一种改进的基于小波变换和全变分模型的图像去噪算法
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1.新疆师范大学数学科学学院;2.新疆师范高等专科学校数理学院

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An improved image denoising algorithm based on wavelet transform and total variation model
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1.School of Mathematical Sciences,Xinjiang Normal University;2.College of Primary Education,Xinjiang Education Institute

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    摘要:

    图像在获取和传输过程中受到各种噪声的干扰,设计一种能够有效去除噪声,又能有效保留图像原有的边缘、纹理和其它细节特征的去噪算法一直是研究学者们的追求目标。在传统的小波阈值图像去噪算法基础上,本文提出了一种改进的图像去噪算法,该算法结合了小波变换和全变分模型。首先,考虑到图像在离散小波变换域中各层小波系数之间的相关性,本算法对各层高频子带选择不同的自适应阈值,自适应调整小波系数的缩小力度,从而去除图像高频噪声。然后,采用图像全变分模型有效控制图像失真度和平滑程度的基础上去除低频噪声。实验结果表明,该算法在去除噪声的同时,更好地保留图像的边缘、纹理等特征,且在峰值信噪比、结构相似性和视觉质量等方面均优于其他相关去噪算法。

    Abstract:

    Images are corrupted by various types of noise during acquisition and transmission. Designing a denoising algorithm that effectively removes noise while preserving the original edges, textures, and other fine details of the image has long been a goal of researchers. Based on the traditional wavelet thresholding image denoising algorithm, this paper proposes an improved image denoising algorithm that combines wavelet transform and total variation models. First, considering the correlation between wavelet coefficients at different levels in the discrete wavelet transform domain of the image, this method selects different adaptive thresholds for the high frequency subbands at each level and adaptively adjusts the shrinkage of the wavelet coefficients to remove high frequency noise from the image. Then, the total variation model is applied to remove low frequency noise while effectively controlling image distortion and smoothing. Experimental results demonstrate that this algorithm effectively removes noise while better preserving image features such as edges and textures. It outperforms other related denoising algorithms in terms of peak signal-to-noise ratio (PSNR), structural similarity(SSIM), and visual quality.

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历史
  • 收稿日期:2025-08-06
  • 最后修改日期:2025-10-22
  • 录用日期:2025-11-20
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