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Bounded Component Analysis (BCA) is a recent approach which enables the separation of both dependent and independent signals from their mixtures. This article introduces a novel deterministic instantaneous BCA approach for the separation of sparse bounded sources. The separation problem is posed as a geometric maximization problem, where the object...
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... the second example, three 240x320 pixel images are mixed by a random Gaussian 4 × 3 matrix and corrupted by Gaussian noise. In Figure 3, the input and mixed images for the proposed algorithm are illustrated for a random mixing matrix. As the first stage of separation, we apply Morlet wavelet transform [23] to the mixtures for the sparsification of the sources generating them. ...
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Citations
... Aforementioned algorithmic BCA frameworks are mostly applicable to source vectors whose samples lie in ∞ -norm ball in high dimensional space, which is illustrated to be a nice fit for digital communication constellations, natural images and harmonic signals. More recently, [5] adapted the geometric approach in [3] for unmixing bounded and sparse natured sources from their memoryless mixtures by replacing the ∞ -norm ball in [3] with the 1 -norm ball. ...
... In this article, we extend the instantaneous Sparse BCA (SBCA) approach in [5] to more general convolutive mixtures. We note that the exploitation of sparsity for solving BSS problem has been referred in literature as Sparse Com-ponent Analysis (SCA), and several different approaches has been proposed especially for the instantaneous mixing problem (see for example [1,6] and the references therein). ...
... As a result, the convolutive channel generates L + M − 1 output samples. Now after defining the BCA setup, we extend the deterministic instantaneous sparse BCA approach introduced in [5] to the convolutive case. ...
In this article, we propose a Bounded Component Analysis (BCA) approach for the separation of the convolutive mixtures of sparse sources. The corresponding algorithm is derived from a geometric objective function defined over a completely deterministic setting. Therefore, it is applicable to sources which can be independent or dependent in both space and time dimensions. We show that all global optima of the proposed objective are perfect separators. We also provide numerical examples to illustrate the performance of the algorithm.
... Then, Erdogan's BCA algorithms were further developed for separating convolutive mixtures [20] [21]. 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]. ...
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.
