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摘要I摘要随着时代的发展，人们可以通过Internet获取大量的信息。这些信息中包含着大量的图像信息，它们占据了很大的数据量，这给信息的存储和传输带来了极大的挑战。图像压缩的目的就是用尽量少的字节来表示图像，并且要求重建图像具有较好的质量。利用图像压缩,可以减轻图像存储和传输的负担,使得图像在网络上实现快速传输和实时处理成为现实。通常，图像中局部区域的像素是高度相关的，因此可以利用先前像素的有关知识来对当前像素的灰度值进行估计，这就是预测。本文介绍了数字图像的预测压缩编码。首先，将图像分成8×8大小的像素块。接着，对每一像素块均采用AR模型，利用Burg算法确定最佳线性预测系数。然后，通过线性差分方程计算得到预测值，最后对实际像素值和预测值之间的差值量化后进行算术编码。从而实现数字图像的预测压缩编码。本文采用MATLAB提供的图形用户界面工具对三幅典型的标准灰度图像进行了预测压缩编码仿真，并用客观标准和主观标准综合评价重建图像的质量。仿真结果表明：重建图像与原始图像几乎没有任何差异，能够满足人们的视觉需求。另外，数据压缩比较高且峰值信噪比均在20dB-40dB之间。因此，采用MATLAB实现数字图像的预测压缩编码是一种较好的压缩编码方法，能够在实际中得到广泛的应用。关键词：图像压缩，线性预测，算术编码，MATLAB，图形用户界面AbstractIIAbstractPeoplecanobtainagreatamountofinformationfromtheInternetwiththedevelopmentoftimesanditincludesagreatamountofimageinformation.Theimageinformationoccupieshugedataanditgivesgreatchallengetoinformationstorageandtransmission.Theaimofimagecompressionistodonateimagewithbytesasfewaspossible.Thereconstructedimageisofrelativelygoodqualityisalsorequired.Theburdenofimagestorageandtransmissioncanbealleviatedbyimagecompressionanditturnsfasttransmissionandreal-timeprocessofanimageininternetintoreality.Generally,thepixelinthepartialregionofanimageishighlycorrelated.Sothecorrelatedknowledgeofforegoingpixelcanbeusedtoestimatethegrayvalueofcurrentpixel.Thisiscalledprediction.Thepaperintroducesthepredictivecompressioncoding.Firstly,theimageisdividedintoseveralsub-imagesofsize8×8.Secondly,ARmodelisusedtoeachsub-imageandthenBurgalgorithmisusedtodeterminetheoptimumlinearpredictioncoefficient.Thirdly,lineardifferentialequationisusedtocalculatethepredictivevalue.Finally,thedifferencebetweenrealpixelvalueandpredictivevalueisquantizedbeforedoingarithmeticcoding.Thenthepredictivecompressioncodingofadigitalimageisrealized.ThepapersimulatethepredictivecompressioncodingastothreetypicalandstandardgrayimagesbyusinggraphicuserinterfacetoolsofferedbyMATLAB.Objectiveandsubjectivestandardisadoptedtoevaluatethequalityofreconstructedimage.Theresultsofsimulationdemonstratethatthereisnodifferencebetweenreconstructedimageandoriginalimageandreconstructedimagecansatisfyhumanvisualrequirements.Additionally,compressionratioisrelativelyhighandpeaksignal-to-noiseratioisbetween20dBto40dB.Therefore,therealizationofpredictivecompressioncodingusingMATLABisarelativelygoodmethodanditcanbewidelyusedinpractice.Keywords:imagecompression,linearprediction,arithmeticcoding,MATLAB,graphicaluserinterface目录III目录第1章引言.........................................................................................................11.1图像压缩的课题来源与发展现状...................................................................................11.1.1课题来源....................................................................................................................................11.1.2发展现状....................................................................................................................................21.2论文结构...........................................................................................................................3第2章数字图像概述与图像压缩评价标准.........................................................42.1数字图像文件存储...........................................................................................................42.2数字图像的文件格式.......................................................................................................42.3图像压缩的评价标准.......................................................................................................52.3.1客观保真度准则........................................................................................................................52.3.2主观保真度准则........................................................................................................................6第3章预测编码.....................................................................................................73.1脉冲编码调制...................................................................................................................73.2差分脉冲编码调制...........................................................................................................8第4章AR模型....................................................................................................104.1时间序列的概率模型.....................................................................................................104.1.1时间序列的参数表征..............................................................................................................104.1.2平稳过程...................................................................................................................................114.1.3纯随机过程...............................................................................................................................114.1.4自回归过程(AR模型)..............................................................................................................114.2AR模型的参数估计.......................................................................................................124.2.1AR模型参数的最小二乘估计...............................................................