As a part of quantum image processing, quantum image filtering is a crucial technology in the development of quantum computing. Low-pass filtering can effectively achieve anti-aliasing effects on images. Currently, most quantum image filterings are based on classical domains and grayscale images, and there are relatively fewer studies on anti-aliasing in the quantum domain. This paper proposes a scheme for anti-aliasing filtering based on quantum grayscale and color image scaling in the spatial domain. It achieves the effect of anti-aliasing filtering on quantum images during the scaling process. First, we use the novel enhanced quantum representation (NEQR) and the improved quantum representation of color images (INCQI) to represent classical images. Since aliasing phenomena are more pronounced when images are scaled down, this paper focuses only on the anti-aliasing effects in the case of reduction. Subsequently, we perform anti-aliasing filtering on the quantum representation of the original image and then use bilinear interpolation to scale down the image, achieving the anti-aliasing effect. The constructed pyramid model is then used to select an appropriate image for upscaling to the original image size. Finally, the complexity of the circuit is analyzed. Compared to the images experiencing aliasing effects solely due to scaling, applying anti-aliasing filtering to the images results in smoother and clearer outputs. Additionally, the anti-aliasing filtering allows for manual intervention to select the desired level of image smoothness.
As a part of quantum image processing, quantum image filtering is a crucial technology in the development of quantum computing. Low-pass filtering can effectively achieve anti-aliasing effects on images. Currently, most quantum image filterings are based on classical domains and grayscale images, and there are relatively fewer studies on anti-aliasing in the quantum domain. This paper proposes a scheme for anti-aliasing filtering based on quantum grayscale and color image scaling in the spatial domain. It achieves the effect of anti-aliasing filtering on quantum images during the scaling process. First, we use the novel enhanced quantum representation (NEQR) and the improved quantum representation of color images (INCQI) to represent classical images. Since aliasing phenomena are more pronounced when images are scaled down, this paper focuses only on the anti-aliasing effects in the case of reduction. Subsequently, we perform anti-aliasing filtering on the quantum representation of the original image and then use bilinear interpolation to scale down the image, achieving the anti-aliasing effect. The constructed pyramid model is then used to select an appropriate image for upscaling to the original image size. Finally, the complexity of the circuit is analyzed. Compared to the images experiencing aliasing effects solely due to scaling, applying anti-aliasing filtering to the images results in smoother and clearer outputs. Additionally, the anti-aliasing filtering allows for manual intervention to select the desired level of image smoothness.
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.
For some image processing algorithms such as edge detection and segmentation, filtering in the spatial domain is an important pre-processing to improve the quality of the image by removing the noise in the images. The time and memory requirements for processing also increase as the size of the images increases. Besides, excessive blurring of the image during noise removal operation can lead to excessive deterioration of image quality. Therefore, the balance between noise reduction and blur needs to be well adjusted. In this paper, a new quantum method for noise reduction on quantum images using QFT-based arithmetic operators is proposed and quantum circuits are designed. Mean filtering operators of different sizes are used to remove noise. First, the classical image is represented by the gray scale quantum image model, the novel enhanced quantum representation (NEQR) model. A quantum method is proposed and circuits are presented for the realization of Mean filters of different sizes on the basis of addition and division operations. Finally, the performance of the method is evaluated by presenting the circuit complexity of the method and the experimental results. In the proposed method, it is aimed to use less resources and reduce the circuit complexity. The optimal filtering operator size is investigated for the balance between noise reduction and image blur.
In recent years, quantum image processing is one of the most active fields in quantum computation and quantum information. Image scaling as a kind of image geometric transformation has been widely studied and applied in the classical image processing, however, the quantum version of which does not exist. This paper is concerned with the feasibility of the classical bilinear interpolation based on novel enhanced quantum image representation (NEQR). Firstly, the feasibility of the bilinear interpolation for NEQR is proven. Then the concrete quantum circuits of the bilinear interpolation including scaling up and scaling down for NEQR are given by using the multiply Control-Not operation, special adding one operation, the reverse parallel adder, parallel subtractor, multiplier and division operations. Finally, the complexity analysis of the quantum network circuit based on the basic quantum gates is deduced. Simulation result shows that the scaled-up image using bilinear interpolation is clearer and less distorted than nearest interpolation.
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.
This work focuses into the emerging field of quantum image representation, which is a key for processing grayscale and color images on quantum computing platforms. We explore foundational methods like the qubit lattice model, the flexible representation for quantum images, the novel enhanced quantum representation, and the generalized quantum image representation, and categorize them into state-based, amplitude-based, and quaternion-based representations - the latter offering holistic color processing. A novel discrete signal representation mapping data on the unit circle will be introduced to simplify the Fourier transform concepts in quantum systems. We will examine crucial quantum operations, including quantum gradients, multiplication, square roots, Fourier transform, and filtering. Challenges in implementing the circular convolution on quantum hardware will be addressed with practical examples such as quantum low-pass and high-pass filters and 3-qubit convolution circuits. Additionally, we will discuss ongoing research into quantum algorithms inspired by classical transform processing, including the Fourier transforms, that leverage quantum states’ unique properties to achieve efficient encoding, transformation, and decoding of images.
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.