實驗四JPEG壓縮實驗原理數(shù)據(jù)分塊對圖像進行編碼前，將每個分量圖像分割成不重疊的8×8像素塊，每一個8×8像素塊稱為一個數(shù)據(jù)單元（DU）。在彩色圖像中，JPEG分別壓縮圖像的每個彩色分量。雖然JPEG可以壓縮通常的紅綠藍分量，但在YCbCr空間的壓縮效果會更好。這是因為人眼對色彩的變化不如對亮度的變化敏感，因而對色彩的編碼可以比對亮度的編碼粗糙些，這主要體現(xiàn)在不同的采樣頻率和量化精度上。因此，編碼前一般先將圖像從RGB空間轉(zhuǎn)換到Y(jié)CbCr空間，再把各分量圖像分割成8×8數(shù)據(jù)塊。在對圖像采樣時，可以采用不同的采樣頻率，這種技術(shù)稱為二次采樣。由于亮度比色彩更重要，因而對Y分量的采樣頻率可高于對Cb、Cr的采樣頻率，這樣有利于節(jié)省存儲空間。常用的采樣方案有YUV422和YUV411。把采樣頻率最低的分量圖像中一個DU所對應(yīng)的像區(qū)上覆蓋的所有各分量上的DU按順序編組為一個最小編碼單元（MCU）。對灰度圖像而言，只有一個Y分量，MCU就是一個數(shù)據(jù)單元。而對彩色圖像而言，以4:1:1的采樣方案為例，則一個MCU由4個Y分量的DU、1個Cb分量的DU和1個Cr分量的DU組成。DCT處理圖像數(shù)據(jù)塊分割后，即以MCU為單位順序?qū)U進行二維離散余弦變換。對以無符號數(shù)表示的具有P位精度的輸入數(shù)據(jù)，在DCT前要減去2P-1，轉(zhuǎn)換成有符號數(shù)，而在IDCT后，應(yīng)加上2P-1，轉(zhuǎn)換成無符號數(shù)。對每個8×8的數(shù)據(jù)塊DU進行DCT后，得到的64個系數(shù)代表了該圖像塊的頻率成分，其中低頻分量集中在左上角，高頻分量分布在右下角。系數(shù)矩陣左上角的叫做直流（DC）系數(shù)，它代表了該數(shù)據(jù)塊的平均值，其余63個叫交流（AC）系數(shù)。3、系數(shù)量化在DCT處理中得到的64個系數(shù)中，低頻分量包含了圖像亮度等主要信息。在從空間域到頻域的變換中，圖像中的緩慢變化比快速變化更易引起人眼的注意，所以在重建圖像時，低頻分量的重要性高于高頻分量。因而在編碼時可以忽略高頻分量，從而達到壓縮的目的，這也是量化的根據(jù)和目的。在JPEG標(biāo)準中，用具有64個獨立元素的量化表來規(guī)定DCT域中相應(yīng)的64個系數(shù)的量化精度，使得對某個系數(shù)的具體量化階取決于人眼對該頻率分量的視覺敏感程度。理論上，對不同的空間分辨率、數(shù)據(jù)精度等情況，應(yīng)該有不同的量化表。不過，一般采用下圖所示的量化表，可取得較好的視覺效果。之所以用兩張量化表，是因為Y分量比Cb和Cr更重要些，因而對Y采用細量化，而對Cb和Cr采用粗量化。量化就是用DCT變換后的系數(shù)除以量化表中相對應(yīng)的量化階后四舍五入取整。由于量化表中左上角的值較小，而右下角的值較大，因而起到了保持低頻分量、抑制高頻分量的作用。亮度量化表 色度量化表Z型掃描DCT系數(shù)量化后，構(gòu)成一個稀疏矩陣，用Z（Zigzag）形掃描將其變成一維數(shù)列，將有利于熵編碼。Z形掃描的順序如圖：DC系數(shù)編碼DC系數(shù)反映了一個8×8數(shù)據(jù)塊的平均亮度，一般與相鄰塊有較大的相關(guān)性。JPEG對DC系數(shù)作差分編碼，即用前一數(shù)據(jù)塊的同一分量的DC系數(shù)作為當(dāng)前塊的預(yù)測值，再對當(dāng)前塊的實際值與預(yù)測值的差值作哈夫曼編碼。若DC系數(shù)的動態(tài)范圍為-1024～+1024，則差值的動態(tài)范圍為-2047～+2047。如果為每個差值賦予一個碼字，則碼表過于龐大。因此，JPEG對碼表進行了簡化，采用“前綴碼（SSSS）+尾碼”來表示。前綴碼指明了尾碼的有效位數(shù)B，可以根據(jù)DIFF從表10-8中查出前綴碼對應(yīng)的哈夫曼編碼。尾碼的取值取決于DC系數(shù)的差值和前綴碼。如果DC系數(shù)的差值DIFF大于等于0，則尾碼的碼字為DIFF的B位原碼；否則，取DIFF的B位反碼。AC系數(shù)編碼經(jīng)Z形排列后的AC系數(shù)，更有可能出現(xiàn)連續(xù)0組成的字符串，從而對其進行行程編碼將有利于壓縮數(shù)據(jù)。JPEG將一個非零DC系數(shù)及其前面的0行程長度（連續(xù)0的個數(shù)）的組合稱為一個事件。將每個事件編碼表示為“NNNN/SSSS+尾碼”，其中，NNNN為0行程的長度，SSSS表示尾碼的有效位數(shù)B（即當(dāng)前非0系數(shù)所占的比特數(shù)），如果非零AC系數(shù)大于等于0，則尾碼的碼字為該系數(shù)的B位原碼，否則，取該系數(shù)的B位反碼。由于只用4位表示0行程的長度，故在JPEG編碼中，最大0行程只能等于15。當(dāng)0行程長度大于16時，需要將其分開多次編碼，即對前面的每16個0以“F/0”表示，對剩余的繼續(xù)編碼。實驗內(nèi)容實現(xiàn)基本JPEG的壓縮和編碼分三個步驟：（1）首先通過DCT變換去除數(shù)據(jù)冗余；（2）使用量化表對DCT系數(shù)進行量化；（3）對量化后的系數(shù)進行Huffman編碼。三、實驗結(jié)果實驗圖片：Lena.bmp LenaRGB.bmp都是５１２＊５１２灰度圖像壓縮比：１２．１１５彩色圖像壓縮比：２８．１７１程序：%%AC_Huffman.mfunctionACH=AC_Huffman(AC,n);%亮度AC系數(shù)碼表T1={'1010''00''01''100''1011''11010''1111000''11111000'

