Singular Value Decomposition Approach to Digital Image Lossy Compression

摘要

The task of digital image compression is the subject of many researches for many years. Up to now this task remains a topic of constant interest. The reason of such interest is that digital media and digital communication are becoming of growing significance worldwide. The subject of this paper is a new original approach to digital image compression. It is based on using singular value decomposition of the image matrix that makes it possible to represent an image as a sum of the most significant layers (MSL). Based on this idea, a new format for image coding is developed. It makes use (1) the MSLs, which are computed according to a simple formal criterion, (2) segmentation of the image into small blocks; (3) special quantization and (4) optimal encoding of singular vectors of the preserved layers. The developed format of image coding makes it possible to achieve up to 15% rate of compression preserving high quality of the uncompressed image. The approach was validated by simulation many images. The software tool implementing the proposed technique was developed. It was used for validation of the paper results.