An Image Compression Method Based on Subspace and Downsampling

Abstract

In this study, a new Karhunen-Loeve transform based algorithm with acceptable computational complexity is developed for lossy image compression. This method is based on obtaining an autocorrelation matrix by clustering the highly correlated image rows obtained by applying downsampling to the image. The KLT is applied to the blocks created from the downsampled image using the eigenvector (or transform) matrix obtained from the autocorrelation matrix; thus, the transform coefficient matrices are obtained. Then these coefficients were compressed by the lossless coding method. One of the proposed method’s essential features is sufficient for a test image to have one transform matrix, which has low dimensional. While most image compression studies using PCA (or KLT) in the literature are used in hybrid methods, the proposed study presents a simple algorithm that only downsamples images and applies KLT. The proposed method is compared with JPEG, BPG, and JPEG2000 compression methods for the PSNR-HVS and the SSIM metrics. In the results found for the test images, the average PSNR-HVS and SSIM results of the proposed method are higher than JPEG, very close to JPEG2000, and lower than BPG. It has been observed that the proposed method generally gives better results than other methods in images containing low-frequency components with high compression ratios.