Papers › A Decoupled Approach for Composite Sparse-plus-Smooth Penalized Optimization
A Decoupled Approach for Composite Sparse-plus-Smooth Penalized Optimization
Adrian Jarret, Valérie Costa, Julien Fageot
We consider a linear inverse problem whose solution is expressed as a sum of two components: one smooth and the other sparse. This problem is addressed by minimizing an objective function with a least squares data-fidelity term and a different regularization term applied to each of the components. Sparsity is promoted with an ℓ₁ norm, while the smooth component is penalized with an ℓ₂ norm. We characterize the solution set of this composite optimization problem by stating a Representer Theorem. Consequently, we identify that solving the optimization problem can be decoupled by first identifying the sparse solution as a solution of a modified single-variable problem and then deducing the smooth component. We illustrate that this decoupled solving method can lead to significant computational speedups in applications, considering the problem of Dirac recovery over a smooth background with two-dimensional partial Fourier measurements.
Code
Repository list and official/mentioned flags are the archive's, frozen 2025-07-28. Reachability, where shown, is from one Syntology probe window (2026-09-16 to 2026-09-18); repositories not probed show nothing. GitHub stars are not tracked.
Code Syntology ran Syntology
Not run by Syntology. Nothing on this page verifies that the listed code works.
Results from the paper archive 2025-07-28
No leaderboard rows for this paper in the archive.
Methods
Report a problem or propose a change · a person checks every report against the paper or source before anything changes; decisions are listed on /corrections