Sparsity-Based Algorithms for Line Spectral Estimation

Line spectral estimation is a classical problem in signal processing. It has found broad application in for example array processing, wireless communication, localization, radar, radio astronomy and audio. In the last decade we have seen significant research into sparsity-based processing techniques. The use of sparsity-based techniques has allowed for advances to both the design and analysis of algorithms for line spectral estimation. In this thesis we study the design of such algorithms.

The uniting theme of our contributions is the design of algorithms that make sparsity-based line spectral estimation viable in practice. First it is demonstrated that these schemes can be applied to the estimation of wireless channels of not only specular but also of diffuse nature. We attribute that to a low-rank property of the channel covariance matrix, a concept that we elaborate on.

The design of algorithms for sparsity-based line spectral estimation in a general context is then considered. The obtained algorithms are computationally feasible for much larger problems than what concurrent algorithms can practically deal with and show high estimation accuracy.