Nawres A. Alwan, Suzan J. Obaiys, Nadia M. G. Al-Saidi, Nurul Fazmidar Binti Mohd Noor, Yeliz Karaca, and colleagues have introduced a novel quantum image representation (QIR) model utilizing the hue, saturation, and intensity (HSI) color model. Published November 17, 2025, in Scientific Reports, this adjacency Fourier quantum image representation of HSI (AFQIRHSI) integrates an adjacency matrix with a Fourier transform for pixel intensity encoding, employing a dual-entanglement structure. AFQIRHSI requires (2 n+p+3) qubits to store a colour digital image of size (2^n \times 2^n) and demonstrates enhanced storage capacity, achieving improvements of factors four and two over existing QIRHSI and EQIRHSI models.
Quantum Image Processing Foundations
Quantum image processing (QIP) integrates quantum computing and image analysis, offering potential benefits like exponential storage gains and leveraging quantum properties such as entanglement and parallelism. This field focuses on quantum image representation (QIR) and processing algorithms to improve the handling of visual data. Numerous QIR models have been developed over the years, including qubit lattice, entangled images, and more recent approaches like FRQI and NEQR, all aiming to represent images using qubits instead of classical bits efficiently.
The study introduces a novel QIR model, the adjacency Fourier quantum image representation of HSI (AFQIRHSI), built on the hue-saturation-intensity (HSI) colour model. AFQIRHSI uniquely combines an adjacency matrix – capturing spatial pixel relationships – with a Fourier transform (FT) representation of pixel intensity. This model utilizes (2 n+p+3) qubits to store a colour digital image of size (2^n \times 2^n), offering improved storage capacity.
AFQIRHSI demonstrates enhanced storage compared to earlier models: it achieves improvements of factors four and two over QIRHSI and EQIRHSI respectively. The research also presents quantum image operations like complement colour transformation, global colour transformation, quantum image retrieval, and quantum image detection. These advancements position AFQIRHSI as a robust foundation for applications in areas like medical imaging and AI-based image classification.
Quantum Computing Advantages
Quantum computing offers advantages in data storage and computational efficiency due to quantum characteristics like coherence, superposition, and entanglement. This has driven research into quantum image processing (QIP), aiming to improve image handling through qubit-based systems and algorithms. QIP builds upon foundational knowledge of quantum information and computing, addressing inefficiencies found in classical computation and opening doors for advancements in fields like AI and machine learning.
The newly developed adjacency Fourier quantum image representation of HSI (AFQIRHSI) demonstrates enhanced storage capacity. Specifically, AFQIRHSI utilizes (2 n+p+3) qubits to store a (2^n \times 2^n) colour digital image, providing improvements of factors four and two compared to earlier models like QIRHSI and EQIRHSI. This model uniquely integrates an adjacency matrix with a Fourier transform to capture spatial pixel relationships and pixel intensity, furthering image encoding techniques.
Recent progress in QIP has led to a variety of quantum image representation models, including those leveraging Fourier transformations and HSI/HSL colour spaces. Building on these, the QIRHSI model was proposed in 2022, integrating FRQI and NEQR, and subsequently enhanced with the EQIRHSI method. These developments demonstrate a growing body of research focused on efficient quantum image handling, storage, and processing techniques.
Quantum Image Representation (QIR) Overview
Quantum Image Representation (QIR) is a crucial area within quantum computing, driven by the potential of leveraging quantum mechanics for enhanced image processing. Research focuses on developing efficient ways to represent images using qubits, addressing limitations of classical computation in handling visual data. Several QIR models have been proposed over the years, including methods utilizing Fourier transforms and color spaces like HSI and HSL, with the goal of achieving gains in storage and processing capabilities.
The Adjacency Fourier Quantum Image Representation of HSI (AFQIRHSI) is a novel QIR model that utilizes (2n+p+3) qubits to store a colour digital image of size (2^n \times 2^n). It uniquely integrates an adjacency matrix—capturing spatial pixel relationships—with a Fourier transform for pixel intensity. This model builds on earlier work, such as QIRHSI and EQIRHSI, and offers improved storage capacity, providing factors of four and two improvements over those previous methods.
