Nonparametric Basis Pursuit via Sparse Kernel-Based Learning: A Unifying View with Advances in Blind Methods

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 (RKHSs). Endowing this vantage point with contemporary advances in sparsity-aware modeling and processing promotes the nonparametric basis pursuit advocated in this article 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 multikernel 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.