Approximation of Nonnegative Systems by Finite Impulse Response Convolutions

Abstract

We pose the deterministic, nonparametric, approximation problem for scalar nonnegative input/output systems via finite impulse response convolutions, based on repeated observations of input/output signal pairs. The problem is converted into a nonnegative matrix factorization with special structure for which we use Csiszár's I-divergence as the criterion of optimality. Conditions are given, on the input/output data, that guarantee the existence and uniqueness of the minimum. We propose a standard algorithm of the alternating minimization type for I-divergence minimization, and study its asymptotic behavior. We also provide a statistical version of the minimization problem and give its large sample properties.

This paper was previously posted under the name "Nonnegative Deconvolution with Repeated Measurements". The current version is slightly different

References in corpus (1)

• Nonnegative Matrix Factorization and I-Divergence Alternating Minimization

Cited by in corpus (4)

• The inverse problem of positive autoconvolution
• Approximate factor analysis model building via alternating I-divergence minimization
• Synchronous deautoconvolution algorithm for discrete-time positive signals via I-divergence approximation
• Approximation of nonnegative systems by moving averages of fixed order