  Recently, sparsity-based algorithms are proposed for super-resolution
spectrum estimation. However, to achieve adequately high resolution in
real-world signal analysis, the dictionary atoms have to be close to each other
in frequency, thereby resulting in a coherent design. The popular convex
compressed sensing methods break down in presence of high coherence and large
noise. We propose a new regularization approach to handle model collinearity
and obtain parsimonious frequency selection simultaneously. It takes advantage
of the pairing structure of sine and cosine atoms in the frequency dictionary.
A probabilistic spectrum screening is also developed for fast computation in
high dimensions. A data-resampling version of high-dimensional Bayesian
Information Criterion is used to determine the regularization parameters.
Experiments show the efficacy and efficiency of the proposed algorithms in
challenging situations with small sample size, high frequency resolution, and
low signal-to-noise ratio.
