Unsupervised feature extraction, signal labeling, and blind signal separation in a state space world

Abstract

Abstract-The paper addresses the problem of joint signal separation and estimation in a single-channel discrete-time signal composed of a wandering baseline and overlapping repetitions of unknown (or known) signal shapes. All signals are represented by a linear state space model (LSSM). The baseline model is driven by white Gaussian noise, but the other signal models are triggered by sparse inputs. Sparsity is achieved by normal priors with unknown variance (NUV) from sparse Bayesian learning. All signals and system parameters are jointly estimated with an efficient expectation maximization (EM) algorithm based on Gaussian message passing, which works both for known and unknown signal shapes. The proposed method outputs a sparse multi-channel representation of the given signal, which can be interpreted as a signal labeling.

A Bayesian Modeling Approach to Situated Design of Personalized Soundscaping Algorithms

“…The first model is based on the Algonquin-based source mixing model, in which the individual signals are represented by Gaussian mixture models. This first probabilistic model is fully specified by ( 8), ( 12)- (16). Secondly, an alternative model has been presented, which is based on Gaussian scale models.…”

“…Secondly, an alternative model has been presented, which is based on Gaussian scale models. This probabilistic model is fully specified by ( 11)- (16). The soundscaping framework supports different acoustic models, concerning both the source mixing models as the source models.…”

“…On the interface of blind and informed source separation in a probabilistic context recently new works have been published. In [16] a blind signal separation algorithm is presented, based on earlier works in [17][18][19]. Here the individual signals are represented by state space models with a sparse input.…”

Windowed State-Space Filters for Signal Detection and Separation

“…2) Precomputation of W k (and Its Inverse): If all parameters are independent of k, i.e., w k = w and γ k = γ (cf. Table II), then the recursions for W k as in (27) and (31) lead to a steady state. As such, when W k +1 = W k , equations ( 27) and (31) result in a Lyapunov equations [14,Appendix D].…”

“…Second, the proposed method cannot handle significant superpositions of independent pulses. This latter limitation is overcome by the (more complex) method of [27] and [16, Part III].…”