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.
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.
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 scheme is proposed to watermark and recover unmarked greyscale images on quantum computers. The hitherto inaccessible data from a quantum image-watermark pair is extracted from their classical (conventional or non-quantum) versions using which two quantum sub-circuits are used to execute the two-tier transformations comprising of changes that: 1 embed a visible and translucent watermark logo in a predetermined sub-area of the quantum replica of the cover image 2 modify the remaining content of the cover image in a manner dictated by the watermark signal, so that the resulting distortions on the watermarked image are not easily discernible. Classical simulations of the image-watermark pairs and the various sub-circuits required to obtain the marked and unmarked images demonstrate the feasibility of the proposed scheme when the necessary quantum hardware are realised. The proposal advances available literature geared towards safeguarding quantum resources from unauthorised reproduction and confirmation of their proprietorship in cases of dispute thereby leading to commercial applications of quantum information.
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.
The Flexible Representation of Quantum Images (FRQI) is widely used for encoding images into normalized quantum states for secure processing. However, it suffers from high computational and qubit complexity, limiting its scalability. In addition, quantum comparator models, often employed for qubit comparison, remain vulnerable to geometric attacks such as scaling and rotation and require a slow embedding and extraction rate. To address these challenges, this paper proposes a novel quantum watermarking technique that integrates Quantum Image Representation (QIR) with the Novel Enhanced Quantum Representation (NEQR), offering improved efficiency, robustness, and security for quantum image processing (QIP). The proposed technique initiates watermark qubit (QB) generation by integrating pixel position bits (PPB) with an arithmetic average (AA)-based logic, implemented through a quantum circuit comprising reverse parallel adder (RPA), dividing-4 (D4) models, and controlled-NOT (CNOT) gates. For watermark embedding, the proposed circuit employs RPA, quantum equal (QE) models, CNOT gates, and Pauli-X gates, embedding the watermark via a least significant bit (LSB) strategy within the NEQR-encoded image. The extraction process mirrors the embedding architecture, utilizing reverse parallel subtractor (RPS), QE models, CNOT, and Pauli-X gates to ensure accurate watermark retrieval. Experimental results demonstrate high robustness by achieving the highest peak-signal-to-noise-ratio(PSNR) values of 59.97 decibels (dB) along with a structural similarity index matrix (SSIM) of 0.9999. The proposed framework is validated using IBM Qiskit-based quantum circuit simulation on classical computing hardware and is not intended to demonstrate fault-tolerant quantum hardware execution or provable quantum computational advantage. Rather, the work focuses on simulation-level reversible quantum-circuit modelling for secure image watermarking using NEQR-based image representation and quantum-compatible reversible logic structures. Furthermore, the proposed technique is subjected to a range of image processing attacks, quantum noise and decoherence to rigorously evaluate its resilience and performance. In addition, an AI-assisted attack classification module is incorporated to automatically identify the type of distortion applied to the attacked watermarked images. A lightweight Random Forest classifier is trained to classify different attack categories, including no attack, Gaussian noise, salt-and-pepper noise, median filtering, histogram equalization, JPEG compression, cropping, rotation, and text addition. The proposed AI-assisted module achieves an overall classification accuracy of 96.56%, demonstrating its effectiveness in automatic attack identification and further strengthening the applicability of the proposed quantum watermarking framework for secure image authentication. Resource analysis shows that the watermark generation circuit requires 354 QBs (including 320 for RPA, 10 for D4, and 24 for CNOT), while both embedding and extraction consume 400 QBs each. Theoretical evaluation and empirical validation confirm the technique’s effectiveness in preserving image integrity and confidentiality, establishing it as a viable approach for secure quantum image watermarking in real time applications.
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.
The basics of Quantum Information Processing (QIP) is summarized below, in addition to a comprehensive survey of quantum image-based data hiding techniques. QIP is more efficient and provides higher security than classical information processing. A comparative analysis of the Flexible Representation of Quantum Images (FRQI) and Novel Enhanced Quantum Representation (NEQR) model is also presented. QIP is used in various potential applications, hence offering an interesting and demanding area for researchers [1]. Some of the important applications include medicine, military, environmental monitoring, image processing, communications, computations, and cryptography. This article focusses on the processing of information that can be represented using quantum mechanics [2]. Furthermore, coherence, entanglement, and superposition of quantum states makes quantum computing more suitable to its classical counterpart for information storage and processing [1], [3].