We present a method to compress ray information in three-dimensional (3-D) integral imaging (II) using the Karhunen-Loeve transform (KLT). Elemental images in II are highly correlated because they are picked-up by numerous lenslets, thus, the KLT can compress an integral image more effectively than 2-D ordinary images. In the hybrid coding scheme, the KLT is distinctly applied to disjoint subsets which are partitioned by a vector quantization (VQ). In the optical experiments, we show that 3-D image quality degradation is negligible if approximately 10% of eigenvectors with the largest eigenvalues are used. We also evaluate the quality of uncompressed images by signal-to-noise ratio (SNR) and peak-to-peak signal-to-noise ratio (PSNR). The presented coding scheme is shown to be better than JPEG (Joint Photographic Experts Group) for the lower bit rates in the II compression. Optical and numerical experiments are presented.