7,167 research outputs found
Blind separation of underdetermined mixtures with additive white and pink noises
This paper presents an approach for underdetermined
blind source separation in the case of additive Gaussian
white noise and pink noise. Likewise, the proposed approach is applicable in the case of separating I + 3 sources from I mixtures with additive two kinds of noises. This situation is more challenging and suitable to practical real world problems. Moreover, unlike to some conventional approaches, the sparsity conditions are not imposed. Firstly, the mixing matrix is estimated based on an algorithm that combines short time Fourier transform and rough-fuzzy clustering. Then, the mixed
signals are normalized and the source signals are recovered using modified Gradient descent Local Hierarchical Alternating Least Squares Algorithm exploiting the mixing matrix obtained from the previous step as an input and initialized by multiplicative algorithm for matrix factorization based on alpha divergence. The experiments and simulation results
show that the proposed approach can separate I + 3 source
signals from I mixed signals, and it has superior evaluation performance compared to some conventional approaches
Sparse and Non-Negative BSS for Noisy Data
Non-negative blind source separation (BSS) has raised interest in various
fields of research, as testified by the wide literature on the topic of
non-negative matrix factorization (NMF). In this context, it is fundamental
that the sources to be estimated present some diversity in order to be
efficiently retrieved. Sparsity is known to enhance such contrast between the
sources while producing very robust approaches, especially to noise. In this
paper we introduce a new algorithm in order to tackle the blind separation of
non-negative sparse sources from noisy measurements. We first show that
sparsity and non-negativity constraints have to be carefully applied on the
sought-after solution. In fact, improperly constrained solutions are unlikely
to be stable and are therefore sub-optimal. The proposed algorithm, named nGMCA
(non-negative Generalized Morphological Component Analysis), makes use of
proximal calculus techniques to provide properly constrained solutions. The
performance of nGMCA compared to other state-of-the-art algorithms is
demonstrated by numerical experiments encompassing a wide variety of settings,
with negligible parameter tuning. In particular, nGMCA is shown to provide
robustness to noise and performs well on synthetic mixtures of real NMR
spectra.Comment: 13 pages, 18 figures, to be published in IEEE Transactions on Signal
Processin
Painless Breakups -- Efficient Demixing of Low Rank Matrices
Assume we are given a sum of linear measurements of different rank-
matrices of the form . When and under
which conditions is it possible to extract (demix) the individual matrices
from the single measurement vector ? And can we do the demixing
numerically efficiently? We present two computationally efficient algorithms
based on hard thresholding to solve this low rank demixing problem. We prove
that under suitable conditions these algorithms are guaranteed to converge to
the correct solution at a linear rate. We discuss applications in connection
with quantum tomography and the Internet-of-Things. Numerical simulations
demonstrate empirically the performance of the proposed algorithms
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