基于SVD的图像压缩

原始图像大小为32 X 32=1024像素，利用SVD来对数据降维，实现图像的压缩 新建一个svdRec.py文件，加入如下代码： ~~~ #printMat()函数用于打印矩阵 def printMat(inMat, thresh=0.8): for i in range(32): for k in range(32): if float(inMat[i,k]) > thresh: print 1, else: print 0, print '' #imgCompress()实现图像压缩 def imgCompress(numSV=3, thresh=0.8): myl = [] for line in open('0_5.txt').readlines(): newRow = [] for i in range(32): newRow.append(int(line[i])) myl.append(newRow) myMat = mat(myl) print "****original matrix******" printMat(myMat, thresh) U,Sigma,VT = la.svd(myMat) SigRecon = mat(zeros((numSV, numSV))) for k in range(numSV):#construct diagonal matrix from vector SigRecon[k,k] = Sigma[k] reconMat = U[:,:numSV]*SigRecon*VT[:numSV,:] print "****reconstructed matrix using %d singular values******" % numSV printMat(reconMat, thresh) ~~~ 先打开存储图像像素值的文本文件‘0_5.txt’，并从文件中以数值的方式读入字符，然后对原始图像进行SVD分解并重构图像。 运行效果： ~~~ >>> reload(svdRec) <module 'svdRec' from 'svdRec.py'> >>> svdRec.imgCompress(2) ****original matrix****** 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 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0 0 0 0 0 0 0 ****reconstructed matrix using 2 singular values****** 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 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 1 1 1 1 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 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 0 0 0 0 0 0 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0 0 0 0 0 0 1 1 1 1 1 1 1 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 0 0 0 0 >>> Sigma array([ 9.72140007e+00, 5.29397912e+00, 6.84226362e-01, 1.67441533e-15, 3.39639411e-16]) ~~~ 可以看出，只需要两个奇异值就能相当精确地对图像实现重构，U和V.T都是32X2的矩阵，有两个奇异值，因此总数字数目为64+64+2=130，和原始图像像素数目1024相比，实现了几乎10倍的压缩比。