AFQIRHSI utilizes a dual-entanglement structure, with one state encoding adjacency and intensity information, and another efficiently representing hue and saturation. The development of QIR models like AFQIRHSI is motivated by the need for efficient visual data management, a challenge amplified by the exponential increase in image and video content captured by modern devices. It allows for advances in areas like medical imaging and AI-based image classification.
Challenges in Early Quantum Computing
Early quantum computing faces challenges specifically in representing images within quantum states and then preparing and processing those quantum images on quantum computers. Despite advancements in quantum computation leveraging superposition and entanglement for data storage and processing, efficiently handling visual data remains a key hurdle. Numerous quantum image representation (QIR) models have been proposed – including FRQI, NEQR, and QIRHSI – demonstrating ongoing efforts to overcome these limitations and bridge quantum computing with image analysis.
The development of effective quantum image representations requires careful consideration of qubit usage and storage capacity. A newly introduced adjacency Fourier quantum image representation of HSI (AFQIRHSI) utilizes (2 n+p+3) qubits to store a colour digital image of size (2^n \times 2^n). This model improves upon earlier representations like QIRHSI and EQIRHSI, offering enhanced storage capacity by factors of four and two respectively, highlighting the drive for more efficient quantum image encoding.
Research has explored various colour spaces, like HIS and HSL, to optimize quantum image representation. Models such as QIRHSI, which integrates FRQI and NEQR, and EQIRHSI represent incremental progress. The development of quantum image processing (QIP) algorithms – for tasks like retrieval, storage, and compression – is ongoing, alongside the exploration of quantum features like entanglement and parallelism to enhance visual data handling.
QIP and Classical Image Processing
Quantum image processing (QIP) integrates quantum computing with image analysis, offering potential benefits like increased storage capacity and leveraging quantum properties such as entanglement and parallelism. This field focuses on quantum image representations (QIR) and processing algorithms to improve visual data handling. Several QIR models have been developed over the years, including qubit lattice, entangled images, and more recently, models utilizing the Hue, Saturation, and Intensity (HSI) colour space to represent image data efficiently.
A novel approach, the adjacency Fourier quantum image representation of HSI (AFQIRHSI), utilizes (2n + p + 3) qubits to store a colour digital image of size (2^n \times 2^n). This model combines an adjacency matrix to capture spatial pixel relationships with a Fourier transform for pixel intensity, encoding hue and saturation with a dual-entanglement structure. AFQIRHSI demonstrates enhanced storage capacity, achieving improvements of four and two times over earlier models like QIRHSI and EQIRHSI.
Building on previous work with HSI colour models, researchers proposed QIRHSI in 2022, integrating FRQI and NEQR models. This was followed by EQIRHSI, an enhanced version. These advancements highlight a trend toward leveraging quantum computing to address inefficiencies in classical computation, particularly in tasks involving large volumes of visual data and demanding image processing applications like medical imaging and AI-based image classification.
Quantum Algorithms for Image Tasks
Quantum image processing seeks to improve image handling by leveraging quantum computing’s advantages in data storage and computational efficiency. This field utilizes properties like quantum coherence, superposition, and entanglement to address inefficiencies in classical computation. Research focuses on quantum image representations (QIR), algorithms, and measurement, requiring careful preparation of quantum images and analysis of involved qubits. Several QIR models have been proposed, including qubit lattice, entangled images, and FRQI, to enhance visual data handling.
A novel approach, the adjacency Fourier quantum image representation of HSI (AFQIRHSI), was introduced as an advancement in QIR. AFQIRHSI utilizes (2n+p+3) qubits to store a colour digital image of size (2^n \times 2^n), integrating an adjacency matrix and Fourier transform for pixel intensity within the HSI colour space. This model utilizes a dual-entanglement structure for hue, saturation, and intensity data.