'1111110110''1111111110000010''1111111110000011';'1100''11011''1111001''111110110''11111110110'

'1111111110000100''1111111110000101''1111111110000110'

'1111111110000111''1111111110001000''0';'11100''11111001''1111110111''111111110100'

'1111111110001001''1111111110001010''1111111110001011'

'1111111110001100''1111111110001101''1111111110001110''0';'111010''111110111''111111110101''1111111110001111'

'1111111110010000''1111111110010001''1111111110010010'

'1111111110010011''1111111110010100''1111111110010101''0';'111011''1111111000''1111111110010110''1111111110010111'

'1111111110011000''1111111110011001''1111111110011010'

'1111111110011011''1111111110011100''1111111110011101''0';'1111010''11111110111''1111111110011110'

'1111111110011111''1111111110100000''1111111110100001'

'1111111110100010''1111111110100011''1111111110100100'

'1111111110100001''0';'1111011''111111110110''1111111110100110'

'1111111110100111''1111111110101000''1111111110101001'

'1111111110101010''1111111110101011''1111111110101100'

'1111111110101101''0';'11111010''111111110111''1111111110101110'

'1111111110101111''1111111110110000''1111111110110001'

'1111111110110010''1111111110110011''1111111110110100'

'1111111110110101''0';'111111000''111111111000000''1111111110110110'

'1111111110110111''1111111110111000''1111111110111001'

'1111111110111010''1111111110111011''1111111110111100'

'1111111110111101''0';'111111001''1111111110111110''1111111110111111'

'1111111111000000''1111111111000001''1111111111000010'

'1111111111000011''1111111111000100''1111111111000101'

'1111111111000110''0';'111111010''1111111111000111''1111111111001000'

'1111111111001001''1111111111001010''1111111111001011'

'1111111111001100''1111111111001101''1111111111001110'

'1111111111001111''0';'1111111001''1111111111010000''1111111111010001'

'1111111111010010''1111111111010011''1111111111010100'

'1111111111010101''1111111111010110''1111111111010111'

'1111111111011000''0';'1111111010''1111111111011001''1111111111011010'

'1111111111011011''1111111111011100''1111111111011101'

'1111111111011110''1111111111011111''1111111111100000'

'1111111111100001''0';'11111111000''1111111111100010''1111111111100011'

'1111111111100100''1111111111100101''1111111111100110'

'1111111111100111''1111111111101000''1111111111101001'

'1111111111101010''0';'1111111111101011''1111111111101100''1111111111101101'

