Data Independent Karhunen-Loéve Transform for Image and Video Coding - Tan, Wen; Liu, Xue-Dong; Huang, Chuang-Ceng; Wan, Jun (2018 IEEE 4th Information Technology and Mechatronics Engineering Conference (ITOEC), 2018)
Transform coding plays an important role in image and video compression. The Karhunen-Loéve transform (KLT) is the optimal transform for its full decorrelation ability. However, there is no general algorithm that enables its fast computation since the KLT is data dependent. Instead, the discrete cosine transform (DCT) is used widely for its good energy compaction and fast implementation algorithm. The DCT matrix can be derived by letting the correlation coefficient ρ be 1 for the Markov-1 model of signal. Since such a perfectly correlated signal is rare the DCT is usually suboptimal. In this letter, taking the real image signal into consideration and setting the ρ to be a value ρ* closer to the actual correlation coefficient in the real image, we obtain the data independent KLT (diKLT). Experimental results show that the diKLT outperforms DCT in terms of the mean square error (MSE) and structural similarity (SSIM) as long as the ρ* is big enough and the retained transform coefficients are sufficient. Although the superiority of diKLT over DCT is not prominent the advantage that a transform independent of data outperforms DCT is worthy to be noticed.