Linear inverse problems and state estimation: Regularization, Observability and Convergence

Solving tomographic inverse problems in real-time is a challenging task due to the dimension of the problem, the nonlinearities involved and the fact that they are ill-posed problems. Efficient algorithms are required to address the application of tomographic technologies in the process industries. Several authors have proposed to address this issue by augmenting the measurement vector with fictitious outputs in order to solve the problem using state estimators. This paper analyses the solution of linear inverse problems from the perspective of a state estimation problem, providing links between regularization, observability and convergence of the algorithms. In addition, it also proposes an alternative way to define the fictitious outputs, leading to observers with fewer parameters than the one widely used in the literature. The simulation of a simple example illustrates the main ideas of this work.