Abstract:

In the traditional super-resolution image reconstruction algorithm, the gradient of the image, the texture structure and other features are usually extracted by artificially designed rules. For complex and content-rich images, the extracted features cannot accurately represent all the information of the image, the edge of the image and local details will be missing. Moreover, in the image training process, there are also problems that the the number offeature maps of LR and HR image is inconsistent, and the feature matching degree is low. Therefore, how to extract the more expressive features as the accurate representation of the source image and improve the image feature matching during the training process is essential for the super-resolution reconstruction of the image. Aiming at the above problems, a super-resolution image reconstruction algorithm based on PCANet model is proposed. Firstly, the deep feature of the image is extracted by the PCANet model with Gaussian kernel function, and the sparse optimization algorithm is added to iteratively optimize the output feature map matrix to obtain the optimal projection matrix, which effectively improves the robustness of the feature map. Then, the deep learning feature of the extracted image is decomposed into multiple sparse features by using the learned LR filter. After the optimal solution is obtained by using the ADMM algorithm and the SA-ADMM algorithm to iteratively update, the sparse feature and mapping function of the LR image are combined. The sparse feature representation of the HR image is estimated, and finally convolved and summed with the corresponding HR filter to obtain the final reconstructed image. The experimental results show that this method can better retain the detailed information of the reconstructed image, the edge texture of the image is clearer, and the average value of the objective evaluation index has increased by more than 0.21?dB, which effectively improves the quality of image reconstruction.

Key words: PCANet model, sparse optimization, SA-ADMM algorithm, sparse feature, super-resolution image reconstruction

摘要：

在传统超分辨率图像重建算法中，图像的梯度、纹理结构等特征通常是由人工设计的规则提取的，对于结构复杂、内容丰富的图像，这样提取到的特征不能精确地表达图像的全部信息，对图像的边缘和局部细节信息会造成缺失。而且在图像训练过程中，还会出现低分辨率[(LR)]和高分辨率[(HR)]图像特征图数量不一致、特征匹配度较低的问题。因此，如何提取表达能力更强的特征作为源图像的精确表示和训练过程中提高图像特征匹配度对图像的超分辨率重建至关重要。针对上述问题，提出了一种基于[PCANet]模型的超分辨率图像重建算法。首先通过具有高斯内核函数的[PCANet]模型提取图像的深层次特征，并且加入稀疏优化算法，对输出的特征映射矩阵迭代优化，得到其最佳投影矩阵，有效提升了特征映射的鲁棒性。然后利用学习获得的LR滤波器将提取到的图像的深度学习特征分解为多个稀疏特征，使用[ADMM]算法和SA-ADMM算法迭代更新得到其最优解以后，结合[LR]图像的稀疏特征和映射函数估计出HR图像的稀疏特征表示，最后和相应的[HR]滤波器进行卷积求和得到最终的重建图像。实验结果表明，该方法使重建图像的细节信息更好地保留，图像的边缘纹理更加清晰，客观评价指标平均[PSNR]值提高了0.21?dB以上，有效提升了图像重建的质量。

关键词: PCANet模型, 稀疏优化, SA-ADMM算法, 稀疏特征, 超分辨率图像重建