Optimizing Image Compression Using Singular Value Decomposition Based on Structural Similarity Index

Abstract

Image compression is an extensively deployed process used to represent and reduce image data by eliminating redundant data and at the same time retaining an acceptable level of vision quality. Based on this, there should be a technique in order to keep the image quality as good as possible while performing compression (i.e. to select the best level of compression that provides the required vision quality). This paper proposes an approach that performs this using Singular Value Decomposition (SVD). The proposed technique optimizes the image compression while maintaining a given level of vision quality. The algorithm is based on using the Structural Similarity Index (SSIM). Simply, for an image to be compressed by SVD method and given the required vision quality of the compressed version by SSIM level, the algorithm selects the number of singular values (i.e. rank) of the SVD that fulfills the required vision quality. Using the selected rank, Compression Ratio (CR), Peak Signal to Noise Ratio (PSNR), Mean Square Error (MSE) and correlation (ρ) may be computed for the resulted compressed image in order to extensively compare it with the original image. This approach was tested using several image benchmarks like: Lena, Cameraman, Peppers and Einstein images. The obtained results of application of this algorithm showed that this approach provides a good facility to the user to select the required level of the image quality for the compressed image. From the results, it has been noticed that the compressed image measures (CR, PSNR, MSE and ρ) are significantly affected by the SSIM degrees.
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