pylops.optimization.sparsity.splitbregman#

pylops.optimization.sparsity.splitbregman(Op, y, RegsL1, x0=None, niter_outer=3, niter_inner=5, RegsL2=None, dataregsL2=None, mu=1.0, epsRL1s=None, epsRL2s=None, tol=1e-10, tau=1.0, restart=False, show=False, itershow=(10, 10, 10), show_inner=False, callback=None, **kwargs_lsqr)[source]#

Split Bregman for mixed L2-L1 norms.

Solve an unconstrained system of equations with mixed \(L_2\) and \(L_1\) regularization terms given the operator Op, a list of \(L_1\) regularization terms RegsL1, and an optional list of \(L_2\) regularization terms RegsL2.

Parameters

Oppylops.LinearOperator: Operator to invert
ynumpy.ndarray: Data
RegsL1list: \(L_1\) regularization operators
x0numpy.ndarray, optional: Initial guess
niter_outerint: Number of iterations of outer loop
niter_innerint: Number of iterations of inner loop of first step of the Split Bregman algorithm. A small number of iterations is generally sufficient and for many applications optimal efficiency is obtained when only one iteration is performed.
RegsL2list: Additional \(L_2\) regularization operators (if None, \(L_2\) regularization is not added to the problem)
dataregsL2list, optional: \(L_2\) Regularization data (must have the same number of elements of RegsL2 or equal to None to use a zero data for every regularization operator in RegsL2)
mufloat, optional: Data term damping
epsRL1slist: \(L_1\) Regularization dampings (must have the same number of elements as RegsL1)
epsRL2slist: \(L_2\) Regularization dampings (must have the same number of elements as RegsL2)
tolfloat, optional: Tolerance. Stop outer iterations if difference between inverted model at subsequent iterations is smaller than tol
taufloat, optional: Scaling factor in the Bregman update (must be close to 1)
restartbool, optional: The unconstrained inverse problem in inner loop is initialized with the initial guess (True) or with the last estimate (False)
showbool, optional: Display iterations log
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.
show_innerbool, optional: Display inner iteration logs of lsqr
callbackcallable, optional: Function with signature (callback(x)) to call after each iteration where x is the current model vector
**kwargs_lsqr: Arbitrary keyword arguments for scipy.sparse.linalg.lsqr solver used to solve the first subproblem in the first step of the Split Bregman algorithm.

Returns