Three-dimensional quantum wavelet transforms

Abstract

Wavelet transform is being widely used in the field of information processing. One-dimension and two-dimension quantum wavelet transforms have been investigated as important tool algorithms. However, three-dimensional quantum wavelet transforms have not been reported. This paper proposes a multi-level three-dimensional quantum wavelet transform theory to implement the wavelet transform for quantum videos. Then, we construct the iterative formulas for the multi-level three-dimensional Haar and Daubechies D4 quantum wavelet transforms, respectively. Next, we design quantum circuits of the two wavelet transforms using iterative methods. Complexity analysis shows that the proposed wavelet transforms offer exponential speed-up over their classical counterparts. Finally, the proposed quantum wavelet transforms are selected to realize quantum video compression as a primary application. Simulation results reveal that the proposed wavelet transforms have better compression performance for quantum videos than two-dimension quantum wavelet transforms.

Graphical abstract

Keywords

wavelet transform / wavelet video coding / quantum wavelet transform / quantum information processing / quantum image processing

Haisheng Li received the MS degree in computer science from Chongqing University, China in 2004 and the PhD degree in computer science from University of Electronic Science and Technology of China, China in 2014. He is currently a Professor with Guangxi Normal University, China. His research interests include quantum information processing, quantum neural network and image processing

Guiqiong Li received the BS degree in electronic information engineering from Guangxi Normal University, China in 2018. She is currently pursuing the MS degree with Electronic Engineering, Guangxi Normal University, China. Her current research interests include quantum algorithm and machine learning

Haiying Xia received MS and PHD degrees in the Department of Electronic and Information Engineering from Huazhong University of Science and Technology, China in 2007 and 2011, respectively. She is currently working as a professor with Guangxi Normal University, China. Her current research includes pattern recognition, quantum image processing and neural networks

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Acknowledgements

This work was supported by the Science and Technology Project of Guangxi (2020GXNSFDA238023), and the National Natural Science Foundation of China (Grant No .61762012).

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2023 Higher Education Press