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

正如任何句子都可以由字典中的几个词来构造一样，任何信号或图像都可以由“字典”中的几个“词”来表示。与词典中大量的单词相比，一个句子通常由很少的单词组成，因此这些单词被稀疏地映射到词典中。这样构造出的句子可以称之为有字典的稀疏编码。类似地，利用用于信号或图像的字典，可以表示任何信号或图像，并且这也可以被称为稀疏编码。通常，字典中的单词多于单词的长度，即，词典过于完整，词典具有框架结构（数学概念）。本文的研究目的是寻找更有效的稀疏表示方法，并将其应用于盲源分离（BSS）中。 ...更多信息 y估计字典的初始化。在第一步中，对于给定的字典进行字典的稀疏表示。在第二步中，部分地学习字典并修改相应的稀疏表示，而保留稀疏表示的其他部分。在这两个步骤中，字典学习是比较重要的一个步骤，目前有效的方法还很少，为此，我们提出了一种自适应非正交稀疏化变换的方法。在该方法中，我们采取的框架和稀疏矩阵的乘法作为源信号的估计。虽然可能有许多可能的解决方案，我们选择稀疏的一个作为我们的结果。作为该方法的一个特点，字典中的单词是按其能量排序的，而不是像通常的字典中那样随机排序的。在上述方法中，字典学习和源估计可能收敛得非常慢，并且计算也非常消耗。为了解决这些问题，我们还提出了一种方法，其中字典和源同时估计，通过调用非负矩阵分解（NMF）。在实际应用中，存在着许多非负信号，如图像等.然而，通常，NMF的结果不是唯一的，并且不是所有的都是稀疏的。为了解决这个问题，我们提出了一种稀疏NMF方法，该方法通过约束条件从非唯一解中选择一个稀疏解。我们提出了一个测量源信号的稀疏性，并使用其最小化的约束。作为一种替代方法，我们还建议对字典而不是对源使用约束，因为源通常很长，对它们的约束将是计算消耗的。我们发现，最大化字典中单词所占的空间是一个很好的约束条件。评估表明，我们的方法是有效的。然后将其应用于盲谱分解、盲信号分离或图像去噪、波束形成和波达方向估计。少

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