# pylops.optimization.sparsity.irls¶

pylops.optimization.sparsity.irls(Op, y, x0=None, nouter=10, threshR=False, epsR=1e-10, epsI=1e-10, tolIRLS=1e-10, kind='data', show=False, itershow=[10, 10, 10], callback=None, **kwargs_solver)[source]

Iteratively reweighted least squares.

Solve an optimization problem with $$L_1$$ cost function (data IRLS) or $$L_1$$ regularization term (model IRLS) given the operator Op and data y.

In the data IRLS, the cost function is minimized by iteratively solving a weighted least squares problem with the weight at iteration $$i$$ being based on the data residual at iteration $$i-1$$. This IRLS solver is robust to outliers since the L1 norm given less weight to large residuals than L2 norm does.

Similarly in the model IRLS, the weight at at iteration $$i$$ is based on the model at iteration $$i-1$$. This IRLS solver inverts for a sparse model vector.

Parameters: Op : pylops.LinearOperator Operator to invert data : numpy.ndarray Data x0 : numpy.ndarray, optional Initial guess nouter : int, optional Number of outer iterations threshR : bool, optional Apply thresholding in creation of weight (True) or damping (False) epsR : float, optional Damping to be applied to residuals for weighting term espI : float, optional Tikhonov damping tolIRLS : float, optional Tolerance. Stop outer iterations if difference between inverted model at subsequent iterations is smaller than tolIRLS kind : str, optional Kind of solver (data or model) show : bool, optional Display logs itershow : list, optional Display set log for the first N1 steps, last N2 steps, and every N3 steps in between where N1, N2, N3 are the three element of the list. callback : callable, optional Function with signature (callback(x)) to call after each iteration where x is the current model vector **kwargs_solver Arbitrary keyword arguments for scipy.sparse.linalg.cg solver for data IRLS and scipy.sparse.linalg.lsqr solver for model IRLS when using numpy data(or pylops.optimization.solver.cg and pylops.optimization.solver.cgls when using cupy data) xinv : numpy.ndarray Inverted model nouter : int Number of effective outer iterations

Notes