GD TV

Gradient descent with built in TV and flexible encoding model.

mr_utils.cs.convex.gd_tv.GD_TV(y, forward_fun, inverse_fun, alpha=0.5, lam=0.01, do_reordering=False, x=None, ignore_residual=False, disp=False, maxiter=200)[source]

Gradient descent for a generic encoding model and TV constraint.

Parameters:
  • y (array_like) – Measured data (i.e., y = Ax).
  • forward_fun (callable) – A, the forward transformation function.
  • inverse_fun (callable) – A^H, the inverse transformation function.
  • alpha (float, optional) – Step size.
  • lam (float, optional) – TV constraint weight.
  • do_reordering (bool, optional) – Whether or not to reorder for sparsity constraint.
  • x (array_like, optional) – The true image we are trying to reconstruct.
  • ignore_residual (bool, optional) – Whether or not to break out of loop if resid increases.
  • disp (bool, optional) – Whether or not to display iteration info.
  • maxiter (int, optional) – Maximum number of iterations.
Returns:

x_hat – Estimate of x.
Return type:

array_like

Notes

Solves the problem:

\[\min_x || y - Ax ||^2_2 + \lambda \text{TV}(x)\]

If x=None, then MSE will not be calculated.