optim.PRIDU

optim.PRIDU#

class bartorch.optim.PRIDU#

Bases:

Primal-dual iteration (Chambolle-Pock), looping PRIDUBlock.

Solves \(\min_x \tfrac12 \| A x - y \|^2 + \sum_j g_j(G_j x)\) with no inner solve.

Parameters:

  • regularizers (Regularizer or ImplicitPrior, or an iterable of them, default=None) – The terms \(g_j\), with any transform \(G_j\), including terms with auxiliary variables.

  • maxiter (int, default=30) – Maximum number of iterations.

  • step (float, default=0.95) – Product of the dual and primal step sizes, \(\sigma \tau\).

  • sigma_tau_ratio (float, default=1.0) – \(\sigma / \tau\), so \(\sigma = \sqrt{\text{step}}\,\text{ratio}\) and \(\tau = \sqrt{\text{step}} / \text{ratio}\). BART’s reconstructions set it to the data_scaling() factor.

  • adaptive_step (bool, default=False) – Adapt \(\sigma\) and \(\tau\) at every iteration.

  • eigen (bool, default=False) – Divide \(\sigma\) and \(\tau\) by the square root of maxeigen() over the encoding and the dual terms.

  • hogwild (bool, default=False) – Relax iteration \(k\) by \(0.95^k\): each variable moves that fraction of the way to its update.

  • cclambda (float, default=0.0) – Weight of an identity added to the normal operator.

  • precond (LinearOperator, default=None) – Left preconditioner \(M\) from A.ishape to itself, positive definite (lsqr2_create’s precond_op); BART’s reconstructions use none.

Notes

The first term is applied as the primal proximal step when its transform is the identity, and every other term through a dual variable. The run stops early when the primal and dual residuals sum below 1e-4.

__call__()#

Solve for the image.

Parameters:

  • y (tensor) – Data of A.oshape, or (batch, *A.oshape); a batch is solved one item at a time, each as its own run.

  • A (LinearOperator) – Encoding operator. A BART-backed operator is applied inside the library; a Python-defined one is called back once per application.

  • x0 (tensor, default=None) – Starting image of A.ishape, or one per batch item; zero when omitted.

Returns:

Complex64 image of A.ishape, with y’s batch axis in front.

Return type:

torch.Tensor

Raises:

ValueError – y requires a gradient and a BART term has not been detached (detach()): its proximal operator has no backward pass.

Notes

The iterations are torch operations, so a solve is differentiated by unrolling. Step sizes and weights are fixed; bartorch.optim’s blocks and Unrolled expose them as parameters.