Dynamical structure function identifiability conditions enabling signal structure reconstruction

Networks of controlled dynamical systems exhibit a variety of interconnection patterns that could be interpreted as the structure of the system. One such interpretation of system structure is a system's signal structure, characterized as the open-loop causal dependencies among manifest variables and represented by its dynamical structure function. Although this notion of structure is among the weakest available, previous work has shown that if no a priori structural information is known about the system, not even the Boolean structure of the dynamical structure function is identifiable. Consequently, one method previously suggested for obtaining the necessary a priori structural information is to leverage knowledge about target specificity of the controlled inputs. This work extends these results to demonstrate precisely the a priori structural information that is both necessary and sufficient to reconstruct the network from input-output data. This extension is important because it significantly broadens the applicability of the identifiability conditions, enabling the design of network reconstruction experiments that were previously impossible due to practical constraints on the types of actuation mechanisms available to the engineer or scientist. The work is motivated by the proteomics problem of reconstructing the Per-Arnt-Sim Kinase pathway used in the metabolism of sugars. © 2012 IEEE.

Bayesian inference for multidimensional NMR image reconstruction

Reconstruction of an image from a set of projections has been adapted to generate multidimensional nuclear magnetic resonance (NMR) spectra, which have discrete features that are relatively sparsely distributed in space. For this reason, a reliable reconstruction can be made from a small number of projections. This new concept is called Projection Reconstruction NMR (PR-NMR). In this paper, multidimensional NMR spectra are reconstructed by Reversible Jump Markov Chain Monte Carlo (RJMCMC). This statistical method generates samples under the assumption that each peak consists of a small number of parameters: position of peak centres, peak amplitude, and peak width. In order to find the number of peaks and shape, RJMCMC has several moves: birth, death, merge, split, and invariant updating. The reconstruction schemes are tested on a set of six projections derived from the three-dimensional 700 MHz HNCO spectrum of a protein HasA.

Multi-channel signal separation

The separation of independent sources from mixed observed data is a fundamental and challenging problem. In many practical situations, observations may be modelled as linear mixtures of a number of source signals, i.e. a linear multi-input multi-output system. A typical example is speech recordings made in an acoustic environment in the presence of background noise and/or competing speakers. Other examples include EEG signals, passive sonar applications and cross-talk in data communications. In this paper, we propose iterative algorithms to solve the n × n linear time invariant system under two different constraints. Some existing solutions for 2 × 2 systems are reviewed and compared.

Robust noise reduction for speech and audio signals

Statistical model-based methods are presented for the reconstruction of autocorrelated signals in impulsive plus continuous noise environments. Signals are modelled as autoregressive and noise sources as discrete and continuous mixtures of Gaussians, allowing for robustness in highly impulsive and non-Gaussian environments. Markov Chain Monte Carlo methods are used for reconstruction of the corrupted waveforms within a Bayesian probabilistic framework and results are presented for contaminated voice and audio signals.

Towards a perceptually optimal spectral amplitude estimator for audio signal enhancement

We present a statistical model-based approach to signal enhancement in the case of additive broadband noise. Because broadband noise is localised in neither time nor frequency, its removal is one of the most pervasive and difficult signal enhancement tasks. In order to improve perceived signal quality, we take advantage of human perception and define a best estimate of the original signal in terms of a cost function incorporating perceptual optimality criteria. We derive the resultant signal estimator and implement it in a short-time spectral attenuation framework. Audio examples, references, and further information may be found at http://www-sigproc.eng.cam.ac.uk/~pjw47.