基于SVD图像压缩技术研究

Technology Research of Image Compression Based on SVD

数字图像处理方法的研究源于两个主要领域:一是便于人们分解图像,对图像信息进行改进;二是使机器能自动理解图像。后者正是我们所要研究的内容。众所周知,在计算机中,图像是通过矩阵来表示的,一幅图像对应着一个矩阵,对图像的压缩就转换成了对矩阵的处理。在数学中,对矩阵进行奇异值分解可以把一个矩阵分解成只用几个数来表示,而且这种分解具有很好的稳定性、唯一性和自相似性。通过这种方法,就能用比较少的数据来表示相应的图像。本文就是通过对图像的矩阵进行奇异值分解,将一幅图像转换成只包含几个非零值的奇异值矩阵,实现图像压缩。

The theory about DIP（Digital Image Processing） is used in two filed.One is the improvement of the information about image,and the other is the saving,transport and display.And the latter is the object that we researched.It is well known that the graph is presented by matrix in computer.So we can deal with a graph by using the matrix.In math by using the multiresolution SVD,the matrix can be decomposed into just a few numbers,and the decomposition is very stable,unique,and self-similar.By this method,we can express digital image witn less data.This paper proposes a multiresolution form of the singular value decomposition（SVD）,and shows how it may be used for signal analysis and approximation.Digital image is transformed into singular value matrix that contains nonzero singular values by singular value decomposition（SVD） so that the image is compressed.