研究字典学习中稀疏性与图像恢复质量的平衡关系
Quality Versus Sparsity in Image Recovery by Dictionary Learning Using Iterative Shrinkage
- 通过迭代收缩算法优化字典学习中的稀疏表示
- 高稀疏性并不降低图像恢复质量，即使与训练数据差异大
- 不同优化方法存在不同的稀疏性适用范围
稀疏字典学习（SDL）是图像处理中的基础技术，可应用于图像恢复任务，该问题可建模为非光滑优化问题。迭代收缩方法是一类强大的算法，正受到持续研究。稀疏性是学习解的重要属性，因其能实现高效后续处理或存储——即恢复图像由尽可能少的字典元素组合而成。因此，需探究在字典学习中应多大程度上强制稀疏性，以免损害恢复质量。本文聚焦于多种优化方法所获得解的稀疏性表现。结果表明，不同方法存在不同的稀疏性适用区间。此外，我们证实：即使恢复图像与训练数据库差异较大，高稀疏性通常也不会降低恢复质量。
原文摘要 · Abstract (English)
Sparse dictionary learning (SDL) is a fundamental technique that is useful for many image processing tasks. As an example we consider here image recovery, where SDL can be cast as a nonsmooth optimization problem. For this kind of problems, iterative shrinkage methods represent a powerful class of algorithms that are subject of ongoing research. Sparsity is an important property of the learned solutions, as exactly the sparsity enables efficient further processing or storage. The sparsity implies that a recovered image is determined as a combination of a number of dictionary elements that is as low as possible. Therefore, the question arises, to which degree sparsity should be enforced in SDL in order to not compromise recovery quality. In this paper we focus on the sparsity of solutions that can be obtained using a variety of optimization methods. It turns out that there are different sparsity regimes depending on the method in use. Furthermore, we illustrate that high sparsity does in general not compromise recovery quality, even if the recovered image is quite different from the learning database.
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