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Quantum Machine Intelligence

Quantum convolution image processing by quantum wavelet transform for extraction of features

Shyam R. Sihare

Published Dec 1, 2025• 2 citations
Publisher
DOI
10.1007/s42484-025-00324-x

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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.