On-line Nonlinear Sparse Approximation of Functions

Abstract — This paper provides new insights into online nonlinear sparse approximation of functions based on the coherence criterion. We revisit previous work, and propose tighter bounds on the approximation error based on the coherence criterion. Moreover, we study the connections between the coherence criterion and both the approximate linear dependence criterion and the principal component analysis. Finally, we derive a kernel normalized LMS algorithm based on the coherence criterion, which has linear computational complexity on the model order. Initial experimental results are presented on the algorithm’s performance. I