proximal_convex_conj_l1_l2¶
- odl.solvers.nonsmooth.proximal_operators.proximal_convex_conj_l1_l2(space, lam=1, g=None)[source]¶
Proximal operator factory of the L1-L2 norm/distance convex conjugate.
Implements the proximal operator of the convex conjugate 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
ofLinearSpace
spaces Domain of the functional F
- lampositive float, optional
Scaling factor or regularization parameter.
- g
space
element, optional Element to which the L1 distance is taken. Default:
space.zero
.
- space
- Returns:
- prox_factoryfunction
Factory for the proximal operator to be initialized.
See also
proximal_convex_conj_l1
Scalar or non-isotropic vectorial variant
Notes
The convex conjugate of the functional
is given by
where is the indicator function of the unit ball with respect to .
For a step size , the proximal operator of is given by
Here, all operations are to be read pointwise.