  Signal processing tasks as fundamental as sampling, reconstruction, minimum
mean-square error interpolation and prediction can be viewed under the prism of
reproducing kernel Hilbert spaces. Endowing this vantage point with
contemporary advances in sparsity-aware modeling and processing, promotes the
nonparametric basis pursuit advocated in this paper as the overarching
framework for the confluence of kernel-based learning (KBL) approaches
leveraging sparse linear regression, nuclear-norm regularization, and
dictionary learning. The novel sparse KBL toolbox goes beyond translating
sparse parametric approaches to their nonparametric counterparts, to
incorporate new possibilities such as multi-kernel selection and matrix
smoothing. The impact of sparse KBL to signal processing applications is
illustrated through test cases from cognitive radio sensing, microarray data
imputation, and network traffic prediction.
