中国物理B ›› 2024, Vol. 33 ›› Issue (4): 40302-040302.doi: 10.1088/1674-1056/ad1b40

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Integer multiple quantum image scaling based on NEQR and bicubic interpolation

Shuo Cai(蔡硕)1,2, Ri-Gui Zhou(周日贵)1,2,†, Jia Luo(罗佳)1,2,4,‡, and Si-Zhe Chen(陈思哲)3   

  1. 1 College of Information Engineering, Shanghai Maritime University, Shanghai 201306, China;
    2 Research Center of Intelligent Information Processing and Quantum Intelligent Computing, Shanghai 201306, China;
    3 College of Merchant Marine, Shanghai Maritime University, Shanghai 201306, China;
    4 School of Mathematics and Computational Science, Shangrao Normal University, Shangrao 334001, China
  • 收稿日期:2023-06-27 修回日期:2023-12-10 接受日期:2024-01-05 出版日期:2024-03-19 发布日期:2024-03-22
  • 通讯作者: Ri-Gui Zhou, Jia Luo E-mail:rgzhou@shmtu.edu.cn;luojia@shmtu.edu.cn
  • 基金资助:
    Project supported by the Scientific Research Fund of Hunan Provincial Education Department, China (Grant No. 21A0470), the Natural Science Foundation of Hunan Province, China (Grant No. 2023JJ50268), the National Natural Science Foundation of China (Grant Nos. 62172268 and 62302289), and the Shanghai Science and Technology Project, China (Grant Nos. 21JC1402800 and 23YF1416200).

Integer multiple quantum image scaling based on NEQR and bicubic interpolation

Shuo Cai(蔡硕)1,2, Ri-Gui Zhou(周日贵)1,2,†, Jia Luo(罗佳)1,2,4,‡, and Si-Zhe Chen(陈思哲)3   

  1. 1 College of Information Engineering, Shanghai Maritime University, Shanghai 201306, China;
    2 Research Center of Intelligent Information Processing and Quantum Intelligent Computing, Shanghai 201306, China;
    3 College of Merchant Marine, Shanghai Maritime University, Shanghai 201306, China;
    4 School of Mathematics and Computational Science, Shangrao Normal University, Shangrao 334001, China
  • Received:2023-06-27 Revised:2023-12-10 Accepted:2024-01-05 Online:2024-03-19 Published:2024-03-22
  • Contact: Ri-Gui Zhou, Jia Luo E-mail:rgzhou@shmtu.edu.cn;luojia@shmtu.edu.cn
  • Supported by:
    Project supported by the Scientific Research Fund of Hunan Provincial Education Department, China (Grant No. 21A0470), the Natural Science Foundation of Hunan Province, China (Grant No. 2023JJ50268), the National Natural Science Foundation of China (Grant Nos. 62172268 and 62302289), and the Shanghai Science and Technology Project, China (Grant Nos. 21JC1402800 and 23YF1416200).

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摘要： As a branch of quantum image processing, quantum image scaling has been widely studied. However, most of the existing quantum image scaling algorithms are based on nearest-neighbor interpolation and bilinear interpolation, the quantum version of bicubic interpolation has not yet been studied. In this work, we present the first quantum image scaling scheme for bicubic interpolation based on the novel enhanced quantum representation (NEQR). Our scheme can realize synchronous enlargement and reduction of the image with the size of 2n×2n by integral multiple. Firstly, the image is represented by NEQR and the original image coordinates are obtained through multiple CNOT modules. Then, 16 neighborhood pixels are obtained by quantum operation circuits, and the corresponding weights of these pixels are calculated by quantum arithmetic modules. Finally, a quantum matrix operation, instead of a classical convolution operation, is used to realize the sum of convolution of these pixels. Through simulation experiments and complexity analysis, we demonstrate that our scheme achieves exponential speedup over the classical bicubic interpolation algorithm, and has better effect than the quantum version of bilinear interpolation.

关键词: quantum image processing, image scaling, bicubic interpolation, quantum circuit

Abstract: As a branch of quantum image processing, quantum image scaling has been widely studied. However, most of the existing quantum image scaling algorithms are based on nearest-neighbor interpolation and bilinear interpolation, the quantum version of bicubic interpolation has not yet been studied. In this work, we present the first quantum image scaling scheme for bicubic interpolation based on the novel enhanced quantum representation (NEQR). Our scheme can realize synchronous enlargement and reduction of the image with the size of 2n×2n by integral multiple. Firstly, the image is represented by NEQR and the original image coordinates are obtained through multiple CNOT modules. Then, 16 neighborhood pixels are obtained by quantum operation circuits, and the corresponding weights of these pixels are calculated by quantum arithmetic modules. Finally, a quantum matrix operation, instead of a classical convolution operation, is used to realize the sum of convolution of these pixels. Through simulation experiments and complexity analysis, we demonstrate that our scheme achieves exponential speedup over the classical bicubic interpolation algorithm, and has better effect than the quantum version of bilinear interpolation.

Key words: quantum image processing, image scaling, bicubic interpolation, quantum circuit

中图分类号:  (Quantum information)

  • 03.67.-a
03.67.Ac (Quantum algorithms, protocols, and simulations) 07.05.Pj (Image processing) 03.67.Lx (Quantum computation architectures and implementations)