第八章 小波分析理论及应用
表8.6-2 IEEE标准测试图压缩实验结果
比特/象素 常规小波变换 Lena图 SPIHT 无算术编码 SPIHT 有算术编码 0.08 0.125 0.25 0.5 1 2 4 28.60 30.23 33.17 36.18 39.42 43.71 53.32 28.86 30.72 33.70 36.84 39.98 44.34 54.13 29.35 31.10 34.11 37.21 40.41 45.07 55.86 观察表8.6-1和表8.6-2可得如下结论：对于所有种类的图像，SPIHT加了算术编码后比不加算术编码时峰值信噪比（PSNR）改善约为0.3dB~0.7dB；对于SAR图像，SPIHT不加算术编码时的PSNR与常规小波变换编码方法的PSNR相当；对于IEEE标准测试图Lena，SPIHT不加算术编码时的PSNR就优于常规小波变换编码方式。以上结果一方面说明了SPIHT算法的有效性，另一方面也说明了SAR图像不同于自然图像的特点。 SPIHT算法把量化过程隐含在编码过程中，且不要进行最优比特分配，运行速度要远快于常规小波变换编码方法，但运行速度与具体机器相关，这里不给出实际数据。
附 录 常用小波变换滤波器系数
1）哈尔小波：{
12,12 }
2）几个Daubechies 滤波器
DB4：{ 0.4829629131445341, 0.8365163037378077, 0.2241438680420134, -0.1294095225512603 } DB6：{ 0.3326705529500825, 0.8068915093110924, 0.4598775021184914,
-0.1350110200102546, -0.0854412738820267, 0.0352262918857095 }
DB8：{ 0.2303778133088964, 0.7148465705529154, 0.6308807679398587,
-0.0279837694168599, -0.1870348117190931, 0.0308413818355607,
0.0328830116668852, -0.0105974017850690 }
3) 7-9 滤波器： 综合滤波器：
{ -6.453888262893856e-02, -4.068941760955867e-02, 4.180922732222124e-01, 7.884856164056651e-01, 4.180922732222124e-01, -4.068941760955867e-02, -6.453888262893856e-02 } 分析滤波器：
{ 3.782845550699535e-02, -2.384946501937986e-02, -1.106244044184226e-01, 3.774028556126536e-01, 8.526986790094022e-01, 3.774028556126537e-01, -1.106244044184226e-01, -2.384946501937986e-02, 3.782845550699535e-02 }
4）取自文献[18]的滤波器 Villa1分析滤波器：
46
第八章 小波分析理论及应用
{ 3.782845550699535e-02, -2.384946501937986e-02, -1.106244044184226e-01, 3.774028556126536e-01, 8.526986790094022e-01, 3.774028556126537e-01, -1.106244044184226e-01, -2.384946501937986e-02, 3.782845550699535e-02} Villa1综合滤波器
{ -6.453888262893856e-02, -4.068941760955867e-02, 4.180922732222124e-01, 7.884856164056651e-01, 4.180922732222124e-01, -4.068941760955867e-02, -6.453888262893856e-02}
Villa2分析滤波器：
{ -8.472827741318157e-03, 3.759210316686883e-03, 4.728175282882753e-02, -3.347508104780150e-02, -6.887811419061032e-02, 3.832692613243884e-01, 7.672451593927493e-01, 3.832692613243889e-01, -6.887811419061045e-02, -3.347508104780156e-02, 4.728175282882753e-02, 3.759210316686883e-03, -8.472827741318157e-03} Villa2综合滤波器：
{ 1.418215589126359e-02, 6.292315666859828e-03, -1.087373652243805e-01, -6.916271012030040e-02, 4.481085999263908e-01, 8.328475700934288e-01,
4.481085999263908e-01, -6.916271012030040e-02, -1.087373652243805e-01, 6.292315666859828e-03, 1.418215589126359e-02}
Villa3分析滤波器：
{ -1.290777652578771e-01, 4.769893003875977e-02, 7.884856164056651e-01, 7.884856164056651e-01, 4.769893003875977e-02, -1.290777652578771e-01} Villa3综合滤波器：
{ 1.891422775349768e-02, 6.989495243807747e-03, -6.723693471890128e-02, 1.333892255971154e-01, 6.150507673110278e-01, 6.150507673110278e-01, 1.333892255971154e-01, -6.723693471890128e-02, 6.989495243807747e-03, 1.891422775349768e-02}
Villa4分析滤波器：
{ -1.767766952966369e-01, 3.535533905932738e-01, 1.060660171779821e+00, 3.535533905932738e-01, -1.767766952966369e-01} Villa4综合滤波器：
{ 3.535533905932738e-01, 7.071067811865476e-01, 3.535533905932738e-01}
Villa5分析滤波器：
{ 7.071067811865476e-01, 7.071067811865476e-01} Villa5综合滤波器：
{ -8.838834764831845e-02, 8.838834764831845e-02, 7.071067811865476e-01, 7.071067811865476e-01, 8.838834764831845e-02, -8.838834764831845e-02}
Villa6分析滤波器：
{ 3.314563036811943e-02, -6.629126073623885e-02, -1.767766952966369e-01, 4.198446513295127e-01, 9.943689110435828e-01, 4.198446513295127e-01, -1.767766952966369e-01, -6.629126073623885e-02, 3.314563036811943e-02} Villa6综合滤波器：
{ 3.535533905932738e-01, 7.071067811865476e-01, 3.535533905932738e-01}
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第八章 小波分析理论及应用
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小波分析及其应用（精品教程）
