On Decomposition Models in Imaging Sciences and Multi-time Hamilton-Jacobi Partial Differential Equations

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This paper provides new theoretical connections between multi-time Hamilton-Jacobi partial differential equations and variational image decomposition models in imaging sciences.

• We show that the minimal values of these optimization problems are governed by multi-time Hamilton-Jacobi partial differential equations.
• The minimizers of these optimization problems can be represented using the momentum in the corresponding Hamilton-Jacobi partial differential equation.
• Moreover, variational behaviors of both the minimizers and the momentum are investigated as the regularization parameters approach zero.