Tomography short notes, Introductory discussion

Tomography

• Introduction

Tomography is used in many disciplines. It is a technique that relies on solving a system of linear algebraic equation to find the distribution of medium property with space. A long time ago, the topic seemed complex and difficult to understand. By time and experience, things looked simpler than it seemed before. We need to choose proper dimensions for blocks  or nodes (a subdivision of the medium assuming a constant value of the property there), trace the trajectories of the fields and a good starting model. The latter is not always needed depending on the nature of the problem and the inversion technique used.  For instance, Newton's methods inversion family requires as good a priori model as possible as the inversion may lose its way to maybe one of the local minima. The inversion problem by itself is non-linear in nature.  Non-linear problems are usually solved either by linearizing the system or by iterative techniques.  

Recently, conventional inversion methods are losing interest due to many problems related to the inversion of the system itself. Many attempts are applied today to solve the problem using a family of random methods like Genetic algorithm and neural network.  These techniques do not actually tend to invert the system, rather it uses a forward modeling strategy by developing a possible solution to the parameters then estimate the goodness of fit. This method is successful to some extent to provide a good solution. However, as life is not always happy, some cases show failures of these approaches. After all, there is no such medication that can cure all diseases.

As the topic is still interesting, I have planned to write short notes representing the different parts of the problem to the best of my knowledge. Hoping this will be beneficial to some of us.