Paper Info
Title
Multilevel 2-D Quantum Wavelet Transforms
Abstract
Wavelet transform is being widely used in classical image processing. One-dimension quantum wavelet transforms (QWTs) have been proposed. Generalizations of the 1-D QWT into multilevel and multidimension have been investigated but restricted to the quantum wavelet packet transform (QWPTs), which is the direct product of 1-D QWPTs, and there is no transform between the packets in different dimensions. A 2-D QWT is vital for image processing. We construct the multilevel 2-D QWT’s general theory. Explicitly, we built multilevel 2-D Haar QWT and the multilevel Daubechies D4 QWT, respectively. We have given the complete quantum circuits for these wavelet transforms, using both noniterative and iterative methods. Compared to the 1-D QWT and wavelet packet transform, the multilevel 2-D QWT involves the entanglement between components in different degrees. Complexity analysis reveals that the proposed transforms offer exponential speedup over their classical counterparts. Also, the proposed wavelet transforms are used to realize quantum image compression. Simulation results demonstrate that the proposed wavelet transforms are significant and obtain the same results as their classical counterparts with an exponential speedup.
Year
DOI
Venue
2022
10.1109/TCYB.2021.3049509
IEEE Transactions on Cybernetics
Keywords
DocType
Volume
Multilevel 2-D-Daubechies quantum wavelet transform (QWT),multilevel 2-D-Haar QWT,quantum image processing
Journal
52
Issue
ISSN
Citations 
8
2168-2267
0
PageRank 
References 
Authors
0.34
26
5
Name
Order
Citations
PageRank
Hai-Sheng Li1898.43
Ping Fan200.34
Huiling Peng361.10
Shuxiang Song4195.36
Guilu Long56616.18