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Article http://dx.doi.org/10.26855/jamc.2026.03.003

Image Denoising and Compression Based on Slant Haar Type Orthogonal Transforms

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Xiuqiao Xiang¹, Baochang Shi^2,*, Jianga Shang¹, Linquan Yang¹, Yuhong Jiang¹

¹School of Computer Science, China University of Geosciences, Wuhan 430078, Hubei, China.

²School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan 430074, Hubei, China.

*Corresponding author:Baochang Shi

This work was supported by the National Natural Science Foundation of China [Grant number. 6120205].

Published: March 9,2026

Abstract

The orthogonal transforms play a key role in signal processing, image processing, information security, etc. Despite their flexible generation and potential of the parameterized Slant Haar Type Orthogonal Transforms (SHTOT), SHTOT have received limited attention in the literature. In this work, we first investigate the recursive generation of Haar type orthogonal matrix (HTOT), slant matrix, and slant Haar matrix from the viewpoint of matrix. Then, the recursive generation and fast algorithms of SHTOT are achieved by combining HTOT and the slant matrix. In the end, we introduce SHTOT to the denoising and compression of standard images, and carry out a series of numerical experiments. The research in this paper demonstrates that different SHTOT with fast algorithms may be generated conveniently in the same program code only by varying any one value of two parameters. Moreover, SHTOT, particularly with parameters (s=2, r=1), achieves compression and denoising performance competitive with or superior to Haar, Walsh, slant transforms, discrete cosine transform, and discrete wavelet transform in several test cases, while offering a unified generation framework.

Keywords

Slant Haar type orthogonal transform; fast algorithm; image compression; image denoising; signal processing

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How to cite this paper

Image Denoising and Compression Based on Slant Haar Type Orthogonal Transforms

How to cite this paper: Xiuqiao Xiang, Baochang Shi, Jianga Shang, Linquan Yang, Yuhong Jiang. (2026) Image Denoising and Compression Based on Slant Haar Type Orthogonal Transforms. Journal of Applied Mathematics and Computation, 10(1), 21-33.

DOI: http://dx.doi.org/10.26855/jamc.2026.03.003