The Karhunen-Lo\`eve transform (KLT) is often used for data decorrelation and dimensionality reduction. The KLT is able to optimally retain the signal energy in only few transform components, being mathematically suitable for image and video compression. However, in practice, because of its high computational cost and dependence on the input signal, its application in real-time scenarios is precluded. This work proposes low-computational cost approximations for the KLT. We focus on the blocklengths $N \in \{4, 8, 16, 32 \}$ because they are widely employed in image and video coding standards such as JPEG and high efficiency video coding (HEVC). Extensive computational experiments demonstrate the suitability of the proposed low-complexity transforms for image and video compression.
翻译：Karhunen-Lo ⁇ ⁇ éeve变换(KLT)通常用于数据规范化和维度减低。KLT能够在数学上适合图像和视频压缩的少数变换部件中以最佳方式保留信号能量,但在实践中,由于计算成本高,依赖输入信号,因此无法实时应用。这项工作为KLT提出了低计算成本近似值。我们侧重于块长$N $@in 4、8、16、32 $,因为它们被广泛用于图像和视频编码标准,如JPEG和高效视频编码(HEVC)。广泛的计算实验表明,拟议的低兼容度变换成图像和视频压缩是合宜的。
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