improve the documentation of the source_localization package

docs/source/source_localization.rst

 source\_localization package
 ============================
 
-Submodules
-----------
+.. automodule:: source_localization
+   :members:
+   :undoc-members:
+   :show-inheritance:
 
-.. toctree::
-   :maxdepth: 4
 
-   ./source_localization/adjoint_convection_diffusion_2D
-   ./source_localization/control
-   ./source_localization/cost
-   ./source_localization/gradient_descent
-   ./source_localization/obs
-   ./source_localization/population_dynamique
-   ./source_localization/proximal_gradient
+The main feature of the package :mod:`source_localization` is to estimate the quantity of pheromone emitted by the insects :math:`s_a` by solving the following optimization problem:
 
+.. math::
+   s_a(x,y,t)=\underset{s(x,y,t)}{\arg\text{min}}~j(s)\text{ with } j(s)=j_{obs}(s)+j_{reg}(s)
 
-Module contents
----------------
+with the cost function :math:`j` of the following form:
 
-.. automodule:: source_localization
-   :members:
-   :undoc-members:
-   :show-inheritance:
+.. math::
+   j(s)=\|m\left(c(s)\right)-m^{obs}\|_{\mathbf{R}^{-1}}^2 + \sum_{i} \alpha_{reg,i} j_{reg,i}(s)
+
+with :math:`\|m\left(c(s)\right)-m^{obs}\|_{\mathbf{R}^{-1}}^2` the term of discrepancy between the data :math:`m^{obs}`
+and the estimate computed using the pheromone propagation model :math:`m\left(c(s)\right)`,
+:math:`j_{reg,i}` some regularization terms based on biological information and
+:math:`\alpha_{reg,i}` the associated weight coefficient.
+
+To solve such optimization problems, the package includes: 
+
+   - a submodule :mod:`~source_localization.cost` that contains the cost function :math:`j`, tools to construct the cost function and to minimize it;
+   - a submodule :mod:`~source_localization.obs` that contains all the features related to the sensors and the observations, including the observations :math:`m^{obs}` and the observation operator :math:`c\mapsto m(c)`;
+   - a submodule :mod:`~source_localization.control` containing the control variable to optimize :math:`s(x,y,t)` and all its prior known features;
+   - a submodule :mod:`~source_localization.population_dynamique` containing population dynamic models used as prior knowledge of the control variable and their implementation;
+   - a submodule :mod:`~source_localization.adjoint_convection_diffusion_2D` that contains the adjoint model used to compute the gradient of the cost function;
+   - submodules :mod:`~source_localization.gradient_descent` and :mod:`~source_localization.proximal_gradient` that contain algorithms to solve the optimization problem.
+
+.. toctree::
+   :maxdepth: 4
+
+   The cost function and its related tools <./source_localization/cost>
+   The sensors, its observations and its features <./source_localization/obs>
+   The control variable and all its prior known features <./source_localization/control>
+   The population dynamic models and its implementation <./source_localization/population_dynamique>
+   The adjoint model, its implementation and its solvers <./source_localization/adjoint_convection_diffusion_2D>
+   The implementation of the gradient descent algorithm <./source_localization/gradient_descent>
+   The implementation of the proximal gradient algorithm <./source_localization/proximal_gradient>