AFQIRHSI demonstrates improved storage capacity compared to earlier models like QIRHSI and EQIRHSI, offering gains of factors four and two respectively. The study also presents quantum image operations, including colour transformations and image retrieval/detection. Building upon prior work utilizing Fourier transformations and HSI/HSL colour spaces, AFQIRHSI offers a robust foundation for advanced quantum image processing, particularly in areas like medical imaging and AI-based classification.
Quantum Image Storage and Efficiency
The Adjacency Fourier Quantum Image Representation of HSI (AFQIRHSI) is a new quantum image representation (QIR) model. It utilizes (2n+p+3) qubits to store a colour digital image of size (2^n \times 2^n). This model uniquely combines an adjacency matrix – capturing spatial pixel relationships – with a Fourier transform (FT) representation of pixel intensity, building upon the hue, saturation, and intensity (HSI) colour model. AFQIRHSI employs a dual-entanglement structure for efficient encoding.
AFQIRHSI demonstrates improved storage capacity compared to earlier QIR models. Specifically, it offers enhancements of factors of four and two over the QIRHSI and EQIRHSI models, respectively. The development builds on previous work utilizing HSI and HSL colour spaces, and leverages advancements in quantum Fourier transforms for image representation. This makes it a potentially valuable advancement in the field of quantum image processing.
Recent progress in quantum image processing (QIP) has led to numerous QIR models, including FRQI, NEQR, and QIRHSI. The source highlights the importance of efficiently managing increasing volumes of visual data captured by modern devices. QIP aims to leverage quantum properties like entanglement and parallelism to improve both storage and processing capabilities beyond those of classical computing methods for image analysis.
Existing Quantum Image Representation Models
Recent advancements have focused on developing various quantum image representation (QIR) models to efficiently handle visual data. Several approaches exist, including qubit lattice, entangled images, and flexible representation of quantum images (FRQI). Notably, researchers have explored models based on Fourier transformations, with Artyom et al. proposing a model using the quantum Fourier transform (QFT) in 2020. These models aim to leverage quantum mechanics for improvements in image storage and processing capabilities.
A specific focus has been on utilizing the hue, saturation, and intensity (HSI) colour space for QIR. In 2022, a quantum image representation for HSI (QIRHSI) was proposed, integrating FRQI and NEQR models. Building upon this, researchers introduced the Enhanced Quantum Image Representation for HSI Colour Model (EQIRHSI) in 2023. These HSI-based models demonstrate a trend toward utilising colour information within quantum representations.
The newly introduced adjacency Fourier quantum image representation of HSI (AFQIRHSI) utilizes (2 n+p+3) qubits to store a colour digital image of size (2^n \times 2^n). This model enhances storage capacity by factors of four and two compared to earlier models like QIRHSI and EQIRHSI, by uniquely integrating an adjacency matrix to capture spatial pixel relationships with a Fourier transform (FT) representation for pixel intensity. This offers a robust foundation for advanced quantum image processing applications.
Fourier Transform in Quantum Imaging
The study introduces a novel quantum image representation (QIR) model, named adjacency Fourier quantum image representation of HSI (AFQIRHSI), which utilizes the hue, saturation, and intensity (HSI) color model. AFQIRHSI uniquely integrates an adjacency matrix – capturing spatial pixel relationships – with a Fourier transform (FT) representation for pixel intensity. This approach leverages the benefits of both spatial and frequency domain information for image encoding, building on prior work with models like FRQI and NEQR, and representing images using (2 n+p+3) qubits for a (2^n \times 2^n) image.
Researchers have previously explored quantum image representation using Fourier transformations, with Artyom et al. proposing a model using the quantum Fourier transform (QFT) in 2020. Building on this, the new AFQIRHSI model aims to enhance storage capacity. Comparative analyses demonstrate AFQIRHSI offers improvements, achieving storage capacity gains by factors of four and two when compared to earlier QIRHSI and EQIRHSI models. The integration of the Fourier transform is key to this improved efficiency.
