proximal_l1_l2¶
- odl.solvers.nonsmooth.proximal_operators.proximal_l1_l2(space, lam=1, g=None)[source]¶
Proximal operator factory of the group-L1-L2 norm/distance.
Implements the proximal operator of the functional
F(x) = lam || |x - g|_2 ||_1
with
x
andg
elements inspace
, and scaling factorlam
. Here,|.|_2
is the pointwise Euclidean norm of a vector-valued function.- Parameters:
- space
LinearSpace
orProductSpace
Domain of the functional.
- lampositive float, optional
Scaling factor or regularization parameter.
- g
space
element, optional Element to which the L1-L2 distance is taken. Default:
space.zero
.
- space
- Returns:
- prox_factoryfunction
Factory for the proximal operator to be initialized
See also
proximal_l1
Scalar or non-isotropic vectorial variant
Notes
For the functional
and a step size , the proximal operator of is given as the "soft-shrinkage" operator
Here, all operations are to be read pointwise.