スパース表現と辞書学習に基づく画像処理アルゴリズム研究

最后，我们提出了一种新的字典学习算法，该算法具有对数正则化和基于近邻算子的相干惩罚。我们提出的算法简单地采用分解方案和交替优化，将整个问题转化为一组单向量变量子问题，这些子问题要么有一个字典原子，要么有一个系数向量。虽然子问题仍然是非光滑甚至非凸的，但显著的是，它们可以用近邻算子求解，并且直接显式地得到字典原子和系数向量的闭形式解。据我们所知，之前的字典学习研究还没有将近邻算子应用于使用对数正则化器的稀疏编码，同时应用于使用相干惩罚的字典更新。根据我们的分析和仿真研究，该算法的主要优点是具有更高的学习效率和更快的收敛速度。此外，对于现实世界的信号，我们提出的算法可以获得比使用l1范数的稀疏性的算法更低的近似误差。

In the last,we propose a novel dictionary learning algorithm with the log regularizer and simultaneously with the coherence penalty based on proximal operators. Our proposed algorithm simply employs a decomposition scheme and alternating optimization, which transforms the overall problem into a set of single-vector variables subproblems, with either one dictionary atom or one coefficient vector. Although the subproblems are still nonsmooth and even nonconvex, remarkably they can be solved by proximal operators, and the closed-form solutions of the dictionary atoms and the coefficient vectors are obtained directly and explicitly. To the best of our knowledge, no previous studies of dictionary learning have applied proximal operators to sparse coding with the log-regularizer and simultaneously to dictionary updating with the coherence penalty. According to our analysis and simulation study, the main advantages of the proposed algorithm are its greater efficiency in learning and its higher convergence rate than state-of-the-art algorithms. In addition, for real-world signals, our proposed algorithm can obtain lower approximation errors than an algorithm that uses the L1-norm for sparsity.