GD Fourier Encoded TV

Gradient descent algorithm for Fourier encoding model and TV constraint.

mr_utils.cs.convex.gd_fourier_encoded_tv.GD_FE_TV(kspace, samp, alpha=0.5, lam=0.01, do_reordering=False, im_true=None, ignore_residual=False, disp=False, maxiter=200)[source]

Gradient descent for Fourier encoding model and TV constraint.

Parameters:
  • kspace (array_like) – Measured image.
  • samp (array_like) – Sampling mask.
  • alpha (float, optional) – Step size.
  • lam (float, optional) – TV constraint weight.
  • do_reordering (bool, optional) – Whether or not to reorder for sparsity constraint.
  • im_true (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:

m_hat – Estimate of im_true.
Return type:

array_like

Notes

Solves the problem:

\[\min_x || d - \text{FT}(I \odot S) ||^2_2 + \lambda \text{TV}(I)\]

where d is measured k-space, I is the image estimate, S is the undersampling mask, and TV is the total variation operator.

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