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@@ -41,10 +41,54 @@ In `ccpi.framework` we define a number of common classes normally used in tomogr ### `ccpi.optimisation` - This package allows writing of optimisation algorithms. The main actors here are: + 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. - * `Function` - * `Operator` + 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 optimisation algorithm to solve a particular generic optimisation problem. These are currently python functions by may be changed to operators in another release. + + #### `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. + + #### `Function` + + A `function` represents a mathematical function of one or more inputs and is intended + to accept `DataContainer`s 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 `grad` 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 + `prox` should return the proxial 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`. + + #### `Algorithm` + + A number of generic algorithm implementations are provided including CGLS and FISTA. An algorithm + is designed for a particular generic optimisation problem accepts and number of `function`s and/or + `operator`s as input to define a specific instance of the generic optimisation problem to be solved. + + #### Examples + + Please see the demos for examples of defining and using operators, functions and algorithms + to specify and solve optimisation-based reconstruction problems. |