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A Flexible Representation of Quantum Images for Polynomial Preparation, Image Compression and Processing Operations

カン フック レー, Quang Phuc Le, 芳艶 董, fangyan dong, 薫 廣田, Kaoru HIROTA

Published Feb 1, 2011• 0 citations
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In recent year, quantum image processing got a lot of attention in the field of image processing due to opportunity to place huge image data in quantum Hilbert space. Hilbert space or Euclidean space has infinite dimension to locate and process the image data faster. Moreover, several researches show that, the computational time of quantum process is faster than classical computer. By encoding and compressing the image in quantum domain is still challenging issue. From literature survey, we have proposed a DCTEFRQI (Direct Cosine Transform Efficient Flexible Representation of Quantum Image) algorithm to represent and compress gray image efficiently which save computational time and minimize the complexity of preparation. The objective of this work is to represent and compress various gray image size in quantum computer using DCT(Discrete Cosine Transform) and EFRQI (Efficient Flexible Representation of Quantum Image) approach together. Quirk simulation tool is used to design corresponding quantum image circuit. Due to limitation of qubit, total 16 numbers of qubit are used to represent the gray scale image among those 8 are used to map the coefficient values and the rest 8 are used to generate the corresponding coefficient position. Theoretical analysis and experimental result show that, proposed DCTEFRQI scheme provides better representation and compression compare to DCT-GQIR, DWT-GQIR and DWT-EFRQI in terms of PSNR(Peak Signal to Noise Ratio) and bit rate..

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Flexible Representation of Quantum Images (FRQI) is proposed to provide a representation of images that enables efficient preparation and image processing operators on quantum computers. FRQI captures colors and their corresponding positions in an image into a quantum state. The preparation with polynomial simple operations for FRQI turning a quantum computer from the initialized state to the FRQI state is done by using Hadamard and controlled rotation gates. The Quantum Image Compression (QIC) algorithm reduces simple operations used in the preparation process based on the minimization of Boolean equations are from same color groups of positions. Quantum image processing operators on FRQI based unitary transforms dealing with only colors, colors at some positions and the combination by the quantum Fourier transform of both colors and positions are addressed. The experiments for the storage and retrieval of images using FRQI are implemented in Matlab. The compression ratio of QIC among same color groups ranges from 6.67% to 31.62% on the Lena image.
Quantum image representation is an essential component of quantum image processing and plays a critical role in quantum information processing. Flexible Representation of Quantum Images (FRQI) presents pixel colors and associated locations as a state to represent images on quantum computers. A fundamental part of the quantum image processing system is quantum image compression (QIC), which is utilized to maintain and retrieve binary images. This compression allows us to minimize the number of controlled rotation gates in the quantum circuits. This paper designed optimized quantum circuits and simulated them using Qiskit on a real quantum computer based on minimum boolean expressions to retrieve the 8×4 binary single-digit images. To demonstrate the feasibility and efficacy of quantum image representation, quantum circuits for images were developed using FRQI, and quantum image representation experiments were done on IBM Quantum Experience (IBMQ). We were able to visualize quantum information by doing the quantum measurement on the image information that we had prepared. Without utilizing this method, the number of controlled rotation gates is equal to the number of pixels in the image; however, we showed that by using the QIC algorithm, we could decrease the number of gates significantly. On these images, the maximum and minimum compression ratios of QIC are 90.63% and 68.75%, respectively.
In recent year, quantum image processing got a lot of attention in the field of image processing due to opportunity to place huge image data in quantum Hilbert space. Hilbert space or Euclidean space has infinite dimension to locate and process the image data faster. Moreover, several researches show that, the computational time of quantum process is faster than classical computer. By encoding and compressing the image in quantum domain is still challenging issue. From literature survey, we have proposed a DCTEFRQI (Direct Cosine Transform Efficient Flexible Representation of Quantum Image) algorithm to represent and compress gray image efficiently which save computational time and minimize the complexity of preparation. The objective of this work is to represent and compress various gray image size in quantum computer using DCT(Discrete Cosine Transform) and EFRQI (Efficient Flexible Representation of Quantum Image) approach together. Quirk simulation tool is used to design corresponding quantum image circuit. Due to limitation of qubit, total 16 numbers of qubit are used to represent the gray scale image among those 8 are used to map the coefficient values and the rest 8 are used to generate the corresponding coefficient position. Theoretical analysis and experimental result show that, proposed DCTEFRQI scheme provides better representation and compression compare to DCT-GQIR, DWT-GQIR and DWT-EFRQI in terms of PSNR(Peak Signal to Noise Ratio) and bit rate..