Regularization and solvers¶

The usage guide introduces RegPy’s solver interface. This section describes the underlying regularization setting in more detail.

Solvers inherit from regpy.solvers.Solver, which provides a common iteration interface. Most regularization methods inherit from regpy.solvers.RegSolver and operate on a regpy.solvers.Setting. A setting combines

a forward operator,
a penalty functional, and
a data-fidelity functional.

A typical construction is:

from regpy.solvers import Setting

setting = Setting(
    op=operator,
    penalty=penalty_functional,
    data_fid=data_fidelity_functional,
)

Both penalty and data_fid may be concrete functionals. A Hilbert space may be supplied instead, in which case RegPy uses the corresponding squared Hilbert-space norm. Abstract functionals and Hilbert spaces are often more convenient because they select an implementation appropriate for the operator’s domain or codomain:

from regpy.hilbert import H1, L2
from regpy.solvers import Setting

setting = Setting(
    op=operator,
    penalty=L2,
    data_fid=H1,
)

Likewise, abstract functionals can be used directly:

from regpy.functionals import L1, TV
from regpy.solvers import Setting

setting = Setting(
    op=operator,
    penalty=TV,
    data_fid=L1,
)

The chosen abstract objects must have concrete implementations for the operator’s domain and codomain. Construction of the setting raises an error if no suitable implementation is registered.

Logging¶

Solvers use Python’s logging module. Configure log levels, handlers, and formatters through the standard logging API; see the Python logging documentation.