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Exact Continuous Relaxations for the ℓ0-Regularized Least-Squares Criteria

E. Soubies

SIAM Conference on Imaging Science (SIS'18), Bologna, Italian Republic, June 5-8, 2018, session MS37-2.



Several continuous non-convex relaxations of the ℓ0 pseudo-norm have been proposed over the past. In this talk, considering the ℓ0-regularized least-squares minimization problem (ℓ2-ℓ0), I will present theoretical results which allow to compare such relaxations from the perspective of their fidelity to the initial ℓ2-ℓ0 problem. I will exhibit necessary and sufficient conditions on separable penalties approximating the ℓ0 pseudo-norm which ensure that the associated regularized least-squares functional preserves the global minimizers of the initial one and do not add new local minimizers. From these conditions, we get a class of penalties said to be exact regarding to their properties concerning the relaxed functional.


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address="Bologna, Italian Republic",
month="June 5-8,",
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