Quantum image mid-point filter
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Quantum image mid-point filter Abdalla Essam Ali1
· Hala Abdel-Galil1 · Soha Mohamed1
Received: 30 December 2019 / Accepted: 23 June 2020 © Springer Science+Business Media, LLC, part of Springer Nature 2020
Abstract Mid-point filter is an order statistic filter which cannot be realized in the frequency domain. It is used for de-noising Gaussian noise effectively. In this paper, a new method for quantum realization mid-point filter in the spatial domain is proposed. An enhanced method for preparing multiple copies of the same image is also proposed. The modular design of the quantum circuit was utilized with an articulation on reducing the number of ancillary qubits. In this work, we present the quantum circuit for the three basic modules (cyclic shift, swap and division by two) and four composite modules (full adder, comparator, sort and maximum–minimum extraction). Also, the enhanced quantum preparation of multiple copies of an image is introduced. Moreover, the design of maximum–minimum extraction is modified to adapt our quantum circuit design. Finally, the complete quantum circuit which implements the mid-point filtering task is constructed and the results of several simulation experiments with different noise patterns are presented on some grayscale images. Apparently, the proposed approach has identical noise suppression of the classical version; however, there is a clear reduction in the complexity from exponential function of image size O(22n ) to the second-order polynomial O(n 2 + q). Keywords Quantum image processing · Quantum image filtering · Quantum image spatial filtering · Quantum image de-noising
1 Introduction Quantum computation is the use of quantum mechanical phenomena, like superposition and entanglement, to perform computations and improve its time performance. Quantum computation was first proposed by Feynman [5]. He stated that quantum mechanical systems cannot be simulated by a classical universal computer but, can
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Abdalla Essam Ali [email protected] Computer Science Department, Faculty of Computers and Artificial Intelligence, Helwan University, Cairo, Egypt 0123456789().: V,-vol
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be simulated by some class of quantum mechanical system. Afterward, the power of quantum computing took attention when a quantum algorithm for performing prime factorization of integers in polynomial time was proposed by Shor [21], and a search algorithm in database was proposed by, Grover [7]. The spectacular properties of quantum computing and the promising results of early research opened the doors for other fields such as image processing. Quantum image processing (QImP) focuses on extending conventional image processing techniques with quantum computing properties [26]. To be able to use image processing in quantum computing, quantum image representation (QIR) is needed to encode classical images using quantum computing characteristics. The work done in [2] distinguished two classes of QIR. The first one encodes the color information in the
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