An Image Denoising Technique using Quantum Wavelet Transform
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An Image Denoising Technique using Quantum Wavelet Transform Sanjay Chakraborty1 · Soharab Hossain Shaikh2 · Amlan Chakrabarti1 · Ranjan Ghosh1 Received: 30 June 2020 / Accepted: 29 August 2020 / © Springer Science+Business Media, LLC, part of Springer Nature 2020
Abstract The amalgamation of ‘Quantum computing’ with image processing represents the various ways of handling images for different purposes. In this paper,an image denoising scheme based on quantum wavelet transform is proposed.A noisy image is embedded into the wavelet coefficients of the original image. As a result,it affects the visual quality of the original image. The quantum Daubechis kernel of 4th order is used to extract wavelet coefficients from the resultant image. Then a quantum oracle is implemented with a suitable thresholding function to decompose the wavelet coefficients into a greater effect applicable for the original image and lower effect for the noisy image wavelet coefficients. However,original image wavelet coefficients are greater than the noisy wavelet coefficients.A detail computational time complexity analysis is given and compared with some state-of-art denoising techniques. The result analysis shows that the proposed quantum image denoising technique has better visual quality in terms of PSNR,MSE and QIFM values Compare to others. Keywords Quantum computing · Quantum image denoising · Quantum image processing · Quantum wavelet transform · Quantum circuits · Quantum image thresholding
1 Introduction Image is one of the most important pictorial representations of information with various styles that have a huge number of applications on the fields of medical science, biomedicine, meteorology, telecommunication, satellite communication etc. The immense computing power offered by the realization of a quantum computer has led to an increasing interest in the field of machine learning [37, 38], information theory, image processing and so on. This computational power draws towards the use of three major principles coming from quantum physics : quantum entanglement of states, quantum interference and quantum parallelism [23]. From a comparison point of view, a quantum computer is expected Sanjay Chakraborty
[email protected] 1
A.K.Choudhury School of IT, University of Calcutta, Kolkata, India
2
Computer Science and Engineering, BML Munjal University, Gurugram, India
International Journal of Theoretical Physics
to increase greatly the efficiency of solving problems quicker than classical computer such as Deutsch and Jozsa’s algorithm for deciding whether a function is even or balanced, Shor’s factoring large integers, Grover’s database searching algorithm [10, 21]. Because of their high efficiency in terms of computational time complexity, these two quantum algorithms are used extensively. Table 1 shows a short comparison between some popular classical algorithms and their quantum counterparts in terms of computational time complexity. To deal with quantum images, the primary task is to convert the classical images i
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