GroupL1Norm.gradient¶

property GroupL1Norm.gradient¶

Gradient operator of the functional.

The functional is not differentiable in x=0. However, when evaluating the gradient operator in this point it will return 0.

Notes

The gradient is given by

$\left[ \nabla \| \|f\|_1 \|_1 \right]_i = \frac{f_i}{|f_i|}$

$\left[ \nabla \| \|f\|_2 \|_1 \right]_i = \frac{f_i}{\|f\|_2}$

else:

$\left[ \nabla || ||f||_p ||_1 \right]_i = \frac{| f_i |^{p-2} f_i}{||f||_p^{p-1}}$