Low-Complexity Loeffler DCT Approximations for Image and Video Coding

TL;DR

This paper presents a new class of low-complexity Loeffler DCT approximations optimized for image and video coding, demonstrating improved efficiency and integration into standard codecs and FPGA implementations.

Contribution

Introduces a matrix parametrization method for Loeffler DCT, creating a unified framework for eight-point approximations and optimized scaled versions for practical coding applications.

Findings

Achieved Pareto-efficient DCT approximations balancing complexity and performance

Successfully embedded approximations into JPEG, H.264/AVC, and H.265/HEVC codecs

Implemented on FPGA showing improvements in area, speed, and power consumption

Abstract

This paper introduced a matrix parametrization method based on the Loeffler discrete cosine transform (DCT) algorithm. As a result, a new class of eight-point DCT approximations was proposed, capable of unifying the mathematical formalism of several eight-point DCT approximations archived in the literature. Pareto-efficient DCT approximations are obtained through multicriteria optimization, where computational complexity, proximity, and coding performance are considered. Efficient approximations and their scaled 16- and 32-point versions are embedded into image and video encoders, including a JPEG-like codec and H.264/AVC and H.265/HEVC standards. Results are compared to the unmodified standard codecs. Efficient approximations are mapped and implemented on a Xilinx VLX240T FPGA and evaluated for area, speed, and power consumption.