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d-faces of the bounding hyper-rectangle of sources corresponding tô u m (Z) andîandî m (Z) for a scenario with 3 sources and 3 mixtures.
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Bounded Component Analysis (BCA) is a recently introduced approach including Independent Component Analysis (ICA) as a special case under the assumption of source boundedness. In this article, we provide a stationary point analysis for the recently proposed instantaneous BCA algorithms that are capable of separating dependent, even correlated as we...
Contexts in source publication
Context 1
... an example, Figure 2 illustrates the faces F m,+ of the bounding hyper-rectangle of sources, for a scenario with 3-sources and 3-mixtures scenario and ...
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... an example, Figure 3 illustrates the subdifferential setsû setsˆsetsû m (Z) andîandî m (Z) for the example in Figure 2. Based on this figure, we can see that • ∂ ˆ u 1 (Z) and ∂ ˆ l 1 (Z) are 2-faces of the parallelepiped, and they are the images of F 1,+ (Z) and F 1,− (Z) in Figure 2 respectively. ...
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... an example, Figure 3 illustrates the subdifferential setsû setsˆsetsû m (Z) andîandî m (Z) for the example in Figure 2. Based on this figure, we can see that • ∂ ˆ u 1 (Z) and ∂ ˆ l 1 (Z) are 2-faces of the parallelepiped, and they are the images of F 1,+ (Z) and F 1,− (Z) in Figure 2 respectively. ...
Context 4
... ∂ ˆ u 2 and ∂ ˆ l 2 are singleton sets each containing one vertex, and they are the images of F 2,+ (Z) and F 2,− (Z) in Figure 2 respectively. ...
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... ∂ ˆ u 3 and ∂ ˆ l 3 are 1-faces (edges) of the parallelepiped, and they are the images of F 3,+ (Z) and F 3,− (Z) in Figure 2 respectively. We also note that ∂ ˆ u i , ∂ ˆ l i pairs are located symmetrically with respect to the center of the parallelepiped. ...
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... p, what proves the desired equality in (109). Figure 9 illustrates the orthogonality of H † b 1 to the corresponding faces F 1,+ (Z) and F 1,− (Z), for the example in Figure 2. For this example, H † b 1 = (u 1 − l 1 )e 1 and I 1,0 = {2, 3}, which confirms the orthogonality property put forward in (114). ...
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Citations
... Many new technologies are introduced into BSS research. For example, signal sparse component analysis [2,3], dictionary learning [4,5], nonnegative matrix factorization [6,7], bounded component analysis [8,9], tensor decomposition [10,11], and machine learning [12]. However, these algorithms are sensitive to noise. ...
Blind source separation is a widely used technique to analyze multichannel data. In most real-world applications, noise is inevitable and will affect the quality of signal separation and even make signal separation failure. In this paper, a new signal processing framework is proposed to separate noisy mixing sources. It is composed of two different stages. The first step is to process the mixing signal by a certain signal transform method to make the expected signals have energy concentration characteristics in the transform domain. The second stage is formed by a certain BSS algorithm estimating the demixing matrix in the transform domain. In the energy concentration segment, the SNR can reach a high level so that the demixing matrix can be estimated accurately. The analysis process of the proposed algorithm framework is analyzed by taking the wavelet transform as an example. Numerical experiments demonstrate the efficiency of the proposed algorithm to estimate the mixing matrix in comparison with well-known algorithms.
... Third, the channel transmission matrix is full-rank. The author of this article also summarizes the method of studying BSS based on ICA, that is, constructing a cost function based on certain criteria, and obtaining the separation parameters For example, signal sparse component analysis [2][3], dictionary learning [4][5], non-negative matrix factorization [6] [7], bounded component analysis [8] [9] and tensor decomposition [10][ method to search and obtain the global sub-optimal solution of the problem to be solved, so that the separation result has high robustness. This paper is organized as follows. ...
The existing satellite communication anti-jamming technology mostly realizes anti-jamming communication from the perspective of interference suppression, and has defects such as low spectrum efficiency and limited anti-jamming capability. This paper proposes to use the independence of communication signal and interference signal to separate communication signal and interference signal in the waveform domain, and then realize communication anti-interference. This method can realize anti-jamming communication under strong jamming without reducing the spectrum efficiency. The blind source separation problem is essentially a multi-parameter joint optimization problem, and there is no analytical solution. This paper uses an artificial bee colony optimization algorithm to solve the blind separation problem and obtains a sub-optimal solution.
... As the proposed approach relies on the maximization of a non-concave ob- research agenda and we expect it to lead to the same conclusion with [21]. In addition, the empirical results we obtain from the numerical experiments support the conjecture that the algorithm always converges to the vicinity of a desired separation point with an appropriate step size selection. ...
... • By using (21) and the real isomorphic mapping operator Ω defined in section ...
In this paper, we introduce time-domain and frequency-domain versions of a new Blind Source Separation (BSS) approach to extract bounded magnitude sparse sources from convolutive mixtures. We derive algorithms by maximization of the proposed objective functions that are defined in a completely deterministic framework, and prove that global maximums of the objective functions yield perfect separation under suitable conditions. The derived algorithms can be applied to temporal or spatially dependent sources as well as independent sources. We provide experimental results to demonstrate some benefits of the approach, also including an application on blind
speech separation.
... As the proposed approach relies on the maximization of a non-concave ob- research agenda and we expect it to lead to the same conclusion with [21]. In addition, the empirical results we obtain from the numerical experiments support the conjecture that the algorithm always converges to the vicinity of a desired separation point with an appropriate step size selection. ...
... • By using (21) and the real isomorphic mapping operator Ω defined in section ...
In this thesis, a new class of novel Bounded Component Analysis (BCA) algorithms based on sparsity assumption, and their applications on some practical problems are introduced. As an application, the BCA algorithm proposed by Erdogan is demonstrated to separate the direct and reflected echoes which can improve the performance of classical direction of arrival estimation methods based on free space propagation theory. Following, we propose a new BCA framework for the separation of the instantaneous mixtures of sparse and bounded sources. Based on this framework, our first proposed algorithm is named Sparse Bounded Component Analysis (SBCA) which is derived from a geometric objective function defined over a completely deterministic setting. Since the framework is not related to statistical properties of source signal model, it is applicable to sources which can be statistically independent or dependent in both spatial and temporal domains. Then, SBCA framework is extended to the convolutive mixtures of sparse sources and propose time and frequency domain convolutive signal separation algorithms. Finally, a space-time analysis tool is provided to detect and identify brain activity signals that have a non-stationary nature. This tool mainly relies on the short time convergence property of our SBCA framework.
... Furthermore, sparse BCA algorithm was proposed to consider the sparsity of the sources [22]. Recently, a stationary point for instantaneous BCA algorithms was analysed [23]. Although BCA algorithms have attracted much attention and developed quickly, there is still a question whether BCA should be considered as a more general approach than ICA. ...
Bounded Component Analysis (BCA) solves the Blind Source Separation (BSS) problem based on geometric assumptions. This paper introduces a new proof of a BCA contrast function, derived from elementary matrices, Gauss–Jordan elimination and convex geometry. The new proof and further analysis provide additional insight into a key assumption of BCA. In addition, an interpretation is presented to clarify one of the limitations of the instantaneous BCA algorithm. Experiments on audio sources support our analysis.
