spgl1_torch.py

Source: LION/classical_algorithms/spgl1_torch.py

SPGL1 sparse reconstruction with torch operators.

LION.classical_algorithms.spgl1_torch.spgl1_torch(op, y, **spgl1_kwargs)[source]

Solve an l1 sparse reconstruction using SPGL1, wrapping torch operators.

This is a thin wrapper around the Python SPGL1 solver spgl1.spgl1 that uses torch operators for matrix-vector products. SPGL1 is a spectral projected-gradient method for constrained l1 problems; see [BergFriedlander2008] and [BergFriedlander2010].

This wrapper is built on top of the Python implementation spgl1.spgl1 and uses the same calling convention (argument names and behaviour); see [SPGL1Python] for details.

Parameters:

  • op (Operator) – Linear operator implementing the forward map and its adjoint. It is called as op(w) and op.adjoint(r).

  • y (torch.Tensor) – Measurements, shape (M,).

  • spgl1_kwargs (dict) – Extra keyword args forwarded to spgl1.spgl1 (for example tolerances or iteration limits; see [SPGL1Python]).

Returns:

w_hat – Estimated coefficient vector in the same shape as op.adjoint(y*0).

Return type:

torch.Tensor

References

[BergFriedlander2008]

E. van den Berg and M. P. Friedlander, “Probing the Pareto frontier for basis pursuit solutions”, SIAM Journal on Scientific Computing, 31(2):890-912, 2008.

[BergFriedlander2010]

E. van den Berg and M. P. Friedlander, “Sparse optimisation with least-squares constraints”, TR-2010-02, Department of Computer Science, University of British Columbia, 2010.

[SPGL1Python] (1,2)

SPGL1: Spectral Projected Gradient for L1 minimisation, Python package documentation, https://spgl1.readthedocs.io/