Prior research in 2022 introduced the quantum image representation for HSI (QIRHSI), integrating FRQI and NEQR. In 2023, this was enhanced with the EQIRHSI model. The current study builds upon these foundations, proposing AFQIRHSI as a further advancement in quantum image representation, particularly leveraging the HSI color space and the benefits of combining adjacency matrices with Fourier transform techniques for improved storage and processing capabilities.
HSI and HSL Colour Spaces
Research has expanded into utilizing different colour spaces within quantum image processing, specifically exploring hue, saturation, and intensity (HSI) and hue, saturation, and lightness (HSL). In 2020, a model employing the quantum Fourier transform was proposed for representing signals and images in quantum form. Building on this, the quantum image representation for HSI (QIRHSI) was introduced in 2022, integrating the FRQI and NEQR models to represent images using quantum states.
The newly developed adjacency Fourier quantum image representation of HSI (AFQIRHSI) utilises (2 n+p+3) qubits to store a colour digital image of size (2^n \times 2^n). This model demonstrates improved storage capacity, achieving gains of a factor of four and two when compared to earlier representations such as QIRHSI and EQIRHSI. AFQIRHSI achieves this by integrating an adjacency matrix—capturing spatial pixel relationships—with a Fourier transform representation of pixel intensity.
Several quantum image operations have been developed alongside AFQIRHSI, including complement colour transformation ((U_{C C})), global colour transformation ((U_{s t})), quantum image retrieval ((S_{c t})), and quantum image detection (QED). The development of these representations and operations aim to bridge quantum computing and image analysis, enabling benefits like exponential storage gains and the leveraging of quantum features like entanglement and parallelism.
QIRHSI: Quantum Image Representation for HSI
The Adjacency Fourier Quantum Image Representation of HSI (AFQIRHSI) is a new quantum image representation (QIR) model utilizing the hue, saturation, and intensity (HSI) color model. This model uniquely combines an adjacency matrix – capturing spatial pixel relationships – with a Fourier transform (FT) for pixel intensity. AFQIRHSI employs a dual-entanglement structure, using one state for adjacency and intensity, and another for hue and saturation, offering advancements in image encoding techniques.
AFQIRHSI requires (2 n+p+3) qubits to store a color digital image measuring (2^n \times 2^n). Notably, this representation improves storage capacity, achieving gains of a factor of four and two compared to previous models like QIRHSI and EQIRHSI respectively. The development builds on prior research into HSI and HSL color spaces, and existing QIR models such as FRQI and NEQR which were integrated into the earlier QIRHSI model.
Beyond representation, the research also presents several quantum image operations. These include complement color transformation ((U_{C C})), global color transformation ((U_{s t})), quantum image retrieval ((S_{c t})), and quantum image detection (QED). AFQIRHSI is intended to provide a robust foundation for advanced applications, particularly in fields like medical imaging and AI-based image classification, leveraging quantum computing’s benefits in data storage and computational efficiency.
EQIRHSI: Enhanced Quantum HSI Representation
The Adjacency Fourier Quantum Image Representation of HSI (AFQIRHSI) is a novel quantum image representation (QIR) model based on the hue, saturation, and intensity (HSI) color model. It uniquely combines an adjacency matrix—capturing spatial pixel relationships—with a Fourier transform (FT) representation of pixel intensity. This model utilizes (2n+p+3) qubits to store a color digital image of size (2^n \times 2^n), advancing image encoding techniques within quantum computing.
AFQIRHSI demonstrates improved storage capacity compared to previous models; it offers enhancements by factors of four and two over QIRHSI and EQIRHSI, respectively. Building on the Flexible Representation of Quantum Images (FRQI) and Novel Enhanced Quantum Representation (NEQR) models, this representation aims to address inefficiencies in classical computation by leveraging quantum computing’s strengths in data storage and computational efficiency.
Researchers have explored various QIR models, including those based on Fourier transformations, and HSI/HSL color spaces. The development of AFQIRHSI contributes to a growing body of work in quantum image processing, with potential applications in fields like medical imaging and AI-based image classification, pushing the boundaries of quantum information processing beyond classical computing.
