Several applications in biomedical data processing, telecommunications or chemometrics can be tackled by computing a structured tensor decomposition. In this paper, we focus on tensor decompositions with two or more block-Hankel factors, which arise in blind multiple-input-multipleoutput (MIMO) convolutive system identification. By assuming statistically independent inputs, the blind system identification problem can be reformulated as a Hankel structured tensor decomposition. By capitalizing on the available block-Hankel and tensorial structure, a relaxed uniqueness condition for this structured decomposition is obtained. This condition is easy to check, yet very powerful. The uniqueness condition also forms the basis for two subspace-based algorithms, able to blindly identify linear underdetermined MIMO systems with finite impulse response.
Multi-way datasets are widespread in signal processing and play an important role in blind signal separation, array processing and biomedical signal processing, among others. One key strength of tensors is that their decompositions are unique under mild conditions, which allows the recovery of features or source signals. In several applications, such as classification, we wish to compare factor matrices of the decompositions. Though this is possible by first computing the tensor decompositions and subsequently comparing the factors, these decompositions are often computationally expensive. In this paper, we present a similarity method that indicates whether the factors in two modes are essentially equal without explicitly computing them. Essential equality conditions, which ensure the theoretical validity of our approach, are provided for various underlying tensor decompositions. The developed algorithm provides a computationally efficient way to compare factors. The method is illustrated in a context of emitter movement detection and fluorescence data analysis.
Blind system identification (BSI) is an important problem in signal processing, arising in applications such as wireless telecommunications, biomedical signal processing and seismic signal processing. In the past decades, tensors have proven to be useful tools for these blind identification and separation problems. Most often, tensor-based methods based on fourthorder statistics are used, which have been studied extensively for independent component analysis and its convolutive extensions. However, these tensor-based methods have two main drawbacks: the accuracy is often limited by the estimation error of the statistics and the computation of these fourth-order statistics is time-intensive. In this paper, we propose to counter these drawbacks for BSI by coupling the fourth-order statistics with second-order statistics and by using incomplete tensors. By doing so, we can obtain more accurate results or obtain results in a much faster way.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.