图像去噪是图像处理领域的一个基本问题, 其目的是从被噪声污染的图像中恢复出清晰图像, 同时尽量保持图像的细节, 如纹理、边界等信息. 去噪问题是一个病态的反问题,基于模型的变分方法通过人为设计的正则项约束解空间, 是解决这类问题的重要途径之一.变分方法以坚实的数学理论作为支撑, 在模型的可解释性、稳定性、几何性质的描述方面具有优势. 但是, 其依赖于对清晰图像的先验假设, 缺乏高效地处理大数据的能力, 限制了该类方法在实际应用中的去噪效果. 数据驱动型深度去噪网络通过大量的数据来学习图像的深度特征, 进而去除图像噪声. 与基于模型的变分方法相比, 深度去噪网络往往有着更好的数值表现. 但是, 网络结构的设计往往过度依赖经验. 近几年出现的算法展开技术结合了模型方法与深度去噪网络的优势, 受到了人们的广泛关注. 但是, 很少有工作从刻画图像的深度特征的角度考虑, 构造网络结构. 本文基于优化的对偶观点, 利用混合分布模型刻画了不同的深度图像特征,设计了可用于非高斯噪声去除的加权残差学习方法,和可用于高斯白噪声去除的自适应加权的学习型正则项, 并运用变分法将模型先验结合进深度去噪网络结构. 此外, 基于多重网格方法设计了“编码-解码” 型网络结构, 充分利用图像在不同分辨率尺度上的深度特征, 提升模型的去噪能力. 通过多种图像去噪任务验证了所提方法的有效性. 本文的主要工作如下:

    1. 针对深度去噪网络缺乏处理网络中的非高斯残差和图像中的非高斯噪声的有效策略问题, 本文利用高维混合高斯分布模型刻画噪声与数据残差的深度特征的分布, 得到了具有自适应权重的数据保真项, 提出了加权残差学习方法. 根据求解变分模型的数值格式, 构造了具有加权残差连接的网络层, 加权残差连接的自适应权重包含了每个残差特征的参数, 可以帮助提升去除非高斯噪声的效果. 数值实验的结果表明, 本文设计的加权残差网络层在去除非高斯噪声时, 效果优于已有的同类型方法.

    2. 图像的深度特征是复杂的, 对其进行刻画可以帮助网络提取最重要的图像特征. 针对缺乏刻画深度图像特征的现象, 本文利用混合拉普拉斯分布模型刻画深度图像特征的分布, 构造了自适应加权的学习型正则项. 该正则项的自适应权重反映了每个深度特征所属的类别, 从而指导网络提取最重要的图像特征, 提高去噪效果. 本文建立了混合分布先验与“注意力” 机制的联系, 根据对应的数值格式, 构造了具有 “注意力” 机制和残差连接的深度去噪网络结构.数值实验的结果表明,本文设计的自适应加权的学习型正则项可以有效地去除高斯白噪声.

    3. 为了充分利用图像的多尺度特征, 本文基于多重网格方法在不同粗细的网格上快速消除残差的思想, 结合本文提出的自适应加权的学习型正则项模型设计了具有 “编码-解码” 结构的去噪网络.该网络通过在不同分辨率尺度上提取图像的深度特征,有效地提高了模型的去噪能力. 数值实验的结果表明, 利用图像在不同分辨率尺度上的深度特征信息, 可以有效地提高去噪的效果.

    Image denoising is a fundamental problem in the field of image processing. It aims to restore the latent clean image from a noisy observation, and maintains as much detail, such as textures and boundaries, as possible. It is an ill-posed inverse problem. Model-based variational method is one of the most important ways to solve this problem by constraining the solution space through manually designed regularization terms. It is supported by solid mathematical theory and has advantages in the interpretability, stability and description of geometric properties. However, its reliance on the prior assumptions reduces its performance in practical applications, and it lacks the ability to handle big data effectively. The data driven-based deep denoising network learns the deep image features through a large amount of image data to remove noise, and it tends to have better numerical performance than the model-based variational methods. However, the design of the network structure relies too much on experience. In recent years, unrolling technique that combine the advantages of model-based methods and deep denoising networks has received a lot of attention. However, few work designed network structures from the perspective of characterizing the deep image features. This thesis used mixture distribution models to characterize different types of deep images features based on the dual view of optimization. An adaptively weighted residual learning method for non-Gaussian noise removal and an adaptively weighted learnable regularization term for Gaussian noise removal are proposed. The variational method is used to integrate the model prior into the deep denoising network’s architecture. In addition, a deep denoising network with “encoder-decoder” architecture based on the multigrid algorithm is designed to improve the denoising performance through extracting multi-scale deep image features. The performance of the proposed models has been verified in various image denoising tasks. The main contributions of this thesis are as follows:

    1. To address the problem that deep denoising networks lack effective strategies to deal with non-Gaussian residual errors, this thesis used a high-dimensional Gaussian mixture model to characterize the distribution of noise and residual errors in the feature space. A variational model with adaptively weighted fidelity term is proposed, and a weighted residual learning method is designed. Based on the numerical scheme, a network layer with weighted residual connection is constructed. The adaptive weight of the weighted residual connection contains the characteristics of each residual features, thus helping to remove the non-Gaussian noise. Numerical experiments show that the weighted residual network layer designed in this thesis outperforms existing methods of the same type in removing non-Gaussian noise.

    2. The deep image features are difficult to model. Characterizing the deep image features can help the network to extract the most important one. In response to the lack of inscription of deep image features extracted by deep denoising networks, this thesis used a mixture Laplacian distribution model to characterize the distribution of deep image features, and proposed an adaptively weighted learnable regularization term. The adaptive weight of the proposed regularization term reflects the class of each deep image features, thus guiding the deep network to extract the most important features and improve the denoising performance. In addition, this thesis established the
relationship between the mixed distribution prior and the “attention” mechanism in deep learning. A deep denoising network structure with shortcut connection and “attention” module is designed based on the numerical scheme. Numerical experiments show that the adaptively weighted learnable regularization term proposed in this thesis can effectively remove Gaussian noise. 

    3. In order to make full use of multi-scale image features, the idea of quickly removing residuals on different grids from multigrid algorithm is adopted. An “encoder-decoder” network structure is designed through combining the adaptively weighted regularization term proposed in this thesis. The network structure effectively improves the denoising performance by extracting multi-scale image features at different resolution scales. Numerical experiments show that using the idea of multigrid algorithm to extract deep image features at different scales can effectively improve the denoising performance.