Nonparametric Basis Pursuit via Sparse Kernel-based Learning
This work addresses signal processing challenges for applications such as cognitive radio and data imputation, but it appears incremental as it builds on existing sparsity and kernel-based approaches.
The paper tackles the problem of signal processing tasks like sampling and prediction by introducing a nonparametric basis pursuit framework that integrates kernel-based learning with sparsity-aware methods, resulting in a toolbox that extends to multi-kernel selection and matrix smoothing. It demonstrates impact through applications in cognitive radio sensing, microarray data imputation, and network traffic prediction, though no concrete numerical results are provided.
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.