L1Norm

class odl.functionals.default_functionals.L1Norm(*args, **kwargs)[source]

The functional corresponding to L1-norm.

The L1-norm, ||x||_1, is defined as the integral/sum of |x|.

Notes

If the functional is defined on an $\mathbb{R}^n$ -like space, the $\| \cdot \|_1$ -norm is defined as

$\| x \|_1 = \sum_{i=1}^n |x_i|.$

If the functional is defined on an $L_2$ -like space, the $\| \cdot \|_1$ -norm is defined as

$\| x \|_1 = \int_\Omega |x(t)| dt.$

The proximal factory allows using vector-valued stepsizes:

>>> space = odl.rn(3)
>>> f = odl.functionals.L1Norm(space)
>>> x = space.one()
>>> f.proximal([0.5, 1.0, 1.5])(x)
rn(3).element([ 0.5,  0. ,  0. ])

__init__(space)[source]

Initialize a new instance.