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基于跨尺度低秩约束的图像盲解卷积算法

彭天奇 禹晶 肖创柏

彭天奇, 禹晶, 肖创柏. 基于跨尺度低秩约束的图像盲解卷积算法. 自动化学报, 2020, 46(x): 1−18 doi: 10.16383/j.aas.c190845
引用本文: 彭天奇, 禹晶, 肖创柏. 基于跨尺度低秩约束的图像盲解卷积算法. 自动化学报, 2020, 46(x): 1−18 doi: 10.16383/j.aas.c190845
Peng Tian-Qi, Yu Jing, Xiao Chuang-Bai. Blind image deconvolution via cross-scale low rank prior. Acta Automatica Sinica, 2020, 46(x): 1−18 doi: 10.16383/j.aas.c190845
Citation: Peng Tian-Qi, Yu Jing, Xiao Chuang-Bai. Blind image deconvolution via cross-scale low rank prior. Acta Automatica Sinica, 2020, 46(x): 1−18 doi: 10.16383/j.aas.c190845

基于跨尺度低秩约束的图像盲解卷积算法

doi: 10.16383/j.aas.c190845
基金项目: 北京市教育委员会科技发展计划(KM201910005029), 北京市自然科学基金资助项目(4172002)资助
详细信息
    作者简介:

    彭天奇:北京工业大学信息学部计算机学院硕士研究生. 主要研究方向为图像处理、模式识别.E-mail: ptq17812103095@163.com

    禹晶:北京工业大学信息学部计算机学院讲师、硕士生导师. 2011 年获清华大学电子工程系博士学位. 主要研究方向为图像处理与模式识别.E-mail: jing.yu@bjut.edu.cn

    肖创柏:北京工业大学信息学部计算机学院教授、博士生导师. 主要研究方向为数字信号处理, 音视频信号处理与网络通信. 本文通信作者.E-mail: cbxiao@bjut.edu.cn

Blind Image Deconvolution Via Cross-scale Low Rank Prior

Funds: Supported by Scientific Research Common Program of Beijing Municipal Commission of Education(KM201910005029), Beijing Natural Science Foundation(4172002)
  • 摘要: 在模糊核未知的情况下对模糊图像进行复原称为盲解卷积问题, 这是一个欠定逆问题, 现有的大部分盲解卷积算法利用图像的各种先验知识约束问题的解空间. 由于清晰图像的跨尺度自相似性强于模糊图像的跨尺度自相似性, 且降采样模糊图像与清晰图像具有更强的相似性, 本文提出了一种基于跨尺度低秩约束的单幅图像盲解卷积算法, 利用图像跨尺度自相似性, 在降采样图像中搜索相似图像块构成相似图像块组, 从整体上对相似图像块组进行低秩约束, 作为正则项加入到图像盲解卷积的目标函数中, 迫使重建图像的边缘接近清晰图像的边缘. 本文算法没有对噪声进行特殊处理, 由于低秩约束更好地表示了数据的全局结构特性, 因此避免了盲解卷积过程受噪声的干扰. 在模糊图像和模糊有噪图像上的实验验证了本文的算法能够解决大尺寸模糊核的盲复原并对噪声具有良好的鲁棒性.
  • 图  1  清晰图像的多尺度自相似性

    Fig.  1  Multi-scale self-similarity of the sharp image

    图  2  模糊图像的多尺度自相似性

    Fig.  2  Multi-scale self-similarity of the blurry image

    图  3  模糊图像和降采样模糊图像分别与清晰图像的相似性比较

    Fig.  3  Comparison of similarities between the blurry image and the down-sampled blurry image related the sharp image

    图  4  跨尺度自相似性用于图像盲复原的解释

    Fig.  4  Interpretation of cross-scale self-similarity for blind image restoration

    图  5  本文算法流程

    Fig.  5  The pipeline of our method

    图  6  Kohler数据集PSNR的平均值与标准差

    Fig.  6  Mean and standard deviation of PSNR on Kohler et al.'s dataset

    图  7  各个算法对Kohler数据集中一幅小模糊图像复原结果的比较

    Fig.  7  Comparison of the results deblurred by some state-of-the-art methods on a weakly blurred image from Kohler et al.'s dataset

    图  8  各个算法对Kohler数据集中一幅大模糊图像复原结果的比较

    Fig.  8  Comparison of the results deblurred by some state-of-the-art methods on a severely blurred image from Kohler et al.'s dataset

    图  9  加噪Kohler数据集PSNR的平均值与标准差

    Fig.  9  Mean and standard deviation of PSNR on noisy Kohler et al.'s dataset

    图  10  各个算法对加噪Kohler数据集中一幅图像复原结果的比较

    Fig.  10  Comparison of the results deblurred by some state-of-the-art methods on a blurred-noisy image from noisy Kohler et al.'s dataset

    图  11  各个算法对加噪Kohler数据集中另一幅图像复原结果的比较

    Fig.  11  Comparison of the results deblurred by some state-of-the-art methods on another blurred-noisy image from noisy Kohler et al.'s dataset

    图  12  各个算法对一幅真实模糊图像复原结果的比较

    Fig.  12  Visual comparisons with some state-of-the-art methods on one real-world photo

    图  13  各个算法对另一幅真实模糊图像复原结果的比较

    Fig.  13  Visual comparisons with some state-of-the-art methods on another real-world photo

    图  14  各个算法在一幅真实模糊有噪图像上的实验结果

    Fig.  14  Visual comparisons with state-of-the-art some methods on a real blurred-noisy image

    图  15  各个算法在另一幅真实模糊有噪图像上的实验结果

    Fig.  15  Visual comparisons with some state-of-the-art methods on another real blurred-noisy image

    图  16  图像跨尺度自相似性的分析

    Fig.  16  Analysis of cross-scale self-similarity of images

    图  17  本文算法对Sun数据集中三幅自相似性较弱图像的复原结果

    Fig.  17  Visual display of proposed method on three weak self-similarity blurred images from Sun et al.'s dataset

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  • 收稿日期:  2019-12-12
  • 录用日期:  2020-05-26

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