# Low-Complexity Loeffler DCT Approximations for Image and Video Coding

arXiv: https://arxiv.org/abs/2207.14463 · HTML: https://mlsanity.com/paper/2207.14463/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 7 of its 79 references that are in the map.
- First posted on arXiv 29 Jul 2022.

## Builds on (most cited first, 7 of 7)

- [A DCT Approximation for Image Compression](https://mlsanity.com/paper/1402.6034/) (2014)
- [DCT-like Transform for Image Compression Requires 14 Additions Only](https://mlsanity.com/paper/1702.00817/) (2017)
- [Low-complexity 8-point DCT Approximations Based on Integer Functions](https://mlsanity.com/paper/1309.7604/) (2013)
- [Improved 8-point Approximate DCT for Image and Video Compression Requiring Only 14 Additions](https://mlsanity.com/paper/1501.02995/) (2015)
- [An Integer Approximation Method for Discrete Sinusoidal Transforms](https://mlsanity.com/paper/2007.02232/) (2020)
- [A Class of DCT Approximations Based on the Feig-Winograd Algorithm](https://mlsanity.com/paper/1502.00592/) (2015)
- [Low-complexity Pruned 8-point DCT Approximations for Image Encoding](https://mlsanity.com/paper/1612.03461/) (2016)

## Abstract (arXiv)

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.