Data-independent Low-complexity KLT Approximations for Image and Video Coding

TL;DR

This work proposes low-computational cost approximations for the Karhunen-Lo transform and focuses on the blocklengths N because they are widely employed in image and video coding standards such as JPEG and high efficiency video coding (HEVC).

Abstract

The Karhunen-Loève 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.

Figures (15)

• Figure 1: Arithmetic complexity versus the proposed figures of merit for each transform for $N = 4$.
• Figure 2: Arithmetic complexity versus the proposed figures of merit for each transform for $N = 8$.
• Figure 3: Arithmetic complexity versus the proposed figures of merit for each transform for $N = 16$.
• Figure 4: Arithmetic complexity versus the proposed figures of merit for each transform for $N = 32$.
• Figure 5: Original Lena image.