CAJ | 학술논문

为了克服现有彩色图像去噪方法不能有效抑制边缘噪声和保持纹理信息的缺点, 提出了一种结合了离散四元数傅里叶变换（DQFT）和分数阶微分理论的彩色图像去噪改进方法。算法采用四元数矩阵表示一幅彩色图像, 首先对该四元数矩阵进行离散傅里叶变换; 然后将其代入基于分数阶微分的能量泛函极小值求解过程中, 利用变分原理求解并推导出去噪模型, 并与两种传统彩色图像去噪模型进行实验比较。实验结果表明, 提出的模型在去噪效果和纹理保护方面都有更好的表现。
위료극복현유채색도상거조방법불능유효억제변연조성화보지문리신식적결점, 제출료일충결합료리산사원수부리협변환（DQFT）화분수계미분이론적채색도상거조개진방법。산법채용사원수구진표시일폭채색도상, 수선대해사원수구진진행리산부리협변환; 연후장기대입기우분수계미분적능량범함겁소치구해과정중, 이용변분원리구해병추도출거조모형, 병여량충전통채색도상거조모형진행실험비교。실험결과표명, 제출적모형재거조효과화문리보호방면도유경호적표현。
The traditional methods for color image denoising usually can't smooth the edge noise effectively and can't protect the texture information well. To overcome these shortcomings, this paper proposed a novel method for color image denoising which combined DQFT with the theory of fractional order differentiation. The method used a quaternion matrix to represent a color image, and it was carried out by following procedures. Firstly, transformed the quaternion matrix to the DQFT domain. Secondly, applied it to the process of a fractional-order-differentiation-based energy function to seek its minimum, used the variational principle to solve this minimization problem and then inferred the proposed method. Finally, compared the method with two traditional methods for color image denoising to evaluate its superiority. The experimental results show that the proposed method has better performance in denoising and protection of the details.