Histotomography

Seminar given in the Inverse Problems seminar series in te School Of Mathematics , University of Manchester, on Histotomography. Abstract follows: In many tomographic imaging problems the data consists of integrals along lines or curves. Increasingly we are seeing ``rich tomography" problems where the quantity imaged is higher dimensional than a scalar per voxel, including vectors tensors and functions. The data can also be higher dimensional and in many cases consists of a one or two dimensional spectrum for each ray. In many such cases the data contains not just integrals along rays but the distribution of values along the ray. If this is discretized into bins we can think of this as a histogram. In this talk we introduce the concept of ``histotomography". For scalar problems with histogram data this holds the possibility of reconstruction with fewer rays. In vector and tensor problems it holds the promise of reconstruction of images that are in the null space of related integral transforms. We will illustrate with examples from scalar spectral attenuation tomography and tensor tomography methods for strain using neutrons, electrons and x-rays.A Youtube video of the seminar will be available when ready at https://youtu.be/fVCmB3s5H_0 The notes appear as MIMS eprint http://eprints.maths.manchester.ac.uk/2627