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arXiv:1701.01537

A Novel Quantum Image Compression Method Based on JPEG

Jian Wang, Nan Jiang, Zhao, Na

Published Jan 6, 2017• 1 citation
arXivHTMLPDF

Abstract

Quantum image processing has been a hot topic. The first step of it is to store an image into qubits, which is called quantum image preparation. Different quantum image representations may have different preparation methods. In this paper, we use GQIR (the generalized quantum image representation) to represent an image, and try to decrease the operations used in preparation, which is also known as quantum image compression. Our compression scheme is based on JPEG (named from its inventor: the Joint Photographic Experts Group) --- the most widely used method for still image compression in classical computers. We input the quantized JPEG coefficients into qubits and then convert them into pixel values. Theoretical analysis and experimental results show that the compression ratio of our scheme is obviously higher than that of the previous compression method.

DOI
10.48550/arxiv.1701.01537

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Quantum image processing has been a hot topic. The first step of it is to store an image into qubits, which is called quantum image preparation. Different quantum image representations may have different preparation methods. In this paper, we use GQIR (the generalized quantum image representation) to represent an image, and try to decrease the operations used in preparation, which is also known as quantum image compression. Our compression scheme is based on JPEG (named from its inventor: the Joint Photographic Experts Group) --- the most widely used method for still image compression in classical computers. We input the quantized JPEG coefficients into qubits and then convert them into pixel values. Theoretical analysis and experimental results show that the compression ratio of our scheme is obviously higher than that of the previous compression method.
In recent years, quantum image computing draws a lot of attention due to storing and processing image data faster compared to classical computers. A number of approaches have been proposed to represent the quantum image inside a quantum computer. Representing and compressing medium and big-size images inside the quantum computer is still challenging. To address this issue, we have proposed a block-wise DCT-EFRQI (Direct Cosine Transform Efficient Flexible Representation of Quantum Image) approach to represent and compress the gray-scale image efficiently to save computational time and reduce the quantum bits (qubits) for the state preparation. In this work, we have demonstrated the capability of block-wise DCT and DWT transformation inside the quantum domain to investigate their relative performances. The Quirk simulation tool is used to design the corresponding quantum image circuit. In the proposed DCT-EFRQI approach, a total of 17 qubits are used to represent the coefficients, the connection between coefficients and state (i.e., auxiliary), and their position for representing and compressing grayscale images inside a quantum computer. Among those, 8 qubits are used to map the coefficient values and the rest are used to generate the corresponding coefficient XY-coordinate position including one auxiliary qubit. Theoretical analysis and experimental results show that the proposed DCT-EFRQI scheme provides better representation and compression compared to DCT-GQIR, DWT-GQIR, and DWT-EFRQI in terms of rate-distortion performance.
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We present a hybrid classical-quantum image preparation scheme that reduces the quantum implementation cost of image loading for quantum pixel information encoding (QPIE). The proposed method, termed JPEG-assisted QPIE (JQPIE), loads only the quantized JPEG coefficients into a quantum register, leading to substantial reductions in \texttt{CX} gate count and circuit depth while preserving reconstruction quality comparable to classical JPEG compression. We develop two variants of the hybrid strategy. The first realizes the complete JPEG decompression pipeline coherently by implementing inverse quantization via a block-encoded unitary operator. The second, referred to as \emph{quantization-free JQPIE} (QF-JQPIE), omits quantization altogether, thereby avoiding the probabilistic nature of block-encoded quantization. Numerical simulations on standard benchmark image datasets (USC--SIPI and Kodak) demonstrate that both variants achieve significant constant-factor reductions in \texttt{CX} gate count and circuit depth relative to direct QPIE loading, while maintaining high reconstruction quality as measured by PSNR and SSIM.
The joint photographic expert group algorithm compresses a digital image by filtering its high spatial-frequency components. Similarly, we introduce a quantum algorithm that uses the quantum Fourier transform to discard the high spatial-frequency qubits of an image, downsampling it to a lower resolution. This allows one to capture, compress, and send images even with limited quantum resources for storage and communication. We show under which conditions this protocol is advantageous with respect to its classical counterpart.
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..
Quantum computing has emerged as a revolutionary paradigm in numerous fields owing to its basis in quantum mechanical concepts such as quantum entanglement and parallelism. This has potential in various applications including computer vision, particularly, image processing and compression. Applications that depend on largescale image data for storing, processing, and transmission have to rely on compression methods for real-time processing. While the classical methods based on discrete cosine transformations (DCT used in JPEG) and discrete wavelet transformations (DWT) perform image compression efficiently, they suffer from trade-off between loss-less compression and compression ratios. In the current work, we would like to explore the usefulness of implementing quantum wavelet transforms for image compression for better PSNR values and execution times. We compare the application of quantum Haar wavelet transform (QHWT) with different quantum encoding methods such as NASS and FRQI and find that NASS-encoded images on application of QHWT gives better PSNR values and shorter runtime with visibly closer details to the original images, showcasing potential for efficient and faster image compression methods.