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Advances in Electrical and Computer Engineering

Quantum Image Filtering in the Frequency Domain

Simona Caraiman, Vasile Manta

Published Jan 1, 2013• 59 citations
Publisher

Abstract

In this paper we address the emerging field of Quantum Image Processing. We investigate the use of quantum computing systems to represent and manipulate images. In particular, we consider the basic task of image filtering. We prove that a quantum version for this operation can be achieved, even though the quantum convolution of two sequences is physically impossible. In our approach we use the principle of the quantum oracle to implement the filter function. We provide the quantum circuit that implements the filtering task and present the results of several simulation experiments on grayscale images. There are important differences between the classical and the quantum implementations for image filtering. We analyze these differences and show that the major advantage of the quantum approach lies in the exploitation of the efficient implementation of the quantum Fourier transform.

DOI
10.4316/aece.2013.03013

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In this paper we address the emerging field of Quantum Image Processing. We investigate the use of quantum computing systems to represent and manipulate images. In particular, we consider the basic task of image filtering. We prove that a quantum version for this operation can be achieved, even though the quantum convolution of two sequences is physically impossible. In our approach we use the principle of the quantum oracle to implement the filter function. We provide the quantum circuit that implements the filtering task and present the results of several simulation experiments on grayscale images. There are important differences between the classical and the quantum implementations for image filtering. We analyze these differences and show that the major advantage of the quantum approach lies in the exploitation of the efficient implementation of the quantum Fourier transform.
Quantum information processing and its subfield, quantum image processing, are rapidly growing fields as a result of advancements in the practicality of quantum mechanics. In this paper, we propose a quantum algorithm for processing information, such as one-dimensional time series and two-dimensional images, in the frequency domain. The information of interest is encoded into the magnitude of probability amplitude or the coefficient of each basis state. The oracle for filtering operates based on postselection results, and its explicit circuit design is presented. This oracle is versatile enough to perform all basic filtering, including high pass, low pass, band pass, band stop, and many other processing techniques. Finally, we present two novel schemes for transposing matrices in this paper. They use similar encoding rules but with deliberate choices in terms of selecting basis states. These schemes could potentially be useful for other quantum information processing tasks, such as edge detection. The proposed techniques are implemented on the IBM Qiskit quantum simulator. Some results are compared with traditional information processing results to verify their correctness and are presented in this paper.
Quantum information processing can overcome the limitations of classical computation.Consequently, image filtering using quantum computation has become a research hotspot.Here, a quantum algorithm is presented on the basis of the classical image filtering principle to detect and cancel the noise of an image.To this end, a quantum algorithm that completes the image filtering task is proposed and implemented.The novel enhanced quantum representation of digital images is introduced.Then, four basic modules, namely, position-shifting, parallel-CNOT, parallel-swap, and compare the max, are demonstrated.Two composite modules that can be utilised to realise the reversible logic circuit of the proposed quantum algorithm are designed on the basis of these basic modules.Simulation-based experimental results show the feasibility and the capabilities of the proposed quantum image filtering scheme.In addition, our proposal has outperformed its classical counterpart and other existing quantum image filtering schemes supported by detailed theoretical analysis of the computational complexity.Thus, it can potentially be used for highly efficient image filtering in a quantum computer age.
The Fourier transform is a popular tool in many areas of practical mathematics, including data compression and signal processing. The underlying principle of the Fourier transform is that functions with the right characteristics may be expressed as a linear combination of trigonometric functions. Decomposing a signal using trigonometric functions is like taking a time-domain signal and separating its frequency-domain components; this opens up new and more efficient avenues for signal analysis and manipulation. An increasing number of people are looking at quantum image processing (QIP) as a way to enhance the efficiency of conventional methods and their applications by taking use of quantum computing's characteristics. Filtering and rectifying the frequency domain to get important picture information is the goal of both image design and interactive processing in this procedure. We demonstrate the operation of quantum operators and states in the context of quaternions and demonstrate how it may be used to expand the quantum complex Fourier transform (QCFT) to the quantum quaternion Fourier transform (QQFT). We demonstrate why convolution cannot be used to quantum image processing, and we create space-domain and quaternion-Fourier spectrum filters, including an edge detector and a quantum median filter. An enhanced method is used to provide the groundwork for the realization of picture design and interactive technology, drawing on the knowledge of FT and inverse transform.
There is a growing interest in quantum image processing (QIP) that rose from the desire to exploit the properties of quantum computing to improve the performance of classical techniques and their applications. Since the introduction of a quaternion by Hamilton in 1843, quaternions had been used in a lot of applications. We show how the quantum states and quantum operators work in the field of quaternions and how we can use it to extend the quantum complex Fourier transform (QCFT) to the quantum quaternion Fourier transform (QQFT). We propose for the first time the novel algorithm for the QQFT. We explain the impossibility of the use of convolution in quantum image processing; we design filters in the quaternion Fourier spectrum and the space domain an edge detector and a quantum median filter.
This article explores the use of quantum computing for image processing and inversion. The advantages of quantum data processing methods over classical methods are analyzed. A quantum circuit can solve the fundamental image processing task of image inversion. The application of quantum NOT gates to alter pixel states corresponding to grayscale image values was investigated. It has been demonstrated that using amplitude angles to encode pixel values enables the efficient creation of quantum superposition on an image. The solution involved generating a negative of the image using the X-gate and the Hadamard operation. A quantum circuit was designed and tested on a simulator; an algorithm was also proposed for converting measurement results into a finalized image. The study highlights the advantages and disadvantages of the quantum approach, the linearity of transformations, and scalability prospects. Quantum image processing algorithms can enhance performance when handling large datasets.
In the field of quantum image processing, the method for quantum image representation has been a hot issue. However the computational complexity of the whole preparation for the mature model (Flexible Representation of Quantum Images) is too high. In this paper we present a fast image storage method based on the transformation about two quantum image representation models. Then a filtering algorithm is proposed via using quantum Fourier transform. With low time complexity, the good performance of this filtering operation can be presented in the simulation experiments.