In this paper we study the sparse coding problem in the context of sparse dictionary learning for image recovery. To this end, we consider and compare several state-of-the-art sparse optimization methods constructed using the shrinkage operation. As the mathematical setting of these methods, we consider an online approach as algorithmical basis together with the basis pursuit denoising problem that arises by the convex optimization approach to the dictionary learning problem. By a dedicated construction of datasets and corresponding dictionaries, we study the effect of enlarging the underlying learning database on reconstruction quality making use of several error measures. Our study illuminates that the choice of the optimization method may be practically important in the context of availability of training data. In the context of different settings for training data as may be considered part of our study, we illuminate the computational efficiency of the assessed optimization methods.

翻译：本文研究稀疏字典学习用于图像复原背景下的稀疏编码问题。为此，我们考虑并比较了若干采用收缩操作构建的先进稀疏优化方法。在数学框架方面，我们采用在线学习作为算法基础，并结合字典学习问题凸优化方法产生的基追踪去噪问题。通过专门构建的数据集与对应字典，我们利用多种误差度量研究了扩大底层学习数据库对重建质量的影响。研究表明，在训练数据可获取性不同的实际场景中，优化方法的选择具有重要实践意义。结合本研究所涵盖的不同训练数据配置，我们进一步阐明了所评估优化方法的计算效率特性。