The proposed Bayesian framework can be extended to handle more complex conductivity distributions beyond piecewise constant models by incorporating additional prior information or constraints into the model. One approach is to introduce spatial regularization terms that encourage smoothness or continuity in the conductivity distribution. This can be achieved by incorporating total variation (TV) penalties or other regularization techniques that promote spatial coherence in the conductivity values. By including such regularization terms in the Bayesian model, the framework can effectively capture more intricate conductivity structures, such as gradual variations or spatial patterns in the distribution.
Another extension could involve incorporating prior knowledge about the physical properties of the medium being imaged. For example, if certain regions are known to have specific conductivity characteristics or if there are known boundaries or interfaces within the domain, this information can be integrated into the Bayesian model as additional constraints. By leveraging domain-specific knowledge and constraints, the framework can adapt to more complex conductivity distributions and improve the accuracy of the reconstruction.