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.
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.
Exploiting the promise of security and efficiency that quantum computing offers, the basic foundations leading to commercial applications for quantum image processing are proposed. Two mathematical frameworks and algorithms to accomplish the watermarking of quantum images, authentication of ownership of already watermarked images and recovery of their unmarked versions on quantum computers are proposed. Encoding the images as 2n-sized normalised Flexible Representation of Quantum Images (FRQI) states, with n-qubits and 1-qubit dedicated to capturing the respective information about the colour and position of every pixel in the image respectively, the proposed algorithms utilise the flexibility inherent to the FRQI representation, in order to confine the transformations on an image to any predetermined chromatic or spatial (or a combination of both) content of the image as dictated by the watermark embedding, authentication or recovery circuits. Furthermore, by adopting an apt generalisation of the criteria required to realise physical quantum computing hardware, three standalone components that make up the framework to prepare, manipulate and recover the various contents required to represent and produce movies on quantum computers are also proposed. Each of the algorithms and the mathematical foundations for their execution were simulated using classical (i.e., conventional or non-quantum) computing resources, and their results were analysed alongside other longstanding classical computing equivalents. The work presented here, combined together with the extensions suggested, provide the basic foundations towards effectuating secure and efficient classical-like image and video processing applications on the quantum-computing framework.
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.
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.
Quantum image processing represents a transformative approach to visual data analysis, leveraging the principles of quantum computing to overcome classical limitations. This work explores two prominent quantum image encoding methods: FRQI (Flexible Representation of Quantum Images) and NEQR (Novel Enhanced Quantum Representation). FRQI excels in qubit efficiency, making it suitable for hardware implementation, while NEQR offers superior precision in pixel intensity representation, ideal for complex image processing tasks. We detail the implementation of these algorithms, including preprocessing, quantum circuit design, and simulation, using platforms like Qiskit. The study highlights the potential of quantum image processing in fields such as medicine, industry, and environmental monitoring, while addressing challenges like qubit limitations and noise sensitivity. This research contributes to advancing quantum computing applications, paving the way for innovative and sustainable technological solutions.
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.
A Multi-Channel Representation for Quantum Image (MCRQI) is proposed to facilitate the further image processing tasks based on the Flexible Representation for Quantum Image (FRQI). Channel Swapping Operation, One Channel Operation, are proposed as basic image processing operations on MCRQI representation. The simulation experiment results on classical computer show that the channel information of R G B (color) and α (transparency) can be carried easily on quantum computer by employing three qubits to represent the color space, and also indicate that this MCRQI is very flexible to realize some classic-like operations. The MCRQI provides a foundation not only express image in RGBα color space, but also to explore theoretical and practical aspects of image processing on quantum computer.