'1111111111101110''1111111111101111''1111111111110000'

'1111111111110001''1111111111110010''1111111111110011'

'1111111111110100''0';'11111111001''1111111111110101''1111111111110110'

'1111111111110111''1111111111111000''1111111111111001'

'1111111111111010''1111111111111011''1111111111111100'

'1111111111111101''1111111111111111'};%色度AC系數(shù)碼表T2={'00''01''100''1010''11000''11001''111000''1111000'

'111110100''1111110110''111111110100';'1011''111001''11110110''111110101''11111110110'

'111111110101''1111111110001000''1111111110001001'

'1111111110001010''1111111110001011''0';'11010''11110111''1111110111''111111110110'

'111111111000010''1111111110001100''1111111110001101'

'1111111110001110''1111111110001111''1111111110010000''0';'11010''111110111''1111110111''11111110110'

'1111111110010001''1111111110010010''1111111110010011'

'1111111110010100''1111111110010101''1111111110010110''0';'111010''111110110''1111111110010111''1111111110011000'

'1111111110011001''1111111110011010''1111111110011011'

'1111111110011100''1111111110011101''1111111110011110''0';'111011''1111111001''1111111110011111''1111111110100000'

'1111111110100001''1111111110100010''1111111110100011'

'1111111110100100''1111111110100101''1111111110100010''0';'1111001''11111110111''1111111110100111'

'1111111110101000''1111111110101001''1111111110101010'

'1111111110101011''1111111110101100''1111111110101101'

'1111111110101110''0';'1111010''11111111000''1111111110101111'

'1111111110110000''1111111110110001''1111111110110010'

'1111111110110011''1111111110110100''1111111110110101'

'1111111110110110''0';'11111001''1111111110110111''1111111110111000'

'1111111110111001''1111111110111010''1111111110111011'

'1111111110111100''1111111110111101''1111111110111110'

'1111111110111111''0';'111110111''1111111111000000''1111111111000001'

'1111111111000010''1111111111000011''1111111111000100'

'1111111111000101''1111111111000110''1111111111000111'

'1111111111001000''0';'111111000''1111111111001001''1111111111001010'

'1111111111001011''1111111111001100''1111111111001101'

'1111111111001110''1111111111001111''1111111111010000'

'1111111111010001''0';'111111001''1111111111010010''1111111111010011'

'1111111111010100''1111111111010101''1111111111010110'

'1111111111010111''1111111111011000''1111111111011001'

'1111111111011010''0';'111111010''1111111111011011''1111111111011100'

'1111111111011101''1111111111011110''1111111111011111'

'1111111111100000''1111111111100001''1111111111100010'

'1111111111100011''0';'11111111001''1111111111100100''1111111111100101'

'1111111111100110''1111111111100111''1111111111101000'

'1111111111101001''1111111111101010''1111111111101011'

'1111111111101100''0';'11111111100000''1111111111101101''1111111111101110'

'1111111111101111''1111111111110000''1111111111110001'

'1111111111110010''1111111111110011''1111111111110100'

'1111111111110101''0';'1111111010''111111111000011''1111111111110110'

'1111111111110111''1111111111111000''1111111111111001'

'1111111111111010''1111111111111011''1111111111111100'

