# Low-complexity Multidimensional DCT Approximations

arXiv: https://arxiv.org/abs/2306.11724 · HTML: https://mlsanity.com/paper/2306.11724/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 7 of its 134 references that are in the map.
- First posted on arXiv 20 Jun 2023.

## 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 Multiplierless Pruned DCT-like Transformation for Image and Video Compression that Requires 10 Additions Only](https://mlsanity.com/paper/1402.5979/) (2014)
- [Energy-efficient 8-point DCT Approximations: Theory and Hardware Architectures](https://mlsanity.com/paper/1612.00807/) (2016)

## Built on by (most cited first, 1 of 1)

- [Fast Data-independent KLT Approximations Based on Integer Functions](https://mlsanity.com/paper/2410.09227/) (2024)

## Abstract (arXiv)

In this paper, we introduce low-complexity multidimensional discrete cosine transform (DCT) approximations. Three dimensional DCT (3D DCT) approximations are formalized in terms of high-order tensor theory. The formulation is extended to higher dimensions with arbitrary lengths. Several multiplierless 8× 8× 8 approximate methods are proposed and the computational complexity is discussed for the general multidimensional case. The proposed methods complexity cost was assessed, presenting considerably lower arithmetic operations when compared with the exact 3D DCT. The proposed approximations were embedded into 3D DCT-based video coding scheme and a modified quantization step was introduced. The simulation results showed that the approximate 3D DCT coding methods offer almost identical output visual quality when compared with exact 3D DCT scheme. The proposed 3D approximations were also employed as a tool for visual tracking. The approximate 3D DCT-based proposed system performs similarly to the original exact 3D DCT-based method. In general, the suggested methods showed competitive performance at a considerably lower computational cost.