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Quantum Information and Computation

A novel enhanced quantum image representation based on bit-planes for log-polar coordinates

Xiao Chen, Zhihao Liu, Hanwu Chen, Liang Wang

Published Dec 28, 2021• 1 citation
Publisher

Abstract

Quantum image representation has a significant impact in quantum image processing. In this paper, a bit-plane representation for log-polar quantum images (BRLQI) is proposed, which utilizes $(n+4)$ or $(n+6)$ qubits to store and process a grayscale or RGB color image of $2^n$ pixels. Compared to a quantum log-polar image (QUALPI), the storage capacity of BRLQI improves 16 times. Moreover, several quantum operations based on BRLQI are proposed, including color information complement operation, bit-planes reversing operation, bit-planes translation operation and conditional exchange operations between bit-planes. Combining the above operations, we designed an image scrambling circuit suitable for the BRLQI model. Furthermore, comparison results of the scrambling circuits indicate that those operations based on BRLQI have a lower quantum cost than QUALPI. In addition, simulation experiments illustrate that the proposed scrambling algorithm is effective and efficient.

DOI
10.26421/qic22.1-2-2

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Quantum image representation has a significant impact in quantum image processing. In this paper, a bit-plane representation for log-polar quantum images (BRLQI) is proposed, which utilizes (n+4)(n+4)(n+4) or (n+6)(n+6)(n+6) qubits to store and process a grayscale or RGB color image of 2n2^n2n pixels. Compared to a quantum log-polar image (QUALPI), the storage capacity of BRLQI improves 16 times. Moreover, several quantum operations based on BRLQI are proposed, including color information complement operation, bit-planes reversing operation, bit-planes translation operation and conditional exchange operations between bit-planes. Combining the above operations, we designed an image scrambling circuit suitable for the BRLQI model. Furthermore, comparison results of the scrambling circuits indicate that those operations based on BRLQI have a lower quantum cost than QUALPI. In addition, simulation experiments illustrate that the proposed scrambling algorithm is effective and efficient.
Quantum image representation plays an important role in quantum image processing. In this paper, a bitplane representation of quantum images (BRQI) is proposed, which uses (n+4) or (n+6) qubits to store a grayscale or RGB color image of 2npixels. Compared with a novel enhanced quantum representation (NEQR), and a novel quantum representation of color digital images (NCQI), the storage capacity of BRQI improves 16 times and 218times, respectively. Next, some quantum operations based on BRQI are proposed, these operations including complement of colors, reverse of bitplanes, and translation of bitplanes. Analyzed the implementation circuits of these operations, the result indicates that these operations based on BRQI have lower quantum cost than NEQR and NCQI. Furthermore, an image scrambling algorithm based on BRQI is presented by combining the above operations. Simulation experiments and performance analysis show that proposed scrambling algorithm is effective and efficient.
Abstract The quantum image representation based on bit-planes (BRQI) is a widely used model in quantum image processing. It utilizes both the superposition and entanglement properties to store the position and color information of an image effectively, but the time complexity is still high(O(2qn22n)). Here, we propose an improved BRQI model, which still uses log2 q + 1 qubits to represent the color information, and has a low time complexity(O(qn22n)). When storing the value of bit-plane, it can use only one controlled operation to store the values of two adjacent bit-planes at the same time, makes the time and space complexity significantly reduced. Moreover, we design a corresponding quantum image compression algorithm. Simulation experimental results show that the compression efficiency of this model is also better than that of the widely used models NEQR and BRQI, and the time complexity of quantum image representation is further reduced. Hence, our findings will be helpful for further developing the quantum image representation and compression algorithm.
Quantum image processing (QIP) has become one of the most significant fields in quantum computing (QC); it merges quantum mechanics with image processing to improve classical image-processing speed, which involves various operations to advance quantum image representation (QIR). Accordingly, we introduce two new QIRs: The first is based on the wavelength and bit plane, called the quantum image representation bit plane (QIRBP), and the second is based on the wavelength and adjacency pixels, which is called the quantum image representation wavelength correlation (QIRWC). The QIRBP model uses $ b+2n+6 $ quantum bit (qubits) to store a digital color image of size $ {2}^{n}\times {2}^{n} $. In contrast, the QIRWC needs $ 2b+4n+8 $ qubits to store a digital color image of size $ {2}^{n}\times {2}^{n} $ and to entangle the wavelength between two neighboring pixels. While the QIRWC approach is more complex, it is also more efficient on the basis of the transformation data. The complexity arises from the level of information being transmitted. In this work, two new representation methods (QIRBP and QIRWC) are proposed to overcome existing QIR weaknesses by enhancing storage efficiency, enabling compact high-resolution representation, improving data transformation through wavelength correlation and pixel adjacency, reducing noise, achieving greater versatility, and advancing scalable QIR. To prove the efficiency of the proposed methods, they were analyzed and compared with other efficient quantum image representations, outlining their similar and different aspects.
Mostly existing quantum image models represent image in Cartesian coor- dinates. Some complicated affine transformation can not be easily handled in Cartesian coordinates. In this paper, a new representation of Multi-Channel log-polar quantum im- age (MCLPQI) sampled in log-polar coordinates is proposed. This form contains the im- age RGB color information and transparency of the corresponding pixel. Then we give the polynomial preparation process which proves that our quantum image representation state can be made in a feasible time complexity. Finally we discussed color transfor- mation among different channels and single channel color transformations, transparency adjustments. Analysis demonstrates that the MCLPQI is a efficient quantum log-polar color image representation.
Abstract Data encryption is one of the main factors in their transmission. In this paper, we have described an algorithm for color image encryption, some quantum encryption and image scrambling operations will be performed based on bitplane representation of quantum images (BRQI). Next, the image created using the logistic map (key image) is blended with the output of the first step, which was possible with the help of a quantum comparator circuit. Finally we create a secure image as the output of the encryption algorithm. Experiments with simulation and analysis of parameters such as entropy and correlation coefficient of adjacent pixels in three main positions show that the proposed algorithm has been very efficient and effective in securing and encrypting color images.
To address the limitations of existing models that predominantly represent data in Cartesian coordinate systems and RGB color representations, this paper proposes YCrCbQPI (A Quantum Polar Coordinate Color Image Representation Model Based on YCrCb Color Space, YCrCb-QPI). This model integrates luminance and chrominance separation properties of YCrCb with the geometric invariance of logarithmic polar coordinates. Through a differentiated quantum encoding strategy, more qubits are allocated to critical luminance information while less sensitive chrominance information is assigned simplified encoding. Corresponding quantum state preparation circuits are also designed. Theoretical analysis indicates that compared to traditional RGB polar coordinate models, this model achieves significant savings in color information encoding resources while maintaining comparable visual fidelity. Furthermore, the model inherently possesses the rotation and scaling invariance of polar coordinates, establishing a robust foundation for developing efficient quantum image processing algorithms.