'1111111111111101''1111111111111111'};%RLC行程編碼k=0;j=1;fori=1:63ifAC(i)==0&&k<15%非零系數(shù)前的零個數(shù)小于15k=k+1;elseifk==15%非零個數(shù)為15RLC(j)=15;RLC(j+1)=0;else%沒有零在前面RLC(j)=k;RLC(j+1)=AC(i);endk=0;j=j+2;endend%最后一個數(shù)是零ifAC(63)==0RLC(j)=0;RLC(j+1)=0;end%之前有若干組15個連零while(length(RLC)>2)if((RLC(length(RLC))==0)&&(RLC(length(RLC)-2)==0))RLC=RLC(1:length(RLC)-2);RLC(length(RLC)-1)=0;elsebreakendendACH='';fori=1:2:length(RLC)NNNN=RLC(i);ifRLC(i+1)==0SSSS=0;elseifabs(RLC(i+1))==1SSSS=1;elseif(abs(RLC(i+1))>=2&&abs(RLC(i+1))<=3)SSSS=2;elseif(abs(RLC(i+1))>=4&&abs(RLC(i+1))<=7)SSSS=3;elseif(abs(RLC(i+1))>=8&&abs(RLC(i+1))<=15)SSSS=4;elseif(abs(RLC(i+1))>=16&&abs(RLC(i+1))<=31)SSSS=5;elseif(abs(RLC(i+1))>=32&&abs(RLC(i+1))<=63)SSSS=6;elseif(abs(RLC(i+1))>=64&&abs(RLC(i+1))<=127)SSSS=7;elseif(abs(RLC(i+1))>=128&&abs(RLC(i+1))<=255)SSSS=8;elseif(abs(RLC(i+1))>=256&&abs(RLC(i+1))<=511)SSSS=9;elseif(abs(RLC(i+1))>=512&&abs(RLC(i+1))<=1023)SSSS=10;end%%求前綴碼S1ifn==1ifNNNN==0|NNNN==15S1=char(T1(NNNN+1,SSSS+1));elseS1=char(T1(NNNN+1,SSSS));endelseifNNNN==0|NNNN==15S1=char(T2(NNNN+1,SSSS+1));elseS1=char(T2(NNNN+1,SSSS));endend%%求尾碼S2ifRLC(i)==0&&RLC(i+1)==0S2='';elseifRLC(i+1)>=0S2=dec2bin(RLC(i+1));elseS2=dec2bin(abs(RLC(i+1)));fori=1:length(S2)ifS2(i)=='1'S2(i)='0';elseS2(i)='1';endendendendACH=[ACHS1S2];end%%DC_Huffman.mfunctionDCH=DC_Huffman(Z,last_Z,n);%亮度碼字T1={'00''010''011''100''101''110''1110''11110''111110''1111110''11111110''111111110'};%色度碼字T2={'00''01''10''110''1110''11110''111110''1111110''11111110''111111110''1111111110''11111111110'};DIFF=Z-last_Z;ifDIFF==0SSSS=0;elseif(abs(DIFF)==1)SSSS=1;elseif(abs(DIFF)>=2&&abs(DIFF)<=3)SSSS=2;elseif(abs(DIFF)>=4&&abs(DIFF)<=7)SSSS=3;elseif(abs(DIFF)>=8&&abs(DIFF)<=15)SSSS=4;elseif(abs(DIFF)>=16&&abs(DIFF)<=31)SSSS=5;elseif(abs(DIFF)>=32&&abs(DIFF)<=63)SSSS=6;elseif(abs(DIFF)>=64&&abs(DIFF)<=127)SSSS=7;elseif(abs(DIFF)>=128&&abs(DIFF)<=255)SSSS=8;elseif(abs(DIFF)>=256&&abs(DIFF)<=511)SSSS=9;elseif(abs(DIFF)>=512&&abs(DIFF)<=1023)SSSS=10;elseif(abs(DIFF)>=1024&&abs(DIFF)<=2047)SSSS=11;end%前綴碼ifn==1S1=char(T1(SSSS+1));elseS1=char(T2(SSSS+1));end%后綴碼ifDIFF>=0S2=dec2bin(DIFF);elseS2=dec2bin(DIFF);fori=1:length(S2)ifS2(i)=='0';S2(i)='1';elseS(2)='0';endendendDCH=[S1S2];%%exp4.mclearall;closeall;%亮度量化表LQT=[1611101624405161;1212141926586055;1413162440576956;1417222951878062;182237566810910377;243555648110411392;49647887103121120101;7292959811210010399];%色度量化表CQT=[1718244799999999;1821266699999999;2426569999999999;4766999999999999;9999999999999999;9999999999999999;9999999999999999;9999999999999999];%灰度圖象處理I1=double(imread('Lena.bmp'));[M,N]=size(I1);last_Z=0;jpeg1='';fori=0:M/8-1forj=0:N/8-1S=I1((1+8*i):(8*(i+1)),(1+8*j):(8*(j+1)));%分割成8*8處理S=dct2(S);%DCTS=round(S./LQT);%亮度量化Z=Zigzag(S);%Zigzag掃描DCH=DC_Huffman(Z(1),last_Z,1);%直流分量編碼ACH=AC_Huffman(Z(2:end),1);%交流分量編碼last_Z=Z(1);jpeg1=[jpeg1DCHACH];endendrate1=8*M*N/length(jpeg1);%壓縮比%彩色圖像處理I2=double(imread('LenaRGB.bmp'));%轉(zhuǎn)換成亮度I2=rgb2ycbcr(I2);Y=I2(:,:,1);Cr=I2(:,:,2);Cb=I2(:,:,3);[M,N]=size(Y);Y_last_Z=0;Cr_last_Z=0;Cb_last_Z=0;Y_jpeg2='';Cr_jpeg2='';Cb_jpeg2='';fori=0:M/8-1