基于數(shù)學方法和人工神經(jīng)網(wǎng)絡方法的數(shù)據(jù)壓縮

1、基于數(shù)學方法和人工神經(jīng)網(wǎng)絡方法的數(shù)據(jù)壓縮一、使用神經(jīng)網(wǎng)絡進行數(shù)據(jù)壓縮神經(jīng)網(wǎng)絡的原理與流程在此不再贅述，現(xiàn)直接寫出如下matlab程序：clear allinput=0.4 0.1;0.25 0;0.5 0;0.75 0;1 0;0 0.25;0.25 0.25;0.5 0.25;0.75 0.25;1 0.25;0 0.5;0.25 0.5;0.5 0.5;0.75 0.5;1 0.5;0 0.75;0.25 0.75;0.5 0.75;0.75 0.75;1 0.75;0 1;0.25 1;0.5 1;0.75 1;1 1; intialw=0 0;0.25 0;0.5 0;0.75 0;1

2、 0;0 0.25;0.25 0.25;0.5 0.25;0.75 0.25;1 0.25;0 0.5;0.25 0.5;0.5 0.5;0.75 0.5;1 0.5;0 0.75;0.25 0.75;0.5 0.75;0.75 0.75;1 0.75;0 1;0.25 1;0.5 1;0.75 1;1 1; nn, mm=size(input);Inum=mm; M=5; N=5;K=M*N; k=1;for i=1:M for j=1:N PPosition(k,:)=(j-1)*0.25,(i-1)*0.25; k=k+1; endendratemax=0.2;ratemin=0.01;

3、rmax=0.1;rmin=0.05;w=intialw'iteration=10000;for i=1:iteration rate=ratemax-i/iteration*(ratemax-ratemin); r=rmax-i/iteration*(rmax-rmin); k=round(rand(1,1)*24)+1; x=input(k,:); mindist,index=min(dist(x,w); d1=ceil(index/5); d2=mod(index,5); nodeindex=find(dist(0.25*(d2-1) (d1-1)*0.25,PPosition&

4、#39;)<r); for j=1:K if sum(nodeindex=j) w(:,j)=w(:,j)+rate*(x'-w(:,j); end endend for i=1:25 a(i)=w(1,i); b(i)=w(2,i);endx=a b;plot(a,b,'r.') Index=;for i=1:K mindist,index=min(dist(input(i,:),w); Index=Index,index;end for i=1:5 for j=1:5 a(i-1)*5+j)=w(1,j); b(i-1)*5+j)=w(2,j); end x=

5、a b; plot(a,b,'r.')endx=a b;plot(a,b,'r.')二、使用數(shù)學方法進行壓縮DCT變換利用傅立葉變換的性質(zhì)，采用圖像邊界褶翻將像變換為偶函數(shù)形式，然后對圖像進行二維傅立葉變換，變后僅包含余弦項。所以稱之為離散余弦變換。DCT編碼屬于正交變換編碼方式，用于去除圖像數(shù)據(jù)的空間冗余。DCT方法具有一些很好的特性。圖像經(jīng)DCT變換以后，DCT系數(shù)之間的相關性已經(jīng)很小。而且大部分能量集中在少數(shù)的系數(shù)上，因此，DCT變換在圖像壓縮中非常有用，是有損圖像壓縮國際標準JPEG的核心。從原理上講可以對整幅圖像進行DCT變換，但由于圖像各部位上細節(jié)的

6、豐富程度不同，這種整體處理的方式效果不好。為此，發(fā)送者首先將輸入圖像分解為8x8或16x16的塊，然后再對每個圖像塊進行二維DCT變換，接著再對DCT系數(shù)進行量化、編碼和傳輸；接收者通過對量化的DCT系數(shù)進行解碼，并對每個圖像塊進行的二維DCT反變換最后將操作完成后所有的塊拼接起來構(gòu)成一幅單一的圖像。對于一般的圖像而言，大多數(shù)DCT系數(shù)值都接近于0，可以去掉這些系數(shù)而不會對重建圖像的質(zhì)量產(chǎn)生霞大影響。利用DCT進行圈像壓縮確實可以節(jié)約大量的存儲空間在宴驗中，先將輸入的原始的我的照片分為8x8的塊，然后再對每個塊進行二維DCT變換?？梢跃帉懗鋈缦耺atlab程序：clc,clear all;fo

7、rmat shortdisp ('test')pictureData = 142 144 151 156 156 157 156 156; 140 143 148 150 154 155 156 155; 148 150 156 160 158 158 156 158 ; 159 160 162 161 160 159 158 160; 158 162 161 164 162 160 160 162; 160 164 143 162 160 158 157 159; 162 163 148 160 158 156 154 156; 163 160 150 154 154 154

8、 153 155A,B=size(pictureData); %大小disp ('date_aft')pictureData_1 = pictureData - 128disp ('DCT系數(shù)')pictureData_2 = zeros (8,8);pictureData_5 = zeros (8,8);for m = 0:A-1 for n = 0:B-1 s = 0; for x = 0:A-1 for y = 0:B-1 s = (pictureData_1(x+1,y+1) * cos(2*x+1)*m*pi/16) * cos(2*y+1)*n*pi

9、/16) + s; end end if ( m = 0) ck = 1/sqrt(2); else ck = 1; end if ( n=0) cl = 1/sqrt(2); else cl = 1; end pictureData_2(m+1,n+1)=1/4*ck*cl*s; endenddisp (pictureData_2);disp ('sjjqjz')qm = 16 11 10 16 24 40 51 61; 12 12 14 19 26 58 60 55; 14 13 16 24 40 57 69 56; 14 17 22 29 51 87 80 62; 18

