Norm of DA_inv of DPGD

[EnLAI111]

In the algorithm Dual proximal gradient descent, we need $\ || DA^{\dagger} \ ||_2^2$ to calculate stepsize.

When $A$ is a matrix, it's possible to get $A^{\dagger}$ by np.linalg.pinv, but when $A$ is an linear operator, it's difficult to get its inverse. $A$ could be an operation of convolution, and it could also be a mutiplication by a matrix.

We have tried to approximate it

• by $\frac{1}{|| AD^{\dagger} ||_2^2}$, but it turned out its not the same value for every case;
• by np.fft.fft, but it didn't work neither.