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International Journal of Quantum Information

Color image representation model and its application based on an improved FRQI

Panchi Li, Xiande Liu

Published Dec 18, 2017• 27 citations
Publisher

Abstract

To address quantum description for color images, an improved FRQI model called FRQCI is proposed in this paper. In our model, the qubit has two-phase parameters [Formula: see text] and [Formula: see text], and the primary color R is stored in [Formula: see text], the primary colors G and B are stored in [Formula: see text]. We provide several simple image processing operators, including color change and geometric transformation. Next, we focus on an encryption algorithm, which includes two parts: position scrambling and color transformation. All operations involved in this paper are implemented by the rotation of the qubit on the Bloch sphere. The simulation results on classical computer show the effectiveness of the proposed method.

DOI
10.1142/s0219749918500053

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To address quantum description for color images, an improved FRQI model called FRQCI is proposed in this paper. In our model, the qubit has two-phase parameters [Formula: see text] and [Formula: see text], and the primary color R is stored in [Formula: see text], the primary colors G and B are stored in [Formula: see text]. We provide several simple image processing operators, including color change and geometric transformation. Next, we focus on an encryption algorithm, which includes two parts: position scrambling and color transformation. All operations involved in this paper are implemented by the rotation of the qubit on the Bloch sphere. The simulation results on classical computer show the effectiveness of the proposed method.
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.
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.
Most of the studied quantum encryption algorithms are based on square images. In this paper, based on the improved novel quantum representation of color digital images model (INCQI), a quantum color image watermarking scheme is proposed. First, INCQI improved from NCQI is used to represent the carrier and watermark images with the size [Formula: see text] and [Formula: see text], respectively. Secondly, before embedding, the watermarking needs to be preprocessed. That is, the watermark image with the size of [Formula: see text] with 24-qubits color information is disordered by the fast bit-plane scramble algorithm, and then further expanded to an image with the size [Formula: see text] with 6-qubits pixel information by the nearest-neighbor interpolation method. Finally, the dual embedded algorithm is executed and a key image with 3-qubits information is generated for retrieving the original watermark image. The extraction process of the watermark image is the inverse process of its embedding, including inverse embedding, inverse expand and inverse scrambling operations. To show that our method has a better performance in visual quality and histogram graph, a simulation of different carrier and watermark images are conducted on the classical computer’s MATLAB.
Efficient transformations on the color content of images using single qubit operations are proposed based on the Flexible Representation of Quantum Images (FRQI). Utilizing the single qubit dedicated for encoding color information in the FRQI representation, the proposed operations offer massive speed-up in terms of changes in the color information in comparison with classical ones. Simulations of the FRQI images and circuits of these transformations using synthetic and Lena images on classical computers demonstrate the feasibility of the proposal. Together with position related operations, the color transformations could provide the foundation to achieve practical applications which are inefficient at present.
Currently, almost all color image encryption/decryption algorithms are designed based on a classical computer, in which the key space is relatively small, and the huge gains from quantum parallelism are not obtained. To address this problem, we propose a novel color image encryption/decryption method based on random rotation of qubit and Quantum Fourier transform (QFT). First, the color image is represented in a quantum superposition state |Image⟩, in which the color information of each pixel is described by only one qubit |c⟩. Then, the |c⟩ are randomly rotated on the Bloch sphere about three coordinate axis, and the QFT is performed on the |Image⟩. Once again, the |c⟩ is randomly rotated on the Bloch sphere and then the inverse QFT is performed on the |Image⟩, which the encryption process is implemented. The keys are the rotation angles of two above-mentioned rotations. The decryption is the inverse process of the encryption. Our method may run on a quantum computer in the future. The simulation results on the classic computer show that our approaches have better security.
Quantum image representation plays an important role in quantum image processing. In this paper, a bitplane representation of quantum images (BRQI) is proposed, which uses (n+4) or (n+6) qubits to store a grayscale or RGB color image of 2npixels. Compared with a novel enhanced quantum representation (NEQR), and a novel quantum representation of color digital images (NCQI), the storage capacity of BRQI improves 16 times and 218times, respectively. Next, some quantum operations based on BRQI are proposed, these operations including complement of colors, reverse of bitplanes, and translation of bitplanes. Analyzed the implementation circuits of these operations, the result indicates that these operations based on BRQI have lower quantum cost than NEQR and NCQI. Furthermore, an image scrambling algorithm based on BRQI is presented by combining the above operations. Simulation experiments and performance analysis show that proposed scrambling algorithm is effective and efficient.