量子彩色图像的频域滤波

为解决量子彩色图像滤波问题，该文提出一种基于量子傅里叶变换的频域滤波方法。首先采用新颖的增强量子描述(NEQR)方案将彩色图像描述为量子图像，然后对该量子图像实施傅里叶变换，采用基于滤波函数定义的量子Oracle将变换后的图像划分为不同频率的图像，最后通过逆量子傅里叶变换将这些不同频率的量子图像变换到空域，通过对空域量子图像实施测量即可得到不同频率的经典滤波图像。文中给出了具体的量子滤波线路，以彩色图像平滑、锐化、周期噪声消除为例，验证了提出方案的正确性。

Quantum Color Image Filtering in the Frequency Domain

To solve the problem of quantum color image filtering, this paper proposes a frequency domain filtering method based on Quantum Fourier Transform (QFT). Firstly, the classical color image is represented as a quantum image by Novel Enhanced Quantum Representation (NEQR) scheme, then the QFT is applied to the quantum image, and the transformed image is divided into different frequency images using quantum Oracle defined according to filter function. Finally, these quantum images of different frequencies are transformed into spatial domain by Inverter Quantum Fourier Transform (IQFT). Through the measurement, different frequency filtering images can be obtained. In this paper, a specific quantum filter circuit is given, and the correctness of the proposed scheme is verified by taking the color image smoothing, sharpening and periodic noise elimination as an example.