AFQIRHSI: Adjacency Fourier Quantum Representation
The Adjacency Fourier Quantum Image Representation of HSI (AFQIRHSI) is a novel quantum image representation (QIR) model utilizing the hue, saturation, and intensity (HSI) color model. This model uniquely integrates an adjacency matrix—capturing spatial pixel relationships—with a Fourier transform (FT) representation for pixel intensity. AFQIRHSI employs a dual-entanglement structure, with one state encoding adjacency and intensity, and another efficiently encoding hue and saturation, building upon previous QIR models like QIRHSI and EQIRHSI.
AFQIRHSI requires (2n+p+3) qubits to store a colour digital image of size (2^n \times 2^n). Importantly, this representation offers improved storage capacity compared to earlier methods; it achieves factors of four and two enhancements over QIRHSI and EQIRHSI, respectively. The development of AFQIRHSI addresses key hurdles in quantum image processing, specifically the efficient representation of images in quantum states and the preparation/processing of those images on quantum computers.
Beyond representation, the research also introduces several quantum image operations including complement colour transformation ((U_{C C})), global colour transformation ((U_{s t})), quantum image retrieval ((S_{c t})), and quantum image detection (QED). This work positions AFQIRHSI as a robust foundation for advanced quantum image processing, with potential applications in areas like medical imaging and AI-based image classification, extending beyond previous models based on Fourier transformations.
AFQIRHSI Qubit Storage Capacity
The Adjacency Fourier Quantum Image Representation of HSI (AFQIRHSI) utilizes a dual-entanglement structure to store color digital images. One entanglement state links adjacency and intensity information, while the other efficiently encodes hue and saturation. Specifically, AFQIRHSI requires (2n + p + 3) qubits to store an image of size (2^n \times 2^n). This model builds upon previous work, integrating the Flexible Representation of Quantum Images (FRQI) and Novel Enhanced Quantum Representation (NEQR) models for improved image encoding.
AFQIRHSI demonstrates advancements in storage capacity compared to earlier quantum image representations. The source highlights that AFQIRHSI offers improvements by factors of four and two over the QIRHSI and EQIRHSI models, respectively. This enhancement is significant because efficient quantum image storage is a key challenge in the field of quantum image processing, impacting applications like medical imaging and AI-based image classification.
Building on previous models like QIRHSI (proposed in 2022) and EQIRHSI, AFQIRHSI utilizes the HSI color space. Researchers have increasingly focused on HSI and HSL color spaces over the last decade to optimize quantum image representation. The development of AFQIRHSI demonstrates a continued effort to refine quantum image encoding methods, addressing the core challenges of representing images in quantum states and efficiently processing them on quantum computers.
Quantum Image Operations and Analysis
Quantum image processing (QIP) merges quantum computing with image analysis, offering potential gains in storage and processing efficiency due to quantum properties like entanglement and parallelism. This field focuses on quantum image representations (QIR) and processing algorithms to improve visual data handling, extending beyond classical computing which relies on bits. Numerous QIR models have been developed, including qubit lattice, entangled images, and more recent approaches like FRQI and NEQR, all aiming to optimize image storage and manipulation on quantum platforms.
The researchers introduced a novel QIR model, the adjacency Fourier quantum image representation of HSI (AFQIRHSI), which is based on the hue, saturation, and intensity (HSI) colour model. AFQIRHSI utilizes (2 n+p+3) qubits to store a colour digital image of size (2^n \times 2^n). This model integrates an adjacency matrix with a Fourier transform to capture spatial pixel relationships and pixel intensity. Importantly, it offers enhanced storage capacity—four times better than QIRHSI and twice that of EQIRHSI.
Beyond representation, the study also details several quantum image operations, including complement colour transformation ((U_{C C})), global colour transformation ((U_{s t})), quantum image retrieval ((S_{c t})), and quantum image detection (QED). Building on previous work, like the 2022 QIRHSI and 2023 EQIRHSI models, AFQIRHSI is positioned as a robust foundation for advanced applications in areas like medical imaging and AI-based image classification.
