The sparsity of natural signals in a transform domain or dictionary has been extensively exploited in several applications. More recently, the data-driven adaptation of synthesis dictionaries has shown promise in many applications compared to fixed or analytical dictionaries. However, dictionary learning problems are typically non-convex and NP-hard, and the alternating minimization approaches usually adopted to solve these problems are often computationally expensive, with the computations dominated by the NP-hard synthesis sparse coding step. In this work, we investigate an efficient method for dictionary learning by first decomposing the training data set into a sum of sparse rank-one matrices and then using a block coordinate descent approach to estimate the rank-one terms. The proposed algorithm involves efficient closed-form solutions. In particular, the sparse coding step involves a simple form of thresholding. We provide a convergence analysis for the proposed block coordinate descent method that solves a highly non-convex problem. Our experiments show the promising performance and significant speed-ups provided by our method over the classical K-SVD scheme in sparse signal representation and image denoising.

通过使用外积求和估计未知变量，然后使用块坐标下降方法来解决问题，本文探讨了连续稀疏惩罚词典学习的高效方法，并提出了与块坐标下降和外积求和方法有关的新算法来进行自适应图像重构。

高效的外积字典学习（SOUP-DIL）及其在逆问题中的应用