proximal_translation¶

odl.solvers.nonsmooth.proximal_operators.proximal_translation(prox_factory, y)[source]¶

Calculate the proximal of the translated function F(x - y).

Parameters

prox_factorycallable: A factory function that, when called with a step size, returns the proximal operator of F.
yElement in domain of F.

Returns

prox_factoryfunction: Factory for the proximal operator to be initialized

Notes

Given a functional $F$ , this is calculated according to the rule

$\mathrm{prox}_{\sigma F( \cdot - y)}(x) = y + \mathrm{prox}_{\sigma F}(x - y)$

where $y$ is the translation, and $\sigma$ is the step size.

For reference on the identity used, see [CP2011c].

References

[CP2011c] Combettes, P L, and Pesquet, J-C. Proximal splitting methods in signal processing. In: Bauschke, H H, Burachik, R S, Combettes, P L, Elser, V, Luke, D R, and Wolkowicz, H. Fixed-point algorithms for inverse problems in science and engineering, Springer, 2011.