optim.FISTABlock

class bartorch.optim.FISTABlock

Bases: ISTBlock

One iteration of fast iterative soft thresholding, BART’s fista (italgos.c).

ISTBlock with Nesterov’s momentum between the proximal step and the gradient step, \(t_{k+1} = (p + \sqrt{q + r t_k^2}) / 2\).

Parameters:

• prior (Regularizer or ImplicitPrior) – The single term \(g\); its transform must be the identity.

• step (float, default=0.95) – Step size \(\tau\).

• eigen (bool, default=False) – Divide the step by maxeigen() of the normal operator, estimated in start().

• hogwild (bool, default=False) – Halve the step after 10 iterations, and again after each further 20, 40, … iterations.

• pqr (tuple of float, default=None) – \((p, q, r)\); None is BART’s (1, 1, 4).

• cclambda (float, default=0.0) – \(\lambda\), the 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).

Raises:

• ValueError – Not exactly one term; at start(), a term whose transform is not the identity.

• TypeError – A term with auxiliary variables.

start()

Initial state of a run.

Parameters:

• y (tensor) – Data of A.oshape, or (batch, *A.oshape).

• A (LinearOperator) – Encoding operator.

• x0 (tensor, default=None) – Starting image; zero when omitted, as in BART.

Returns:

The start and \(M A^H y\), kept for every step.

Return type:

State

forward()

Take one iteration from state; returns the next state.

Also has the methods and properties of ISTBlock.