# Extensions on Low-complexity DCT Approximations for Larger Blocklengths Based on Minimal Angle Similarity

arXiv: https://arxiv.org/abs/2410.15244 · HTML: https://mlsanity.com/paper/2410.15244/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 14 of its 117 references that are in the map.
- First posted on arXiv 20 Oct 2024.

## Builds on (most cited first, 14 of 14)

- [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)
- [A Class of DCT Approximations Based on the Feig-Winograd Algorithm](https://mlsanity.com/paper/1502.00592/) (2015)
- [A Multiparametric Class of Low-complexity Transforms for Image and Video Coding](https://mlsanity.com/paper/2006.11418/) (2020)
- [Multiplierless 16-point DCT Approximation for Low-complexity Image and Video Coding](https://mlsanity.com/paper/1606.07414/) (2016)
- [Low-complexity 8-point DCT Approximation Based on Angle Similarity for Image and Video Coding](https://mlsanity.com/paper/1808.02950/) (2018)
- [Low-complexity Scaling Methods for DCT-II Approximations](https://mlsanity.com/paper/2108.02119/) (2021)
- [A Multiplierless Pruned DCT-like Transformation for Image and Video Compression that Requires 10 Additions Only](https://mlsanity.com/paper/1402.5979/) (2014)
- [A Digital Hardware Fast Algorithm and FPGA-based Prototype for a Novel 16-point Approximate DCT for Image Compression Applications](https://mlsanity.com/paper/1702.01805/) (2017)
- [Efficient Computation of the 8-point DCT via Summation by Parts](https://mlsanity.com/paper/1801.05832/) (2018)
- [Video Quality Enhancement Using Deep Learning-Based Prediction Models for Quantized DCT Coefficients in MPEG I-frames](https://mlsanity.com/paper/2010.05760/) (2020)
- [Fast Radix-32 Approximate DFTs for 1024-Beam Digital RF Beamforming](https://mlsanity.com/paper/2207.05866/) (2022)

## Abstract (arXiv)

The discrete cosine transform (DCT) is a central tool for image and video coding because it can be related to the Karhunen-Lo`eve transform (KLT), which is the optimal transform in terms of retained transform coefficients and data decorrelation. In this paper, we introduce 16-, 32-, and 64-point low-complexity DCT approximations by minimizing individually the angle between the rows of the exact DCT matrix and the matrix induced by the approximate transforms. According to some classical figures of merit, the proposed transforms outperformed the approximations for the DCT already known in the literature. Fast algorithms were also developed for the low-complexity transforms, asserting a good balance between the performance and its computational cost. Practical applications in image encoding showed the relevance of the transforms in this context. In fact, the experiments showed that the proposed transforms had better results than the known approximations in the literature for the cases of 16, 32, and 64 blocklength.