Contributed talks on Tensors and OptimizationMon 15:00–15:30, SW Raadzaal, Chair: Martijn Boussé
Many real-life signals are compressible, meaning that they can be represented by a number of parameters that is much smaller than the total number of entries. Often a tensor representation of such signals admits an approximate low-rank model. This idea is known in tensor-based scientific computing and has allowed one to solve problems in a number of unknowns that exceeds the number of atoms in the universe. We introduce such a signal model in blind source separation (BSS) to tackle large-scale problems. We show that overall our method reformulates BSS as the computation of a tensor decomposition, assuming the sources admit the hypothesized low-rank structure. The tensor is obtained by applying a deterministic tensorization technique called segmentation on the observed data matrix. Furthermore, in applications with many sensors and/or high sensor density often the mixture is compressible as well and we can apply the same strategy. We extend our method so that it can simultaneously handle the structure on both levels of the BSS problem. The low-rank structure of the sources and/or the mixture enables a very compact representation, allowing us to solve large-scale problems.