proximal_convex_conj_l2_squared¶
- odl.solvers.nonsmooth.proximal_operators.proximal_convex_conj_l2_squared(space, lam=1, g=None)[source]¶
Proximal operator factory of the convex conj of the squared l2-dist
Function for the proximal operator of the convex conjugate of the functional F where F is the l2-norm (or distance to g, if given):
F(x) = lam ||x - g||_2^2
with x and g elements in
space
, scaling factor lam, and given data g.- Parameters:
- space
LinearSpace
Domain of F(x). Needs to be a Hilbert space. That is, have an inner product (
LinearSpace.inner
).- lampositive float, optional
Scaling factor or regularization parameter.
- g
space
element, optional An element in
space
. Default:space.zero
.
- space
- Returns:
- prox_factoryfunction
Factory for the proximal operator to be initialized
See also
proximal_convex_conj_l2
proximal without square
proximal_l2_squared
proximal without convex conjugate
Notes
The squared -norm/distance is given by
The convex conjugate of is given by
For a step size , the proximal operator of is given by