Periodic noise corrupts digital images during acquisition and transmission stages by adding repetitive patterns. This study introduces a new adaptive Gaussian notch filter (AGNF) in Fourier transform domain for effectively restoring images contaminated with periodic, quasi-periodic and Moiré pattern noises. Since periodic noises are sinusoidal functions added to the uncorrupted images, Fourier transform of images make these noisy functions to concentrate as easily distinguishable conjugate peaks in frequency domain. The proposed AGNF effectively identifies the noisy peak positions and adaptively quantifies the associated noisy areas by analysing the ratio of averages of frequencies from adaptively varying neighbourhoods. These identified noisy peaks are then diffused by Gaussian notch filter of adaptively varying sizes. The proposed filter ensures maximum diffusion of identified noisy peak areas by maintaining the minimum frequency values from the outputs of overlapping notch filters. Visual and quantitative experimental analysis of the proposed algorithm with mean absolute error, peak signal-to-noise ratio, mean structural similarity index measure and computation time reveals that AGNF is better in restoring images contaminated with periodic noises when compared to other methods.

中文翻译：

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自适应高斯陷波滤波器，用于消除数字图像中的周期性噪声

通过添加重复模式，周期性噪声会在采集和传输阶段破坏数字图像。这项研究在傅立叶变换域中引入了一种新的自适应高斯陷波滤波器（AGNF），可以有效地恢复被周期性，准周期性和莫尔图案噪声污染的图像。由于周期性噪声是添加到未损坏图像的正弦函数，因此图像的傅立叶变换使这些噪声函数集中为频域中易于区分的共轭峰。所提出的AGNF通过分析来自自适应变化邻域的频率平均值之比，有效地识别出噪声峰值位置并自适应地量化相关的噪声区域。然后，通过自适应变化大小的高斯陷波滤波器将这些识别出的噪声峰值扩散。所提出的滤波器通过保持重叠陷波滤波器输出的最小频率值来确保已识别噪声峰值区域的最大扩散。对所提算法的视觉和定量实验分析，包括平均绝对误差，峰值信噪比，平均结构相似性指标度量和计算时间，发现与其他方法相比，AGNF能够更好地恢复被周期性噪声污染的图像。