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An <span class="MathJax_Preview">\ell_{0}</span><script type="math/tex" id="MathJax-Element-1">\ell_{0}</script> Solution to Sparse Approximation Problems with Continuous Dictionaries | IEEE Conference Publication | IEEE Xplore

An \ell_{0} Solution to Sparse Approximation Problems with Continuous Dictionaries


Abstract:

We address sparse approximation in the particular case where the dictionary is built upon the discretization of a continuous parameter. The resulting dictionary being hig...Show More

Abstract:

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 ℓ0 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 ℓ0-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 ℓ1-norm framework are also proposed. Methods are evaluated on simulated spike train deconvolution problems, where the proposed ℓ0-norm approach with continuous dictionary achieves the best results, although with higher computing time.
Date of Conference: 15-20 April 2018
Date Added to IEEE Xplore: 13 September 2018
ISBN Information:
Electronic ISSN: 2379-190X
Conference Location: Calgary, AB, Canada

References

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