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.

In this paper, we study the problem of feature extraction for pattern classification applications. RELIEF is considered as one of the best-performed algorithms for assessing the quality of features for pattern classification. Its extension, local feature extraction (LFE), was proposed recently and was shown to outperform RELIEF. In this paper, we extend LFE to the nonlinear case, and develop a new algorithm called kernel LFE (KLFE). Compared with other feature extraction algorithms, KLFE enjoys nice properties such as low computational complexity, and high probability of identifying relevant features; this is because KLFE is a nonlinear wrapper feature extraction method and consists of solving a simple convex optimization problem. The experimental results have shown the superiority of KLFE over the existing algorithms.