Blind source separation based on simultaneous learning of the sparse frame representations for multi sources from their mixtures

基于同时学习多源混合中的稀疏帧表示的盲源分离

• 批准号: 20500209
• 负责人: DING Shuxue
• 金额: $ 2.91万
• 依托单位: The University of Aizu
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 2008
• 资助国家: 日本
• 起止时间: 2008 至 2010
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-20500209/
• 关键词: 確率的情報処理; ブラインド信号分離処理; 信号のスパース表現; 信号のフレーム表現; Nonnegative Matrix Factorization; Sparsifying transform; Multiuser Detection; Beamforming

Just as that any sentence can be constructed by several words in a dictionary, any signal or image can be either represented by several "words" in a "dictionary". Comparing with the large number of words in the dictionary, a sentence is usually be constructed by only very few words, so that these words are mapped into the dictionary sparsely. Then constructed sentence may be called as sparse coding with the dictionary. Similarly, with a dictionary for signal or image, one can represent any signal or image, and this can also be termed as sparse coding. Usually, there more words in the dictionary than the length of the words, i.e., the dictionary is over-complete, the dictionary has a structure of frame (a mathematical concept). The motivation of this research is to find more effective methods for finding this sparse representation, and then apply them to blind source separation (BSS).BSS by using the sparse representation usually includes repeated two steps, once it is given an arbitrar … More y initialization of the estimated dictionary. In the first step, for a given dictionary the sparse representation by the dictionary is conducted. In the second step, the dictionary is learned in part and the corresponding sparse representation is modified, while the other parts of sparse representation are kept. In these two steps, the dictionary learning is more important and there still very few effective methods for it. For this purpose, we worked out a method that is termed as adaptive non-orthogonal sparsifying transform. In this method, we take the multiplication of the frame and a sparse matrix as the source signal estimation. Though there may be many possible solutions, we choose the sparsest one as our result. As a feature of the method, the words in the dictionary are ordered by their energy, rather than randomly ordered as in the usual dictionary.In the above method, the dictionary learning and source estimation may converge very slowly and the computation is also very consuming. For solving these problems, we also worked out a method in which the dictionary and the sources are simultaneously estimated, by invoking the nonnegative matrix factorization (NMF). There are many nonnegative signals, such as image, in applications. However, usually, the result of NMF is not unique and not all of them are sparse. For solving this problem, we worked out a sparse NMF method, in which we select a sparse solution from the non unique solutions by a constraint. We propose a measure for measuring the sparsity of source signals and use its minimization as the constraint. As an alternative method, we also proposed to use a constraint on the dictionary, rather than on the sources, since the sources are usually very long and a constraint on them will be computation consuming. We found that the maximization of space spanned by the words in the dictionary is a good constraint.Evaluations showed that our methods are efficient. Then we applied them to blind spectral unmixing, BSS or denoising of images, beamforming and direction of arrival estimation. Less

就像任何句子都可以由字典中的几个单词构造一样，任何信号或图像都可以用“字典”中的几个“单词”表示。与词典中的大量单词相比，通常仅由很少的单词构造一个句子，因此这些单词被稀疏地映射到字典中。然后，构造的句子可以称为用字典稀疏编码。同样，使用信号或图像的字典，可以表示任何信号或图像，也可以称为稀疏编码。通常，字典中的单词比单词的长度（即字典都过度完整，字典）具有更多的单词，字典具有框架的结构（数学概念）。这项研究的动机是找到找到这种稀疏表示形式的更有效的方法，然后将它们应用于盲源分离（BSS）。通过使用稀疏表示，通常包括重复的两个步骤，一旦给出了任意性的估计词典的更初始化。在第一步中，对于给定的词典，进行了字典的稀疏表示。在第二步中，词典是部分学习的，并修改了相应的稀疏表示，而稀疏表示的其他部分则被保留。在这两个步骤中，词典学习更为重要，并且几乎没有有效的方法。为此，我们制定了一种被称为自适应非正交稀疏转换的方法。在这种方法中，我们将帧的乘法和稀疏矩阵作为源信号估计。尽管可能有很多可能的解决方案，但我们选择最稀少的解决方案作为结果。作为该方法的一个特征，字典中的单词是通过其能量排序的，而不是像通常的字典一样随机排序。在上述方法中，词典学习和源估计可能会非常缓慢地收敛，并且计算也非常消耗。为了解决这些问题，我们还研究了一种方法，即通过调用非负矩阵分解（NMF）来简单地估算字典和来源。应用程序中有许多非负信号，例如图像。但是，通常，NMF的结果并非唯一，并且并非所有人都稀疏。为了解决此问题，我们制定了一种稀疏的NMF方法，在这种方法中，我们通过约束从非唯一解决方案中选择一个稀疏的解决方案。我们提出了一种测量源信号稀疏性的措施，并将其最小化作为约束。作为另一种方法，我们还建议对词典使用约束，而不是在来源上使用限制，因为这些来源通常很长，并且对它们的限制将是计算消耗的。我们发现，词典中单词跨越的空间的最大化是一个很好的约束。评论表明我们的方法是有效的。然后，我们将它们应用于盲目的光谱不混合，BSS或图像的降解，光束形成和到达估计的方向。较少的

项目成果

A Robust Gradient-Descent Algorithm for On-Line Independent Component Analysis Based on Negentropy Maximization

基于负熵最大化的在线独立分量分析鲁棒梯度下降算法

• 发表时间: 2008
• 作者: Takahiro Haneda;Shuxue Ding (丁 数学)
• 通讯作者: Shuxue Ding (丁 数学)

Blind Spectral Unmixing Based on Sparse Nonnegative Matrix Factorization

• DOI: 10.1109/tip.2010.2081678
• 发表时间: 2011-04
• 期刊: IEEE Transactions on Image Processing
• 影响因子: 10.6
• 作者: Zuyuan Yang;Guoxu Zhou;S. Xie;Shuxue Ding;Jun-Mei Yang;Jun Zhang

The Diagonal Loading Beamformers for the PAM Communication Systems, International Journal of Innovative Computing

用于 PAM 通信系统的对角加载波束形成器，国际创新计算杂志

• 发表时间: 2009
• 期刊: Information and Control Vol.5, No.9
• 作者: Wenlong Liu;Shuxue Ding
• 通讯作者: Shuxue Ding

Blind source separation by nonnegative matrix factorization with minimum-volume constraint

• DOI: 10.1109/icicip.2010.5565228
• 发表时间: 2010-09
• 期刊: 2010 International Conference on Intelligent Control and Information Processing
• 作者: Zuyuan Yang;Guoxu Zhou;Shuxue Ding;S. Xie

Performance Analysis of the Iterative Decision Method for Optimal Multiuser Detection

最优多用户检测迭代决策方法的性能分析