Image compression method

Abstract

The present invention provides an image compression method, comprising the following steps: generating a data matrix of an image to be compressed, and centralizing or standardizing the data matrix; calculating a variance matrix of the centralized or standardized data matrix; The characteristic polynomial of the variance matrix is ​​converted into a high-order characteristic polynomial, and the number of roots of the high-order characteristic polynomial is judged; according to the number of the roots and the preset initial solution, the high-order characteristic polynomial is iteratively solved. , when the number of roots obtained by iterative solution remains four, calculate the remaining four roots according to the mathematical expression of the characteristic polynomial obtained by the current iterative solution, output all characteristic roots, and calculate the characteristic vector according to the characteristic roots; A transformation matrix is ​​obtained according to the feature vector, and a compressed image is obtained by multiplying the transformation matrix by the data matrix. In the image compression method of the present invention, the method has less calculation amount and faster compression speed during image compression.

Description

technical field [0001] The invention relates to the technical field of image processing, in particular to an image compression method. Background technique [0002] With the explosive growth of digital image data, if image compression is not performed, a large amount of storage and transmission resources will be occupied. PCA (Principal Component Analysis), as an effective means of dimensionality reduction, can effectively reduce the dimensionality of data, and make the error between extracted components and original data reach the mean square minimum, which can be used for data compression and pattern recognition feature extraction. The image compression and reconstruction based on PCA has been proved by theory and practice that the realization method is simple, and the image compression can be realized effectively. At the same time, different data images can be restored according to the number of principal components, meeting the needs of image compression and reconstruc...

AI Technical Summary

Problems solved by technology

This is difficult for high-dimensional applications of image compression, since this produces a high-degree polynomial

There is no precise mathematical analytical formula for high-degree polynomials, so numerical methods have to be used. However, it is difficult to quickly and accurately solve all the eigenvalues ​​of the characteristic equation with traditional numerical methods, which cannot meet the data specification application requirements in the field of image big data.

[0004] Therefore, the existing image compression technology, based on the traditional PCA image compression algorithm, can achieve a relatively ideal compression ratio, but in the face of generally high-dimensional images, that is, a large number of variables, the traditional principal component analysis method has great limitations properties, the compression process is very slow

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