8 research outputs found
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
Sparsity and adaptivity for the blind separation of partially correlated sources
Blind source separation (BSS) is a very popular technique to analyze
multichannel data. In this context, the data are modeled as the linear
combination of sources to be retrieved. For that purpose, standard BSS methods
all rely on some discrimination principle, whether it is statistical
independence or morphological diversity, to distinguish between the sources.
However, dealing with real-world data reveals that such assumptions are rarely
valid in practice: the signals of interest are more likely partially
correlated, which generally hampers the performances of standard BSS methods.
In this article, we introduce a novel sparsity-enforcing BSS method coined
Adaptive Morphological Component Analysis (AMCA), which is designed to retrieve
sparse and partially correlated sources. More precisely, it makes profit of an
adaptive re-weighting scheme to favor/penalize samples based on their level of
correlation. Extensive numerical experiments have been carried out which show
that the proposed method is robust to the partial correlation of sources while
standard BSS techniques fail. The AMCA algorithm is evaluated in the field of
astrophysics for the separation of physical components from microwave data.Comment: submitted to IEEE Transactions on signal processin
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An Adaptive Strategy for Sensory Processing
Recognizing objects and detecting associations among them is essential for the survival of organisms. The ability to perform these tasks is derived from the representations of objects obtained through processing information along sensory pathways. Our current understanding of sensory processing is based on two sets of foundational theories – The Efficient Coding Hypothesis and hierarchical assembly of object representations. These theories suggest that sensory processing aims to identify independent features of the environment and progressively represent objects in terms of comprehensive combinations of these features. Separately, the two sets of theories have successfully explained the detection of associations and perceptual invariance, respectively; however, reconciling them together in one unified theory has remained challenging. Independent features are deemed essential for detecting association by the Efficient coding hypothesis, but to achieve consistency in representations, multiple comprehensive structures corresponding to the same object must be hierarchically assembled, ignoring independence among such structures.
Here we propose an alternative framework for sensory processing in which the system, instead of finding the truly independent components of the environment, aims to represent objects based on their most informative structures. Using theoretical arguments, we show that following such a strategy allows the system to efficiently represent sensory cues without necessarily acquiring knowledge about statistical properties of all possible inputs. Through mathematical simulations, we find that the framework can describe the known characteristics of early sensory processing stages and permits consistent input representations observed at later stages of processing. We also demonstrate that the framework can be implemented in a biologically plausible neuronal circuit and explain aspects of experience and learning from corrupted inputs. Thus, this framework provides a novel perspective and a unified description of sensory processing in its entirety