ProxNest.optimisations.tv_norm_prox.augmented_TV_norm_prox(x, lamb, params)

Compute the augmented total variation proximal operator

Compute the TV proximal operator when an additional linear operator A is incorporated in the TV norm, i.e. solve

\[x^* = \min_{x} ||y - x||_2^2 + \lambda * ||A x||_{TV}\]

where \(y\) is the input vector and the solution \(x^*\) is returned as sol.

Parameters

• x (np.ndarray) – A sample position \(x\) in the posterior space.

• lamb (float) – Regularisation parameter.

• params (dict) – Dictionary of parameters defining the optimisation.

Returns

Optimal solution \(x^*\) of proximal operator.

Return type

np.ndarray

Notes

[1] A. Beck and M. Teboulle, “Fast gradient-based algorithms for constrained Total Variation Image Denoising and Deblurring Problems”, IEEE Transactions on Image Processing, VOL. 18, NO. 11, 2419-2434, November 2009.