"""MLEM (Maximum Likelihood Expectation Maximization) unfolding method.
This module provides the core solve_mlem solver and the unfold_mlem
wrapper for use with the Detector class.
"""
import numpy as np
from typing import Dict, Optional, Any, List, Tuple
from ._base_unfolder import run_unfolding, make_solve_wrapper
__all__ = ["solve_mlem", "unfold_mlem"]
[docs]
def solve_mlem(
A: np.ndarray,
b: np.ndarray,
x0: np.ndarray,
max_iterations: int = 1000,
tolerance: float = 1e-6,
) -> Tuple[np.ndarray, int, bool]:
"""Solve unfolding problem using MLEM iteration.
Parameters
----------
A : np.ndarray
Response matrix (m x n).
b : np.ndarray
Measurement vector (m,).
x0 : np.ndarray
Initial guess (n,).
max_iterations : int, optional
Maximum iterations (default: 1000).
tolerance : float, optional
Convergence tolerance (default: 1e-6).
Returns
-------
Tuple[np.ndarray, int, bool]
Tuple of (solution, iterations, converged).
"""
x = np.maximum(x0.copy(), 1e-10)
AT = A.T
converged = False
iterations = 0
for i in range(max_iterations):
Ax = A @ x
Ax = np.maximum(Ax, 1e-10)
ratio = b / Ax
correction = AT @ ratio
x_new = x * correction
diff = np.linalg.norm(x_new - x) / (np.linalg.norm(x) + 1e-10)
x = np.maximum(x_new, 0)
iterations = i + 1
if diff < tolerance:
converged = True
break
return x, iterations, converged
[docs]
def unfold_mlem(
detector_names: List[str],
n_energy_bins: int,
E_MeV: np.ndarray,
sensitivities: Dict[str, np.ndarray],
cc_icrp116: Dict[str, np.ndarray],
save_result_callback,
readings: Dict[str, float],
initial_spectrum: Optional[np.ndarray] = None,
max_iterations: int = 1000,
tolerance: float = 1e-6,
calculate_errors: bool = False,
noise_level: float = 0.01,
n_montecarlo: int = 100,
save_result: bool = True,
random_state: Optional[int] = None,
) -> Dict[str, Any]:
"""Unfold using MLEM algorithm.
Parameters
----------
detector_names : List[str]
Names of available detectors.
n_energy_bins : int
Number of energy bins.
E_MeV : np.ndarray
Energy grid.
sensitivities : Dict[str, np.ndarray]
Detector sensitivity arrays.
cc_icrp116 : Dict[str, np.ndarray]
ICRP-116 conversion coefficients.
save_result_callback : callable
Callback to save result to history.
readings : Dict[str, float]
Detector readings.
initial_spectrum : Optional[np.ndarray], optional
Initial spectrum guess.
max_iterations : int, optional
Maximum iterations (default: 1000).
tolerance : float, optional
Convergence tolerance (default: 1e-6).
calculate_errors : bool, optional
Calculate Monte-Carlo errors (default: False).
noise_level : float, optional
Noise level for Monte-Carlo (default: 0.01).
n_montecarlo : int, optional
Number of Monte-Carlo samples (default: 100).
save_result : bool, optional
Save result to history (default: True).
random_state : int, optional
Random seed for reproducibility.
Returns
-------
Dict[str, Any]
Unfolding results dictionary.
"""
x0_default = np.ones(n_energy_bins) * 0.5
return run_unfolding(
detector_names=detector_names,
n_energy_bins=n_energy_bins,
E_MeV=E_MeV,
sensitivities=sensitivities,
cc_icrp116=cc_icrp116,
save_result_callback=save_result_callback,
readings=readings,
initial_spectrum=initial_spectrum,
default_initial=x0_default,
solve_func=make_solve_wrapper(
solve_mlem,
max_iterations=max_iterations,
tolerance=tolerance,
),
solve_kwargs={},
method_name="MLEM",
extra_output={},
calculate_errors=calculate_errors,
noise_level=noise_level,
n_montecarlo=n_montecarlo,
random_state=random_state,
save_result=save_result,
)