# A Class of DCT Approximations Based on the Feig-Winograd Algorithm

arXiv: https://arxiv.org/abs/1502.00592 · HTML: https://mlsanity.com/paper/1502.00592/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 2 Feb 2015.

## Built on by (most cited first, 4 of 4)

- [DCT Approximations Based on Chen's Factorization](https://mlsanity.com/paper/2207.11638/) (2022)
- [Low-complexity Approximate Convolutional Neural Networks](https://mlsanity.com/paper/2208.00087/) (2022)
- [Low-Complexity Loeffler DCT Approximations for Image and Video Coding](https://mlsanity.com/paper/2207.14463/) (2022)
- [Extensions on Low-complexity DCT Approximations for Larger Blocklengths Based on Minimal Angle Similarity](https://mlsanity.com/paper/2410.15244/) (2024)

## Abstract (arXiv)

A new class of matrices based on a parametrization of the Feig-Winograd factorization of 8-point DCT is proposed. Such parametrization induces a matrix subspace, which unifies a number of existing methods for DCT approximation. By solving a comprehensive multicriteria optimization problem, we identified several new DCT approximations. Obtained solutions were sought to possess the following properties: (i) low multiplierless computational complexity, (ii) orthogonality or near orthogonality, (iii) low complexity invertibility, and (iv) close proximity and performance to the exact DCT. Proposed approximations were submitted to assessment in terms of proximity to the DCT, coding performance, and suitability for image compression. Considering Pareto efficiency, particular new proposed approximations could outperform various existing methods archived in literature.