Regularization¶

We have slightly touched on the topic how to use the solvers of RegPy in the section Regularisation and Solvers. In this section we will go into more detail about the regularization methods implemented in RegPy.

The solvers in RegPy are implemented as classes that inherit from the base class Solver. The base class provides a common interface for all solvers, allowing you to easily switch between different methods without changing your code. In particular, can you define one regpy.solvers.RegularizationSetting and reuse it for different solvers.

First we have the base class Solver and its derivate RegSolver which is used for many explicit regularization methods. Since the RegSolver is a subclass that explicitly incorporates the regularization setting RegularizationSetting, it is the most commonly used solver in RegPy. However, there are two solvers which do not use the regularization setting that is the Richardson-Lucy solver RichardsonLucy and the \(L^1\) type regularization in IrgnmL1Fid. Thus for almost all regularization methods your are required to define a regularization setting, which is composed of the following three components:

the Operator
the penalty functional
the data fidelity functional

from regpy.solvers import RegularizationSetting
setting = RegularizationSetting(
    operator=operator,
    penalty=penalty_functional,
    data_fid=data_fidelity_functional
)

Note that both the penalty functional and the data fidelity functional are functionals in the sense of Functional. However, if you want to use any squared Hilbert space norm for one of these functionals, you may simply pass the respective Hilbert space when initializing the regularization setting. The initialization then takes care of the treatment. As a general suggestion, you should use abstract functionals or Hilbert spaces in the definition of the regularization setting, since this allows RegPy to automatically choose the correct implementation for your domain and codomain respectively.

from regpy.hilbert import L2, H1
from regpy.solvers import RegularizationSetting
setting = RegularizationSetting(
    operator=operator,
    penalty=L2,
    data_fid=H1
)

from regpy.functionals import L1, TV
from regpy.solvers import RegularizationSetting
setting = RegularizationSetting(
    operator=operator,
    penalty=TV,
    data_fid=L1
)

However, you may want to check whether there exists an implementation for the respective functional and ore Hilbert space for your domain or codomain.

Logging of the Regularization¶

There is a native logging of the regularization of any solver. This is done by the logging and the output can be modified as usual using [logging](https://docs.python.org/3/library/logging.html).