부산대학교 도서관

We address sparse approximation in the particular case where the dictionary is built upon the discretization of a continuous parameter. The resulting dictionary being highly correlated, equivalence between $\ell_{0}$ and suboptimal solutions (e.g. greedy algorithms and convex relaxation) is not guaranteed. To tackle this issue, continuous parameter estimation has been proposed using a dictionary based on polar interpolation [1], [2]. Alternately, the exact $\ell_{0}$ -norm optimization problem can be addressed on moderate size problems through Mixed Integer Programming (MIP) [3]. We propose to merge these two approaches in a new MIP formulation adapted to polar interpolation. Improvements on polar interpolation and refinements on its use in the $\ell_{1}$ -norm framework are also proposed. Methods are evaluated on simulated spike train deconvolution problems, where the proposed $\ell_{0}$ -norm approach with continuous dictionary achieves the best results, although with higher computing time.