MLEMIteration

class deepinv.optim.optim_iterators.MLEMIteration(eps=1e-6, cost_fn=None, **kwargs)

Bases: OptimIterator

Iterator for the Maximum-Likelihood Expectation-Maximization (MLEM) algorithm for Poisson inverse problems.

Class for a single iteration of the MLEM algorithm [1], which is a classic baseline reconstruction method for inverse problems with Poisson noise statistics. More details on the algorithm can be found in the documentation of the deepinv.optim.optimizers.MLEM optimizer.

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References:

[1]

Lawrence A Shepp and Yehuda Vardi. Maximum likelihood reconstruction for emission tomography. IEEE Transactions on Medical Imaging, 1(2):113–122, 1982.

forward(X, cur_data_fidelity, cur_prior, cur_params, y, physics, sensitivity, *args, **kwargs)

Single Maximum-Likelihood Expectation-Maximization (MLEM) iteration.

This corresponds to an update on both the Poisson negative log-likelihood and prior terms if a prior is provided, and only on Poisson negative log-likelihood otherwise.

Parameters:

• X (dict) – Dictionary containing the current iterate and the estimated cost.

• cur_data_fidelity (deepinv.optim.DataFidelity) – Instance of the DataFidelity class defining the current data_fidelity.

• cur_prior (deepinv.optim.Prior) – Instance of the Prior class defining the current prior.

• cur_params (dict) – Dictionary containing the current parameters of the algorithm.

• y (torch.Tensor) – Input data.

• physics (deepinv.physics.Physics) – Instance of the physics modeling the data-fidelity term.

• sensitivity (torch.Tensor) – Precomputed sensitivity map \(A^T \mathbf{1}\).