Xiuqiao Xiang1, Baochang Shi2,*, 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].
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.
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