Using Hankel Structured Low-Rank Approximation for Sparse Signal Recovery

摘要

Structured low-rank approximation is used in model reduction, system identification, and signal processing to find low-complexity models from data. The rank constraint imposes the condition that the approximation has bounded complexity and the optimization criterion aims to find the best match between the data--a trajectory of the system--and the approximation. In some applications, however, the data is sub-sampled from a trajectory, which poses the problem of sparse approximation using the low-rank prior. This paper considers a modified Hankel structured low-rank approximation problem where the observed data is a linear transformation of a system's trajectory with reduced dimension. We reformulate this problem as a Hankel structured low-rank approximation with missing data and propose a solution methods based on the variable projections principle. We compare the Hankel structured low-rank approximation approach with the classical sparsity inducing method of ℓ_1-norm regularization. The ℓ_1-norm regularization method is effective for sum-of-exponentials modeling with a large number of samples, however, it is not suitable for damped system identification.