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.
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.
Flexible Representation of Quantum Images (FRQI) is proposed to provide a representation of images that enables efficient preparation and image processing operators on quantum computers. FRQI captures colors and their corresponding positions in an image into a quantum state. The preparation with polynomial simple operations for FRQI turning a quantum computer from the initialized state to the FRQI state is done by using Hadamard and controlled rotation gates. The Quantum Image Compression (QIC) algorithm reduces simple operations used in the preparation process based on the minimization of Boolean equations are from same color groups of positions. Quantum image processing operators on FRQI based unitary transforms dealing with only colors, colors at some positions and the combination by the quantum Fourier transform of both colors and positions are addressed. The experiments for the storage and retrieval of images using FRQI are implemented in Matlab. The compression ratio of QIC among same color groups ranges from 6.67% to 31.62% on the Lena image.
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 methods for image analysis and processing in the frequency domain represent an innovative approach to image processing using quantum computing. One of the key tools in this field is the quantum Fourier transform (QFT), which can be applied to quantum images to analyze and process data in the frequency domain. The process involves several steps, including quantum image preparation, QFT application, frequency domain data processing, and inverse Fourier transform to reconstruct the spatial domain image. Quantum image processing techniques offer new opportunities for solving complex problems in the field of image processing, especially in the context of the use of quantum computing. However, this area is still under active research and requires further research and technology development for practical application.
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.
A flexible representation of quantum images (FRQI) was proposed to facilitate the extension of classical (non-quantum)-like image processing applications to the quantum computing domain. The representation encodes a quantum image in the form of a normalized state, which captures information about colors and their corresponding positions in the images. Since its conception, a handful of processing transformations have been formulated, among which are the geometric transformations on quantum images (GTQI) and the CTQI that are focused on the color information of the images. In addition, extensions and applications of FRQI representation, such as multi-channel representation for quantum images (MCQI), quantum image data searching, watermarking strategies for quantum images, a framework to produce movies on quantum computers and a blueprint for quantum video encryption and decryption have also been suggested. These proposals extend classical-like image and video processing applications to the quantum computing domain and offer a significant speed-up with low computational resources in comparison to performing the same tasks on traditional computing devices. Each of the algorithms and the mathematical foundations for their execution were simulated using classical computing resources, and their results were analyzed alongside other classical computing equivalents. The work presented in this review is intended to serve as the epitome of advances made in FRQI quantum image processing over the past five years and to simulate further interest geared towards the realization of some secure and efficient image and video processing applications on quantum computers.
Quantum image processing is a new and exciting subdiscipline of quantum computation that aims to extend classical image processing applications on a quantum computer.The research starts with a proposal of a representation of images on a quantum computer, named Multi-Channel Representation for Quantum Images (MCQI).This representation encodes the positions and their corresponding colors in the images as a normalized quantum state.For an n by n sized image, 2n qubits and 3 qubits are used to carry the position and color respectively.The preparation procedure of a quantum image is discussed by the multi-channel polynomial preparation, which turns the initial quantum states to the MC-QI quantum states.The image retrieval procedure by quantum measurement is proposed which converts the quantum states to classical images.Furthermore, based on MCQI, some categories of possible processing transformations are suggested.By considering the structure of MCQI representation, the Channel of Interest (CoI), the Channel Swapping (CS), the Color Space Transformation (CST), and Alpha Blending (αB) quantum image processing operators are discussed using unitary transformations with low complexity.All the 4 operators are used to process the information about color in the images.Their complexity are analyzed in terms of the number of basic quantum gates which are needed to build the transformations, and they can be built by 9, 3, 287, 28 basic quantum gates, respectively.Some strategies for designing new transformations from known ones are proposed as well.These strategies can be used to design further algorithms for image processing.Based on the MCQI representation and the four image processing operators, a quantum measurement based double-key double-domain watermarking strategy for multichannel quantum images (MC-WaQI) is developed.In these application, a revised of the original MCQI representation and some restricted versions of the transformations are considered.The research provides the foundation to design other quantum image processing algorithms and can be extend to the following areas:• MCQI representation can be used to build quantum image database,• new frequency operations on quantum images based on quantum Fourier quantum discrete cosine, and quantum wavelet transformations,• building the special effect on color quantum movie,• image data transmission by quantum communication.