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, warm=False, kind='data', engine='scipy', show=False, itershow=(10, 10, 10), callback=None, preallocate=False, **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

Oppylops.LinearOperator: Operator to invert
ynumpy.ndarray: Data
x0numpy.ndarray, optional: Initial guess
nouterint, optional: Number of outer iterations
threshRbool, optional: Apply thresholding in creation of weight (True) or damping (False)
epsRfloat, optional: Damping to be applied to residuals for weighting term
epsIfloat, optional: Tikhonov damping
tolIRLSfloat, optional: Tolerance. Stop outer iterations if difference between inverted model at subsequent iterations is smaller than tolIRLS
warmbool, optional: Warm start each inversion inner step with previous estimate (True) or not (False). This only applies to kind="data" and kind="datamodel"
kindstr, optional: Kind of solver (model, data or datamodel)
enginestr, optional: Solver to use (scipy or pylops)
showbool, optional: Display logs
itershowtuple, 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.
callbackcallable, optional: Function with signature (callback(x)) to call after each iteration where x is the current model vector
preallocatebool, optional: New in version 2.6.0.

Pre-allocate all variables used by the solver. Note that if y is a JAX array, this option is ignored and variables are not pre-allocated since JAX does not support in-place operations.
**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)

Returns