Introduction (Introduction to: Mathematics of Medical Imaging)

 

Introduction

 
This chapter is sort of a handbook of mathematical tools applied in medical imaging.
Our intention with this chapter is to provide the mathematical basis necessary for understanding how medical imaging equipment works. We hope that the mathematical rigor and the application oriented approach balance out well enough that many types of minds find their way in understanding and following the subject. The material here is meant as an essential overview; those demanding deeper understanding should consult the textbooks cited in the reference section.

First of all, we have to clarify the concept of a picture, its digital representation, which image attributes help describing its quality aspects. In medical applications DICOM format allows for transporting data between vendors and modalities with the joint handling of images and patient data. Projection based (planar) imaging (x-ray, gamma camera, etc.) can be viewed as a linear system , where imaging element properties are superimposed one after the other. When talking about tomography, series of projections of the same object - in mathematical form the Radon transform- are used to rebuild (reconstruct) the original distribution (eg. attenuation coefficients, isotope concentration). Often tomographic scanners use the simpler filtered backprojection, which is being gradually replaced by the iterative reconstruction methodsapplied to an algebraic imaging model. Medical physics is mostly about ionising radiation, particle trajectories deliver information on geometrical distributions. Particle calculations are often performed using the Monte Carlo method, that is suitable for diagnostics and therapy applications both.

We recommend reading the chapters in the order of the table of contents, though we inserted links to relevant background information necessary for understanding a section is someone starts somewhere in medias res.

Picture of a foal in colours

Picture of a foal in grayscale

Radon transform of the image of a foal

Reconstructed image of a foal on fire colouring

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