Reviewing past researches on quantum image scaling, only 2D images are studied. And, in a quantum system, the processing speed increases exponentially since parallel computation can be realized with superposition state when compared with classical computer. Consequently, this paper proposes quantum multidimensional color image scaling based on nearest-neighbor interpolation for the first time. Firstly, flexible representation of quantum images (FRQI) is extended to multidimensional color model. Meantime, the nearest-neighbor interpolation is extended to multidimensional color image and cycle translation operation is designed to perform scaling up operation. Then, the circuits are designed for quantum multidimensional color image scaling, including scaling up and scaling down, based on the extension of FRQI. In addition, complexity analysis shows that the circuits in the paper have lower complexity. Examples and simulation experiments are given to elaborate the procedure of quantum multidimensional scaling.
Reviewing past researches on quantum image scaling, only 2D images are studied. And, in a quantum system, the processing speed increases exponentially since parallel computation can be realized with superposition state when compared with classical computer. Consequently, this paper proposes quantum multidimensional color image scaling based on nearest-neighbor interpolation for the first time. Firstly, flexible representation of quantum images (FRQI) is extended to multidimensional color model. Meantime, the nearest-neighbor interpolation is extended to multidimensional color image and cycle translation operation is designed to perform scaling up operation. Then, the circuits are designed for quantum multidimensional color image scaling, including scaling up and scaling down, based on the extension of FRQI. In addition, complexity analysis shows that the circuits in the paper have lower complexity. Examples and simulation experiments are given to elaborate the procedure of quantum multidimensional scaling.
In this study, an important geometric transformation, multidimensional color image scaling based on an n-qubit normal arbitrary superposition state (NASS), is put forward. In order to reduce the complexity of implementation of image scaling in a quantum system, nearest neighbor interpolation algorithm is chosen to implement image scaling up. And the corresponding quantum circuit of implementation is proposed. Finally, we discuss measurements of the part qubits of a NASS state to realize image scaling down. The paper explores theoretical and practical aspects of image processing on a quantum computer.
In this paper, we present an interpolation scheme for FRQI images based on bilinear interpolation. To accomplish this, we formulated several quantum modules, i.e., assignment module, increment module, and quarter module, and suffused them into our proposed quantum image interpolation circuit. The concrete quantum circuits to accomplish up-scaling and down-scaling based on bilinear for FRQI images are designed and the network complexities of them are analyzed. Finally, to validate the proposed method, simulation experiments to enlarge and reduce the test images are executed, whose results are compared with the nearest neighbor interpolation for FRQI images. The up-scaled images by using proposed interpolation algorithm achieve satisfactory results, and both PSNR and SSIM values are better than those of the nearest neighbor method.
As a part of quantum image processing, quantum image scaling is a significant technology for the development of quantum computation. At present, most of the quantum image scaling schemes are based on grayscale images, with relatively little processing for color images. This paper proposes a quantum color image scaling scheme based on bilinear interpolation, which realizes the 2 n 1 × 2 n 2 quantum color image scaling. Firstly, the improved novel quantum representation of color digital images (INCQI) is employed to represent a 2 n 1 × 2 n 2 quantum color image, and the bilinear interpolation method for calculating pixel values of the interpolated image is presented. Then the quantum color image scaling-up and scaling-down circuits are designed by utilizing a series of quantum modules, and the complexity of the circuits is analyzed. Finally, the experimental simulation results of MATLAB based on the classical computer are given. The ultimate results demonstrate that the complexities of the scaling-up and scaling-down schemes are quadratic and linear, respectively, which are much lower than the cubic function and exponential function of other bilinear interpolation schemes.
Image scaling is the basic operation that is widely used in classic image processing, including nearest-neighbor interpolation, bilinear interpolation, and bicubic interpolation. In quantum image processing (QIP), the research on image scaling is focused on nearest-neighbor interpolation, while the related research of bilinear interpolation is very rare, and that of bicubic interpolation has not been reported yet. In this study, a new method based on quantum Fourier transform (QFT) is designed for bilinear interpolation of images. Firstly, some basic functional modules are constructed, in which the new method based on QFT is adopted for the design of two core modules (i.e. addition and multiplication), and then these modules are used to design quantum circuits for the bilinear interpolation of images, including scaling-up and down. Finally, the complexity analysis of the scaling circuits based on the elementary gates is deduced. Simulation results show that the scaling image using bilinear interpolation is clearer than that using the nearest-neighbor interpolation.
A flexible representation of quantum images (FRQI) was proposed to facilitate the extension of classical (non-quantum)-like image processing applications to the quantum computing domain. The representation encodes a quantum image in the form of a normalized state, which captures information about colors and their corresponding positions in the images. Since its conception, a handful of processing transformations have been formulated, among which are the geometric transformations on quantum images (GTQI) and the CTQI that are focused on the color information of the images. In addition, extensions and applications of FRQI representation, such as multi-channel representation for quantum images (MCQI), quantum image data searching, watermarking strategies for quantum images, a framework to produce movies on quantum computers and a blueprint for quantum video encryption and decryption have also been suggested. These proposals extend classical-like image and video processing applications to the quantum computing domain and offer a significant speed-up with low computational resources in comparison to performing the same tasks on traditional computing devices. Each of the algorithms and the mathematical foundations for their execution were simulated using classical computing resources, and their results were analyzed alongside other classical computing equivalents. The work presented in this review is intended to serve as the epitome of advances made in FRQI quantum image processing over the past five years and to simulate further interest geared towards the realization of some secure and efficient image and video processing applications on quantum computers.
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 2 n × 2 n 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.