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<p>Quantum image processing, as a convergence of quantum computing and image processing, necessitates extensive research into quantum image representations (QIRs), which are among the most significant topics shaping the field of quantum computing (QC) due to their potential opportunities and challenges. This study introduces a novel QIR model based on the hue, saturation, and intensity (HSI) colour model. Our model advances image encoding by uniquely integrating an adjacency matrix to capture spatial pixel relationships with a Fourier transform (FT) representation for pixel intensity. Based on the HSI color space, AFQIRHSI uses a dual-entanglement structure; one state links the adjacency and intensity information, while another efficiently encodes hue and saturation. Named the adjacency Fourier quantum image representation of HSI (AFQIRHSI), this model utilises <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="41598_2025_24168_Article_IEq1.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="76" /> </InlineMediaObject> <EquationSource Format="TEX">\(2 n+p+3\)</EquationSource> </InlineEquation> qubits to store a colour digital image of size <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="41598_2025_24168_Article_IEq2.gif" Format="GIF" Height="15" Rendition="HTML" Resolution="72" Type="Linedraw" Width="54" /> </InlineMediaObject> <EquationSource Format="TEX">\(2^n \times 2^n\)</EquationSource> </InlineEquation>. AFQIRHSI enhances storage capacity by factors of four and two compared to earlier models, such as QIRHSI and EQIRHSI. In this paper, we also present several quantum image operations, including complement colour transformation <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="41598_2025_24168_Article_IEq3.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="44" /> </InlineMediaObject> <EquationSource Format="TEX">\(\left( U_{C C}\right)\)</EquationSource> </InlineEquation>, global colour transformation <InlineEquation ID="IEq4"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="41598_2025_24168_Article_IEq4.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="36" /> </InlineMediaObject> <EquationSource Format="TEX">\(\left( U_{s t}\right)\)</EquationSource> </InlineEquation>, quantum image retrieval <InlineEquation ID="IEq5"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="41598_2025_24168_Article_IEq5.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="34" /> </InlineMediaObject> <EquationSource Format="TEX">\(\left( S_{c t}\right)\)</EquationSource> </InlineEquation>, and quantum image detection (QED). Comparative analyses of various quantum image representations are provided, highlighting their similarities and differences. AFQIRHSI offers a robust foundation for advanced quantum image processing applications, particularly in medical imaging and AI-based image classification.</p>

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 Multilayered quantum computing and simulation system for enhanced image representation of HSI based Fourier transform and adjacency matrix

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年11月17日

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  • Nawres A. Alwan,
  • Suzan J. Obaiys,
  • Nadia M. G. Al-Saidi,
  • Nurul Fazmidar Binti Mohd Noor,
  • Yeliz Karaca

摘要

Quantum image processing, as a convergence of quantum computing and image processing, necessitates extensive research into quantum image representations (QIRs), which are among the most significant topics shaping the field of quantum computing (QC) due to their potential opportunities and challenges. This study introduces a novel QIR model based on the hue, saturation, and intensity (HSI) colour model. Our model advances image encoding by uniquely integrating an adjacency matrix to capture spatial pixel relationships with a Fourier transform (FT) representation for pixel intensity. Based on the HSI color space, AFQIRHSI uses a dual-entanglement structure; one state links the adjacency and intensity information, while another efficiently encodes hue and saturation. Named the adjacency Fourier quantum image representation of HSI (AFQIRHSI), this model utilises \(2 n+p+3\) qubits to store a colour digital image of size \(2^n \times 2^n\) . AFQIRHSI enhances storage capacity by factors of four and two compared to earlier models, such as QIRHSI and EQIRHSI. In this paper, we also present several quantum image operations, including complement colour transformation \(\left( U_{C C}\right)\) , global colour transformation \(\left( U_{s t}\right)\) , quantum image retrieval \(\left( S_{c t}\right)\) , and quantum image detection (QED). Comparative analyses of various quantum image representations are provided, highlighting their similarities and differences. AFQIRHSI offers a robust foundation for advanced quantum image processing applications, particularly in medical imaging and AI-based image classification.