# A Digital Hardware Fast Algorithm and FPGA-based Prototype for a Novel 16-point Approximate DCT for Image Compression Applications

arXiv: https://arxiv.org/abs/1702.01805 · HTML: https://mlsanity.com/paper/1702.01805/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 6 Feb 2017.

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

- [Low-complexity Rounded KLT Approximation for Image Compression](https://mlsanity.com/paper/2111.14239/) (2021)
- [Extensions on Low-complexity DCT Approximations for Larger Blocklengths Based on Minimal Angle Similarity](https://mlsanity.com/paper/2410.15244/) (2024)

## Abstract (arXiv)

The discrete cosine transform (DCT) is the key step in many image and video coding standards. The 8-point DCT is an important special case, possessing several low-complexity approximations widely investigated. However, 16-point DCT transform has energy compaction advantages. In this sense, this paper presents a new 16-point DCT approximation with null multiplicative complexity. The proposed transform matrix is orthogonal and contains only zeros and ones. The proposed transform outperforms the well-know Walsh-Hadamard transform and the current state-of-the-art 16-point approximation. A fast algorithm for the proposed transform is also introduced. This fast algorithm is experimentally validated using hardware implementations that are physically realized and verified on a 40 nm CMOS Xilinx Virtex-6 XC6VLX240T FPGA chip for a maximum clock rate of 342 MHz. Rapid prototypes on FPGA for 8-bit input word size shows significant improvement in compressed image quality by up to 1-2 dB at the cost of only eight adders compared to the state-of-art 16-point DCT approximation algorithm in the literature [S. Bouguezel, M. O. Ahmad, and M. N. S. Swamy. A novel transform for image compression. In em Proceedings of the 53rd IEEE International Midwest Symposium on Circuits and Systems (MWSCAS), 2010].