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-Optimisation framework

-======================

-

-This package allows rapid prototyping of optimisation-based

-reconstruction problems, i.e. defining and solving different

-optimization problems to enforce different properties on the

-reconstructed image.

-

-Firstly, it provides an object-oriented framework for defining

-mathematical operators and functions as well a collection of useful

-example operators and functions. Both smooth and non-smooth functions

-can be used.

-

-Further, it provides a number of high-level generic implementations of

-optimisation algorithms to solve genericlly formulated optimisation

-problems constructed from operator and function objects.

-

-The fundamental components are:

-

--   Operator: A class specifying a (currently linear) operator

--   Function: A class specifying mathematical functions such as a least

-    squares data fidelity.

--   Algorithm: Implementation of an iterative optimisation algorithm to

-    solve a particular generic optimisation problem. Algorithms are

-    iterable Python object which can be run in a for loop. Can be

-    stopped and warm restarted.

-

-Algorithm

----------

-

-A number of generic algorithm implementations are provided including

-Gradient Descent CGLS and FISTA. An algorithm is designed for a

-particular generic optimisation problem accepts and number of Functions

-and/or Operators as input to define a specific instance of the generic

-optimisation problem to be solved. They are iterable objects which can

-be run in a for loop. The user can provide a stopping criterion

-different than the default max\_iteration.

-

-New algorithms can be easily created by extending the Algorithm class.

-The user is required to implement only 4 methods: set\_up, \_\_init\_\_,

-update and update\_objective.

-

--   `set_up` and `__init__` are used to configure the algorithm

--   `update` is the actual iteration updating the solution

--   `update_objective` defines how the objective is calculated.

-

-For example, the implementation of the update of the Gradient Descent

-algorithm to minimise a Function will only be:

-

-The `Algorithm` provides the infrastructure to continue iteration, to

-access the values of the objective function in subsequent iterations,

-the time for each iteration.

-

-::: {.autoclass members="" private-members="" special-members=""}

-ccpi.optimisation.algorithms.Algorithm

-:::

-

-::: {.autoclass members=""}

-ccpi.optimisation.algorithms.GradientDescent

-:::

-

-::: {.autoclass members=""}

-ccpi.optimisation.algorithms.CGLS

-:::

-

-::: {.autoclass members=""}

-ccpi.optimisation.algorithms.FISTA

-:::

-

-Operator

---------

-

-The two most important methods are `direct` and `adjoint` methods that

-describe the result of applying the operator, and its adjoint

-respectively, onto a compatible `DataContainer` input. The output is

-another `DataContainer` object or subclass hereof. An important special

-case is to represent the tomographic forward and backprojection

-operations.

-

-::: {.autoclass members=""}

-ccpi.optimisation.operators.Operator

-:::

-

-::: {.autoclass members=""}

-ccpi.optimisation.operators.LinearOperator

-:::

-

-::: {.autoclass members=""}

-ccpi.optimisation.operators.ScaledOperator

-:::

-

-Function

---------

-

-A `Function` represents a mathematical function of one or more inputs

-and is intended to accept `DataContainers` as input as well as any

-additional parameters.

-

-Fixed parameters can be passed in during the creation of the function

-object. The methods of the function reflect the properties of it, for

-example, if the function represented is differentiable the function

-should contain a method `gradient` which should return the gradient of

-the function evaluated at an input point. If the function is not

-differentiable but allows a simple proximal operator, the method

-`proximal` should return the proximal operator evaluated at an input

-point. The function value is evaluated by calling the function itself,

-e.g. `f(x)` for a `Function f` and input point `x`.

-

-::: {.autoclass members=""}

-ccpi.optimisation.functions.Function

-:::

-

-`Return Home <mastertoc>`{.interpreted-text role="ref"}