基于低阶Tucker分解的图像恢复技术研究

近年来，图像恢复逐渐成为数字图像处理领域的研究焦点，为了有效地对受损的、丢失了的图像数据进行恢复，采用张量数据结构的形式来表示待恢复的图像数据，并且提出了一种基于张量的图像恢复方法，通过充分识别清洁图像中混合噪声的内在结构。具体来说，对于干净的图像内容，使用张量Tucker分解来描述所有频带之间的全局相关性，以及各向异性空间光谱总变化（SSTV）正则化，以表征空间和频域中的分段平滑结构。对于混合噪声的图像内容，采用正则化来检测稀疏噪声，包括条纹，脉冲噪声和死像素，开发了一种用于通过使用增强拉格朗日乘数（ALM）方法来求解所得优化问题的有效算法。最后，对模拟和现实生活中有噪声的图像进行了广泛的实验，结果表明，算法工作良好，收敛快，可使受损图像恢复到一个良好的状态，恢复精度高。

Research on Image Restoration Technology Based on Low-Rank Tucker Decomposition

In recent years, image restoration has gradually become the focus of research in the field of digital image processing. In order to effectively restore the damaged and lost image data, the image data to be recovered is expressed in the form of tensor data structure, Based on the tensor-based image restoration method, by fully recognizing the inherent structure of the mixed noise in the clean image. Specifically, for the clean image content, tensor Tucker decomposition is used to describe the global correlation between all bands, and the anisotropic spatial spectral total change (SSTV) regularization to characterize the spatial and frequency segments Smooth structure. For the content of mixed noise, regularization is used to detect sparse noise, including fringe, impulse noise and dead pixels, an effective method for solving the obtained optimization problem by using the enhanced Lagrangian Multiplier (ALM) method is developed algorithm. Finally, the simulation results show that the algorithm works well and the convergence is fast, which can restore the damaged image to a good state, and the recovery precision is high.