Low-complexity Rounded KLT Approximation for Image Compression

TL;DR

This paper introduces a low-complexity approximation of the KLT for image compression by applying a rounding function to the KLT matrix, enabling faster computation with minimal performance loss.

Contribution

It proposes a novel class of low-complexity transforms derived from the KLT matrix using rounding, along with fast algorithms for implementation.

Findings

The proposed transforms achieve good coding power.

They closely approximate the exact KLT.

They enable low-cost, efficient image compression.

Abstract

The Karhunen-Lo\`eve transform (KLT) is often used for data decorrelation and dimensionality reduction. Because its computation depends on the matrix of covariances of the input signal, the use of the KLT in real-time applications is severely constrained by the difficulty in developing fast algorithms to implement it. In this context, this paper proposes a new class of low-complexity transforms that are obtained through the application of the round function to the elements of the KLT matrix. The proposed transforms are evaluated considering figures of merit that measure the coding power and distance of the proposed approximations to the exact KLT and are also explored in image compression experiments. Fast algorithms are introduced for the proposed approximate transforms. It was shown that the proposed transforms perform well in image compression and require a low implementation cost.