非负稀疏分解的DeepMP
DeepMP for Non-Negative Sparse Decomposition
摘要：
非负信号是一类重要的稀疏信号。许多算法已经被提出来恢复这样的非负表示，其中贪婪和凸松弛算法是最流行的方法。贪婪技术是低计算成本的算法，它也被修改为包含表示的非负性。一个这样的修改已经提出了基于匹配追踪（MP）的算法，它首先选择正系数，并使用非负优化技术，保证非负的系数。贪婪算法的性能，像所有的非穷举搜索方法，遭受与线性生成模型，称为字典的高度一致性。在这里，我们首先以深度神经网络的形式重新制定非负匹配追踪算法。然后，我们表明，训练后的模型产生了显着的改善，在准确的恢复性能相比，其他未经训练的贪婪算法，同时保持低的复杂性。
英文摘要：
Non-negative signals form an important class of sparse signals. Many algorithms have already beenproposed to recover such non-negative representations, where greedy and convex relaxed algorithms are among the most popular methods. The greedy techniques are low computational cost algorithms, which have also been modified to incorporate the non-negativity of the representations. One such modification has been proposed for Matching Pursuit (MP) based algorithms, which first chooses positive coefficients and uses a non-negative optimisation technique that guarantees the non-negativity of the coefficients. The performance of greedy algorithms, like all non-exhaustive search methods, suffer from high coherence with the linear generative model, called the dictionary. We here first reformulate the non-negative matching pursuit algorithm in the form of a deep neural network. We then show that the proposed model after training yields a significant improvement in terms of exact recovery performance, compared to other non-trained greedy algorithms, while keeping the complexity low.
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