In this work, we propose a novel Quantum Generalized Neighbor Interpolation (QGNI) circuit which can be used to implement Nearest Neighbor Interpolation (NNI) as a special case of its operations. Nearest neighbor interpolation (NNI) is used in image processing tasks such as image rotation. The proposed quantum circuit takes as input (i) the perpendicular distance between a transformed pixel value and one of the four adjacent integral coordinate locations and (ii) a weighting factor which determines which of the four adjacent integral coordinate locations a transformed pixel value is projected to. corresponding T gate cost is provided.
In this work, we propose a novel Quantum Generalized Neighbor Interpolation (QGNI) circuit which can be used to implement Nearest Neighbor Interpolation (NNI) as a special case of its operations. Nearest neighbor interpolation (NNI) is used in image processing tasks such as image rotation. The proposed quantum circuit takes as input (i) the perpendicular distance between a transformed pixel value and one of the four adjacent integral coordinate locations and (ii) a weighting factor which determines which of the four adjacent integral coordinate locations a transformed pixel value is projected to. corresponding T gate cost is provided.
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.
In the last few years, tremendous improvement in the field of quantum computing has been witnessed. Although quantum technologies such as ion-trap, NMR, quantum dots have emerged as the promising platforms for implementing quantum circuits but these technologies have faced several design issues. One such important design problem is the nearest neighbor condition, which requires the qubits to interact with adjacent neighbors. This problem can be addressed by adding SWAP gates in the circuit. By doing so, the overhead in the circuit increases thus NN designs with minimum number of SWAP gates need to be developed. Focusing on this, here, in this work, we introduce a heuristic design method for efficient NN realization of quantum circuits in 2D architecture. Our NN transformation process is carried out in two phases, where initially in the first phase, the input circuit is mapped to 2D configuration using a qubit placement strategy and then in the second phase NN designs are obtained through SWAP gate insertion. At the end, the design algorithm has been evaluated over a large set of benchmark functions and the results are compared with some of the existing works. From this comparison, it is seen that our proposed method performs better than the reported works.
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.
The classical computer is becoming inefficient to process the ever-increasing number of images generated on daily basis for various purposes. To address this, researchers have shifted attention to exploring the potential of quantum computing to realize image processing. As image pixels are represented as color intensities of integral points on the cartesian coordinates, there is need for interpolations of the color and positions of the pixels to restore the integral points locations after the image points have undergone some computational transformations. While color interpolation has received some attention in Quantum Image Processing, coordinate interpolation has not been explored. In this work, a novel quantum architecture that does image coordinate interpolation is proposed. Furthermore, the architecture generalizes the concept of nearest neighbor interpolation. By partitioning the distance between two adjacent pixels into 2𝑛 discrete levels, a computed point between them can be interpolated to either way depending on the difference between the computed point and a predetermined coefficient that determines where the user wishes to interpolate to. The proposed architecture is based on a quantum subtractor and a novel quantum conditional incrementor, which is another project that was completed in this study. Likewise, the proposed conditional incrementor is based on a novel circuit for incrementor which is also presented in this dissertation together with its associated decrementor. A novel construction of discrete time quantum walk (DTQW) along a closed ring was also proposed as another application of the proposed incrementor. DTQW has wide applications including "universal computation" and in image processing. Therefore, the contributions of this study include introduction of a coordinate interpolation circuit, design and construction of T-count optimized incrementor, decrementor, conditional incrementor, conditional decrementor, conditional incrementor/decrementor circuits, and a T-count efficient implementation of discrete-time quantum walk.
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.
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.