j ) )>=5)
d_MM( i, j ) = d( i, j );
end
if ( abs( d( i, j ) ) >abs( d( i, j-1 ) ) ) & ( abs( d( i, j ) ) >=abs( d( i, j+1 ) ) ) & (abs( d( i, j ) )>=5)
d_MM( i, j ) = d( i, j );
end
end
end
for i=1:level
d_now = d_MM( i, : );
subplot(level,1,i); plot(x, d_now);
title = sprintf( '2^%d', i-1 );
ylabel(title);
end
figure;
sig_w = ConjugateMM( sig, h, zero_h, g, zero_g, d_MM, 10 );
plot( x , sig_w );
error = sig_w-sig;
errorRatio = sqrt( error*error' )/sqrt( sig*sig' )
