Proximal Thresholding Algorithm for Minimization over Orthonormal Bases

@article{Combettes2007ProximalTA,
  title={Proximal Thresholding Algorithm for Minimization over Orthonormal Bases},
  author={Patrick L. Combettes and Jean-Christophe Pesquet},
  journal={SIAM Journal on Optimization},
  year={2007},
  volume={18},
  pages={1351-1376}
}
The notion of soft thresholding plays a central role in problems from various areas of applied mathematics, in which the ideal solution is known to possess a sparse decomposition in some orthonormal basis. Using convex-analytical tools, we extend this notion to that of proximal thresholding and investigate its properties, providing in particular several characterizations of such thresholders. We then propose a versatile convex variational formulation for optimization over orthonormal bases that… CONTINUE READING

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