Search

In this paper the problem of parallel waveform enhancement via the multi-sensor fusion technology is carefully studied. Through representing the observed multiple noisy observations as a 3-D tensor, we propose two novel approaches in the time domain, i.e. the transforming and filtering (TAF) approach and the direct multidimensional filtering (DMF) approach, for parallel waveform recovery and interference suppression. The term “parallel” indicates the system can produce an estimate of the clean waveform in each sensor channel simultaneously. Specifically, the TAF approach transforms the observed tensor into a different domain where the noise can then be filtered by discarding the insignificant coefficients. The DMF approach directly reduces the noise level by applying multidimensional filtering on the observed tensor. Both DMF and TAF are “blind” because they do not require precise frequency responses between the desired source and distributed sensors. Simulations show that TAF is capable of yielding satisfactory performances for spatially white noise, while DMF can produce satisfactory results on spatially colored noise. Besides, both TAF and DMF can work well in complex real environments. [ABSTRACT FROM AUTHOR]

This paper proposes a new perspective on the problem of multidimensional spectral factorization, through helical mapping: d -dimensional ( d D) data arrays are vectorized, processed by 1D cepstral analysis and then remapped onto the original space. Partial differential equations (PDEs) are the basic framework to describe the evolution of physical phenomena. We observe that the minimum phase helical solution asymptotically converges to the d D semi-causal solution, and allows us to decouple the two solutions arising from PDEs describing physical systems. We prove this equivalence in the theoretical framework of cepstral analysis, and we also illustrate the validity of helical factorization through a 2D wave propagation example and a 3D application to helioseismology. [ABSTRACT FROM AUTHOR]