Martijn Boussé

A Tensor-Based Method for Large-Scale Blind Source Separation Using Segmentation

Many real-life signals are compressible, meaning that they depend on much fewer parameters than their sample size. In this paper, we use low-rank matrix or tensor representations for signal compression. We propose a new deterministic method for blind source separation that exploits the low-rank structure, enabling a unique separation of the source signals and providing a way to cope with large-scale data. We explain that our method reformulates the blind source separation problem as the computation of a tensor decomposition, after reshaping the observed data matrix into a tensor. This deterministic tensorization technique is called segmentation and is closely related to Hankel-based tensorization. We apply the same strategy to the mixing coefficients of the blind source separation problem, as in many large-scale applications, the mixture is also compressible because of many closely located sensors. Moreover, we combine both strategies, resulting in a general technique that allows us to exploit the underlying compactness of the sources and the mixture simultaneously. We illustrate the techniques for fetal electrocardiogram extraction and direction-of-arrival estimation in large-scale antenna arrays.

A novel deterministic method for large-scale blind source separation

A novel deterministic method for blind source separation is presented. In contrast to common methods such as independent component analysis, only mild assumptions are imposed on the sources. On the contrary, the method exploits a hypothesized (approximate) intrinsic low-rank structure of the mixing vectors. This is a very natural assumption for problems with many sensors. As such, the blind source separation problem can be reformulated as the computation of a tensor decomposition by applying a low-rank approximation to the tensorized mixing vectors. This allows the introduction of blind source separation in certain big data applications, where other methods fall short.

A tensor-based method for large-scale blind system identification using segmentation

A new method for the blind identification of large-scale finite impulse response (FIR) systems is presented. It exploits the fact that the system coefficients in large-scale problems often depend on much fewer parameters than the total number of entries in the coefficient vectors. We use low-rank models to compactly represent matricized versions of these compressible system coefficients. We show that blind system identification (BSI) then reduces to the computation of a structured tensor decomposition by using a deterministic tensorization technique called segmentation on the observed outputs. This careful exploitation of the low-rank structure enables the unique identification of both the system coefficients and the inputs. The approach does not require the input signals to be statistically independent.

Tensor-Based Large-Scale Blind System Identification Using Segmentation

Many real-life signals can be described in terms of much fewer parameters than the actual number of samples. Such compressible signals can often be represented very compactly with low-rank matrix and tensor models. The authors have adopted this strategy to enable large-scale instantaneous blind source separation. In this paper, we generalize the approach to the blind identification of large-scale convolutive systems. In particular, we apply the same idea to the system coefficients of finite impulse response systems. This allows us to reformulate blind system identification as a structured tensor decomposition. The tensor is obtained by applying a deterministic tensorization technique called segmentation on the observed output data. Exploiting the low-rank structure of the system coefficients enables a unique identification of the system and estimation of the inputs. We obtain a new type of deterministic uniqueness conditions. Moreover, the compactness of the low-rank models allows one to solve large-scale problems. We illustrate our method for direction-of-arrival estimation in large-scale antenna arrays and neural spike sorting in high-density microelectrode arrays.