利用离散余弦变换进行图像压缩的方法-沙磊

243Vol.24No.319977JOURNALOFCHENGDUUNIVERSITYOFTECHNOLOGYJul.1997X沙　磊()叶　霞()采用复杂图像的程序在每一种计算机应用领域都能见到,随着图形图像所需存储量的激增和廉价数字信号处理芯片的出现,有效的图像有损压缩技术开始逐渐脱离专用硬件设备走到桌面计算机中来。该文在分析了音频和视频数据同异点的基础上阐述了一种基于离散余弦变换的图像压缩方法,并给出了算法的基本步骤和一些技巧。实际计算结果表明,通过该算法在极小甚至没有降低图像质量的情况下可获得极高的压缩率。现存的主要问题是计算速度要达到实时运行仍很困难。有损压缩,离散余弦变换,量化矩阵,编码TP391.4110,7080,,PC10%90%,PCXGIFBMP,PCX,,,,,80,,,,,,,,,,,DAC,,X1996-11-25收稿。第一作者简介:沙磊,男,35岁,在职博士,讲师,应用地球物理学专业。,50%95%,,,,,,,,,;,1,248DCT1Fig.1Flowchartforthelossycompressionalgorithm1,1,DCT,:1.1DCT(discretecosinetransform)DCTDCTFourier(FFT),,,,,,,,xy,,,1.1.1　DCT的特性f(i,j)=12NC(i)C(j)6N-1x=06N-1y=0p(x,y)cos(2x+1)iP2Ncos(2y+1)jP2N(1)C(k)=1/2(k=0)1(k0):DCTNNP,NNFp(x,y)=12N6N-1i=06N-1j=0C(i)C(j)f(i,j)cos(2x+1)iP2Ncos(2y+1)jP2N(2)C(k)=1/2(k=0)1(k0)DCT,,,C(k),NN00,00,DCT,(N-1,N-1),,00(DCT)DCT,,1093:;DCT,,,1.1.2　DCT的实现DCTDCT,O(N*N),NDCT,,256256DCT,DCT,88DCTDCT,,,,15206464DCT41616,1616DCT,88,,DCT,DCTNN,DCT,NNC,cij=1/N(i,j=0)2/Ncos(2j+1)iP2N(i,j0)(3),Ct,DCTF=C*P*Ct(4)*,NN,P,88NN,DCT2N2N,1.1.3　DCT的输出88(2),DCT(3)DCT,(0,0)DCT,,xyDCTDCT,DCT,DCT:DCT,DCT,,DCT11024140144147140140155179175144152140147140148167179152155136167163162152172168145156160152155136160162148156148140136147162147167140155155140136162136156123-1671621441401471481551361551521471471362Fig.2Inputblockofapicture-elementmatrix186-1815-923-9-141921-3426-9-1111147-10-24-26-183-20-1-8-514-15-8-3-38-31081-111818154-2-1888-41-791-34-1-7-1-20-8-2214-6032DCTFig.3Frequency-coefficientmatrixgeneratedbyDCTtotheinputpicture-elementblockillustratedFig.2其中左上角第一个元素称为DCT系数1.2DCTDCT8,-10241023,11DCT,,,DCT,DCT,,DCT,,0255,1,,(0,0):(i,j)=f(i,j)/(i,j)(5)xx,,00,,f(i,j)=(i,j)õ(i,j)(6),,DCT,,,DCTDCT,;,,,,125;25,25,1113:(i,j)=1+(1+i+j)õ(7)24357911131517579111315171979111315171921911131517192123111315171921232513151719212325271517192123252729171921232527293142Fig.4Quantizationmatrixforqualityfactor=21.3:,(0,0)DCT,,DCT,,,0,1.3.1　曲徊排序DCT00,0Huffman0,(RLE,Run-LengthEncoding),,00,5Fig.5Schematicdiagramofazigzagsequence,,,5(7),1.3.2　熵编码DCTDCT,RLE,,::DCT0;:;:DCTHuffmanHuffman,:DCT,,:112241-1,12-3-2,233-7-4,472-15-8,8152-31-16,1631,,Huffman,,,,1.4,,,(RGB)(YUV),1.522,88,140179DCT3,24,,(0,6)DCT160,DCT,,6DCT,,/,0,;DCT,,,262-42-120014-5300000-1-300-10-10001-100000000000000-1000000000000000000000(a)186-2014-922001720-352700000-7-2700-150-1900013-1500000000000000-17000000000000000000000(b)6Fig.6　Quantizationeffect(a)用图4的量化矩阵对图3DCT系数矩阵量化的结果;(b)逆量化结果。与图3比较可看出信息的损失1133:,60%7/,,;5;101520,7/Fig.7Apracticalcomputingexampleforcompression/restoration,85%,Huffman3,DCT,10%DCT,,DCT,,DCT,,DCTFourier,FourierDCT,DCT,114241SchowengerdtRA.TechniquesforImageProcessingandClassificationinRemoteSensing.NewYork:AcademicPress,19832PavlidisT.AlgorithmsforGraphicsandImageProcessing.NewYork:ComputerSeiencePressInc,19823.CD-ROM.:,19954,..:,19945..:,19946BerglandGD.ThefastFouriertransformrecursiveequationsforarbitrarylengthrecords.MathComp,1967,21(98):2362387BerglandGD.ThefastFouriertransformalgorithmusingbase8iterations.MathComp,1968,22(102):2752798.FORTRAN77.:,1990.119..:,197910RogersDF,AdamsJA.MathematicalElementsforComputerGraphics.NewYork:McGraw-Hill,197611DenesPB.Ascan-typegraphicssystemforinteractivecomputing.ProcIEEEConfonComputerGraphics,PatternRecognitionandDataStructure,1975,2112JarvisJF,JudiceCN,NinkeWH.Asurveryoftechniquesfortheimagedisplayofcontinuoustonepictureonbileveldisplays.ComputerGraphicsandImageProcessing,1976,5(1):131413JarvisJF,RobertsCS.Anewtechniquefordisplayingcontinuoustoneimagesonbileveldisplay.IEEETrans,1976,COM-24(8):891898AMETHODFORPICTURECOMPRESSIONUSINGDISCRETECOSINETRANSFORMShaLei(ChengduUniversityofTechnology,China)YeXia(XianInstituteofCoalMiningScience)AbstractSoftwaresadoptedcomplicatedpicturesarecommonineveryareaofcomputerapplication.Asthedemandingofstoragecapacitybyphotographsincreasessharplyandnumericalsignalprocessingunitsbecomemoreandmorecheap,effectivetechniquesoflossycompressionaregenerallyseperatedfromsomespecialhardwaresandappliedtotable-comptersystems.Inthispaper,theauthorsfirstanalyzethesimilaritiesanddifferencesofaudio-andvideo-data,thenexpoundapicturecompressiontechniquebasedupondiscreteco-sinetransform(DCT),andfinallygivedetailedstepsandsomebasicskillsofitsalgorithm.Practicalcomputingresultsbythistechniqueshowthatveryhighcompressionratiosareavailableunderminimum-loweringorevenno-loweringofrawpicturequality.Themainex-tantproblemiscomputingspeed.Itisverydifficulttoreachreal-timeoperationatpresent.Keywordslossycompression;discretecosinetransform;quantizationmatrix;coding1153: