Modern imaging techniques facilitating non-invasive examinations of the inneranatomy of the human body have been gaining importance in the state of the art medical diagnostics. Technological advances these days allow for practical applicability of digital tomosynthesis, a method, which reconstructs the object under examination only when a series of projections with limited angular range is available. The method plays an important role since it meets the needs of screenings by being cheap and using low dose radiation, while providing a diagnostic sensitivity close to that of computer tomography scans.
The crucial step of imaging modalities is the volume projection based three dimensional reconstruction, which constitutes a challenging task demanding that engineers plan thoroughly as common with inversion problems. There are several exact mathematical reconstruction methods for the solution of the problem, which, however, do not explicitly deal with tomographic angle limitation or with noisy projection data, and so are unable to correct their impact.
In the event of modalities using limited angular range, reconstruction of intensity changes of a certain orientation is not possible, not even theoretically. Nevertheless, matrix algebra methods examining geometry driven mapping facilitate the definition of subspaces with different noise sensitivity within the reconstruction space. These types of examinations ensure definition of optimal geometry while meeting predefined quality standards and providing scans of the highest diagnostic value.
My thesis will firstly survey the X-ray based pseudo-three dimensional imaging modalities and their inherent geometries and reconstruction methods. I will give a short summary of the system I have implemented, a system which is able to create projection data well adaptable to the types of examinations.
I will examine the impact of limited tomography angular range and noisy projections on the reconstruction by applying an algebraic (pseudo-inverse) and an analytical (filtered back projection) reconstruction method. In this thesis I will illustrate my observations with examples while presenting mathematical algorithms supporting the procedures.