pylops.optimization.cls_sparsity.FISTA#
- class pylops.optimization.cls_sparsity.FISTA(Op, callbacks=None)[source]#
Fast Iterative Shrinkage-Thresholding Algorithm (FISTA).
Solve an optimization problem with \(L_p, \; p=0, 0.5, 1\) regularization, given the operator
Opand datay. The operator can be real or complex, and should ideally be either square \(N=M\) or underdetermined \(N<M\).- Parameters
- Op
pylops.LinearOperator Operator to invert
- Op
- Raises
- NotImplementedError
If
threshkindis different from hard, soft, half, soft-percentile, or half-percentile- ValueError
If
perc=Nonewhenthreshkindis soft-percentile or half-percentile
See also
OMPOrthogonal Matching Pursuit (OMP).
ISTAIterative Shrinkage-Thresholding Algorithm (ISTA).
SPGL1Spectral Projected-Gradient for L1 norm (SPGL1).
SplitBregmanSplit Bregman for mixed L2-L1 norms.
Notes
Solves the following synthesis problem for the operator \(\mathbf{Op}\) and the data \(\mathbf{y}\):
\[J = \|\mathbf{y} - \mathbf{Op}\,\mathbf{x}\|_2^2 + \epsilon \|\mathbf{x}\|_p\]or the analysis problem:
\[J = \|\mathbf{y} - \mathbf{Op}\,\mathbf{x}\|_2^2 + \epsilon \|\mathbf{SOp}^H\,\mathbf{x}\|_p\]if
SOpis provided.The Fast Iterative Shrinkage-Thresholding Algorithm (FISTA) [1] is used, where \(p=0, 0.5, 1\). This is a modified version of ISTA solver with improved convergence properties and limited additional computational cost. Similarly to the ISTA solver, the choice of the thresholding algorithm to apply at every iteration is based on the choice of \(p\).
- 1
Beck, A., and Teboulle, M., “A Fast Iterative Shrinkage-Thresholding Algorithm for Linear Inverse Problems”, SIAM Journal on Imaging Sciences, vol. 2, pp. 183-202. 2009.
Methods
__init__(Op[, callbacks])callback(x, *args, **kwargs)Callback routine
finalize([show])Finalize solver
run(x[, niter, show, itershow])Run solver
setup(y[, x0, niter, SOp, eps, alpha, ...])Setup solver
solve(y[, x0, niter, SOp, eps, alpha, ...])Run entire solver
step(x, z[, show])Run one step of solver
