optim.cg

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optim.cg#

bartorch.optim.cg()#

Solve a linear least-squares problem by conjugate gradients.

Minimizes \(\| A x - y \|^2 + \lambda \| x \|^2\), and with quadratic penalties \(\sum_i w_i \| G_i x - b_i \|^2\) alongside it. Takes Tikhonov penalties through terms=; proximal regularizers are not accepted.

Parameters:

  • y (tensor) – Data of A.oshape.

  • A (LinearOperator) – The encoding operator.

  • lambda (float, default=0.0) – Tikhonov weight on the image itself.

  • x0 (tensor, default=None) – Warm start of A.ishape; without one the iteration starts at zero.

  • **settings – Settings of CG, among them terms, maxiter (30) and tol.

Returns:

Complex64 solution of A.ishape.

Return type:

torch.Tensor

Notes

The solve is recorded for autograd when y requires a gradient; the backward pass is a second solve with the same normal operator.

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