10、22 37 56 68 109 103 77; 24 35 55 64 81 104 113 92; 49 64 78 87 103 121 120 101; 72 92 95 98 112 100 103 99 disp ('lhxsjz');% pictureData_3 = floor (pictureData_2./qm + 0.5)pictureData_3 = round (pictureData_2./qm ) disp ('restore');pictureData_4 = pictureData_3 .* qmdisp ('rebuil

11、d')for a = 0:A-1 for b = 0:B-1 s_1 = 0; for c = 0:A-1 for d = 0:B-1 s_1 = (pictureData_4(c+1,d+1) * cos(2*c+1)*a*pi/16) * cos(2*d+1)*b*pi/16) + s_1; end end if ( a = 0) ck_1 = 1/sqrt(2); else ck_1 = 1; end if ( b=0) cl_1 = 1/sqrt(2); else cl_1 = 1; end pictureData_5(a+1,b+1)=1/4*ck_1*cl_1*s_1; e

12、ndendpictureData6=pictureData_5 + 128; disp (pictureData6 );disp ('mis')nm=sum(sum(pictureData-pictureData6).2)/sum(sum(pictureData.*pictureData)3、 結(jié)果分析 用DCT方法可以得到如下結(jié)果：原始數(shù)據(jù)Data = 142 144 151 156 156 157 156 156 140 143 148 150 154 155 156 155 148 150 156 160 158 158 156 158 159 160 162 161 1

13、60 159 158 160 158 162 161 164 162 160 160 162 160 164 143 162 160 158 157 159 162 163 148 160 158 156 154 156 163 160 150 154 154 154 153 155電平移位后的數(shù)據(jù)pictureData_1 = 14 16 23 28 28 29 28 28 12 15 20 22 26 27 28 27 20 22 28 32 30 30 28 30 31 32 34 33 32 31 30 32 30 34 33 36 34 32 32 34 32 36 15 34 32

14、 30 29 31 34 35 20 32 30 28 26 28 35 32 22 26 26 26 25 27DCT系數(shù) 225.2500 -9.1756 -4.5265 1.9728 6.2500 -2.7302 -5.7018 -7.0596 -14.7765 -19.4567 -12.6502 -7.9796 -5.4015 3.8743 7.5174 6.5771 -20.7901 -4.2900 1.5392 3.9945 0.3991 0.7327 0.1982 0.0886 2.5330 -3.0845 -0.8731 2.4993 2.3890 -1.4176 -5.466

15、7 -4.1111 8.0000 4.0956 0.4716 -3.6462 -2.5000 1.3844 4.4048 3.6932 5.1289 4.4416 -0.8275 0.1807 1.6221 0.2841 0.0793 -1.5541 0.7642 -0.6359 -0.5518 1.0194 2.2701 0.2209 -1.2892 -2.7573 3.5788 -0.3245 -3.8268 -3.4046 -0.3316 1.1898 1.9949 0.6733視覺加權(quán)矩陣qm = 16 11 10 16 24 40 51 61 12 12 14 19 26 58 60

16、 55 14 13 16 24 40 57 69 56 14 17 22 29 51 87 80 62 18 22 37 56 68 109 103 77 24 35 55 64 81 104 113 92 49 64 78 87 103 121 120 101 72 92 95 98 112 100 103 99量化系數(shù)矩陣pictureData_3 = 14 -1 0 0 0 0 0 0 -1 -2 -1 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

17、0 0 0 0 0 0 0量化恢復后的系數(shù)矩陣pictureData_4 = 224 -11 0 0 0 0 0 0 -12 -24 -14 0 0 0 0 0 -14 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0重建圖像數(shù)據(jù) 146.6250 155.8098 158.9168 160.7373 158.8750 153.0314 144.8243 136.2081 156.2057 169.5076 172.8145 174.3305 171.190

18、9 163.0186 151.7321 139.6996 160.3519 174.1650 174.6374 173.4343 169.0863 161.3325 151.1034 139.7043 163.4594 177.0599 174.0417 169.6040 164.0720 157.3287 149.0181 139.0555 162.6250 174.6308 168.7624 161.8705 155.8750 150.7819 145.0757 137.4029 157.1053 166.2600 159.1849 151.5306 146.0891 142.9367 1

19、39.9169 134.9441 148.2889 154.0960 147.8534 141.3870 137.3648 135.8756 134.8626 132.2843 138.1986 140.9015 137.2709 133.5972 131.4933 131.0150 130.9175 129.9517重建圖像的歸一化均方誤差nm = 0.0098而使用神經(jīng)網(wǎng)絡方法進行數(shù)據(jù)壓縮，可得如下結(jié)果：w = Columns 1 through 8 0 0.2500 0.5000 0.7500 1.0000 0 0.2500 0.5000 0 0 0 0 0 0.2500 0.2500

20、0.2500 Columns 9 through 16 0.7500 1.0000 0 0.2500 0.5000 0.7500 1.0000 0 0.2500 0.2500 0.5000 0.5000 0.5000 0.5000 0.5000 0.7500 Columns 17 through 24 0.2500 0.5000 0.7500 1.0000 0 0.2500 0.5000 0.7500 0.7500 0.7500 0.7500 0.7500 1.0000 1.0000 1.0000 1.0000 Column 25 1.0000 1.0000同時可以用圖形表示壓縮情況，圖一是程序?qū)D