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 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.
RGB multi channel representation is proposed for images on quantum computers (MCQI) that captures information about colors (RGB channels) and their corresponding positions in an image in a normalized quantum state. The proposed representation makes it possible to store the RGB information about an image simultaneously by using 2n+3 qubits for encoding 2n× 2npixel images, whereas pixel-wise processing is necessary in many other quantum image representations, e.g., qubit lattice, grid qubit, and quantum lattice. Simulation of storage and retrieval of MCQI images using human facial images demonstrated that 15 qubits are required for encoding 64 × 64 colored images, and encoded information is retrieved by measurement. Perspectives of designing quantum image operators are also discussed based onMCQI representation, e.g., channel of interest, channel swapping, and restrict version of color transformation.
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 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.
Quantum circuits to realize color operations of channel of interest, channel swapping, and alpha blending on images are proposed using five kinds of quantum gates, i.e., NOT, CNOT, Toffoli, Rotation, and Controlled Rotation gates. Complexities of the proposed circuits are for an N-sized image, whereas the color information must be transformed pixel by pixel in the case of operators on classical computers. Simulations on the proposed three quantum color operations using three human facial and one Japanese style house images demonstrate that at most 9, 3, and 5 basic quantum gates are requested, that shows the feasibility of quantum circuits. Based on proposed three operations, all invertible classical color information transformation on imagesmay be designed and many applications can be realized on quantum computer, and the channel of interest based watermarking is being researched which the experiment results show that from the point of PSNR, our proposal is about 10 dB better than the chosen method of quantum image watermarking.
Comprehensive resource addressing the need for a quantum image processing machine learning model that can outperform classical neural networks Quantum Image Processing in Practice explores the transformative potential of quantum color image processing across various domains, including biomedicine, entertainment, economics, and industry. The rapid growth of image data, especially in facial recognition and autonomous vehicles, demands more efficient processing techniques. Quantum computing promises to accelerate digital image processing (DIP) to meet this demand. This book covers the role of quantum image processing (QIP) in quantum information processing, including mathematical foundations, quantum operations, image processing using quantum filters, quantum image representation, and quantum neural networks. It aims to inspire practical applications and foster innovation in this promising field. Topics include: Qubits and Quantum Logic Gates: Introduces qubits, the fundamental data unit in quantum computing, and their manipulation using quantum logic gates like Pauli matrices, rotations, the CNOT gate, and Hadamard matrices. The concept of entanglement, where qubits become interconnected, is also explored, highlighting its importance for applications like quantum teleportation and cryptography. Two and Multiple Qubit Systems: Demonstrates the importance of using two qubits to process color images, enabling image enhancement, noise reduction, edge detection, and feature extraction. Covers the tensor product, Kronecker sum, SWAP gate, and local and controlled gates. Extends to multi-qubit superpositions, exploring local and control gates for three qubits, such as the Toffoli and Fredkin gates, and describes the measurement of superpositions using projection operators. Transforms and Quantum Image Representations: Covers the Hadamard, Fourier, and Heap transforms and their circuits in quantum computation, highlighting their applications in signal and image processing. Introduces the quantum signal-induced heap transform for image enhancement, classification, compression, and filtration. Explores quantum representations and operations for images using the RGB, XYZ, CMY, HSI, and HSV color models, providing numerous examples. Fourier Transform Qubit Representation: Introduces a new model of quantum image representation, the Fourier transform qubit representation. Describes the algorithm and circuit for calculating the 2-D quantum Fourier transform, enabling advancements in quantum imaging techniques. New Operations and Hypercomplex Algebra: Presents new operations on qubits and quantum representations, including multiplication, division, and inverse operations. Explores hypercomplex algebra, specifically quaternion algebra, for its potential in color image processing. Quantum Neural Networks (QNNs): Discusses QNNs and their circuit implementation as advancements in machine learning driven by quantum mechanics. Summarizes various applications of QNNs and current trends and future developments in this rapidly evolving field. The book also addresses challenges and opportunities in QIP research, aiming to inspire practical applications and innovation. It is a valuable resource for researchers, students, and professionals interested in the intersection of quantum computing and color image processing applications, as well as those in visual communications, multimedia systems, computer vision, entertainment, and biomedical applications.
This work focuses into the emerging field of quantum image representation, which is a key for processing grayscale and color images on quantum computing platforms. We explore foundational methods like the qubit lattice model, the flexible representation for quantum images, the novel enhanced quantum representation, and the generalized quantum image representation, and categorize them into state-based, amplitude-based, and quaternion-based representations - the latter offering holistic color processing. A novel discrete signal representation mapping data on the unit circle will be introduced to simplify the Fourier transform concepts in quantum systems. We will examine crucial quantum operations, including quantum gradients, multiplication, square roots, Fourier transform, and filtering. Challenges in implementing the circular convolution on quantum hardware will be addressed with practical examples such as quantum low-pass and high-pass filters and 3-qubit convolution circuits. Additionally, we will discuss ongoing research into quantum algorithms inspired by classical transform processing, including the Fourier transforms, that leverage quantum states’ unique properties to achieve efficient encoding, transformation, and decoding of images.