# Low-complexity Rounded KLT Approximation for Image Compression

arXiv: https://arxiv.org/abs/2111.14239 · HTML: https://mlsanity.com/paper/2111.14239/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 57 references that are in the map.
- First posted on arXiv 28 Nov 2021.

## Builds on (most cited first, 10 of 10)

- [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 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 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)

## Built on by (most cited first, 2 of 2)

- [Discrete Cosine Transform Based Decorrelated Attention for Vision Transformers](https://mlsanity.com/paper/2405.13901/) (2024)
- [Fast Data-independent KLT Approximations Based on Integer Functions](https://mlsanity.com/paper/2410.09227/) (2024)

## Abstract (arXiv)

The Karhunen-Lo`eve transform (KLT) is often used for data decorrelation and dimensionality reduction. Because its computation depends on the matrix of covariances of the input signal, the use of the KLT in real-time applications is severely constrained by the difficulty in developing fast algorithms to implement it. In this context, this paper proposes a new class of low-complexity transforms that are obtained through the application of the round function to the elements of the KLT matrix. The proposed transforms are evaluated considering figures of merit that measure the coding power and distance of the proposed approximations to the exact KLT and are also explored in image compression experiments. Fast algorithms are introduced for the proposed approximate transforms. It was shown that the proposed transforms perform well in image compression and require a low implementation cost.