Circular arc Radon transforms are transforms that associate to a function, its integrals along arcs of circles. The inversion of such transforms are of natural interest in several imaging modalities such as thermoacoustic and photoacoustic tomography, ultrasound and intravascular imaging. In this work, we present an efficient algorithm that gives a numerical inversion of such transforms, with limited data in angular as well as radial direction.
The setup of transfor is illustrated in the figure below.

Nuclear imaging modalities like Positron emission tomography (PET) are characterized by a low SNR value due to the underlying signal generation mechanism. With its higher packing density and larger and symmetrical neighbourhood, the hexagonal lattice offers a natural robustness to degradation in signal. Based on this observation, we propose an alternate solution to denoising, namely by changing the sampling lattice. We use filtered back projection for reconstruction, followed by a sparse dictionary based denoising and compare noise-free reconstruction on the Square and Hexagonal lattices.

Improving resolution of tomographic images has been an active area of research in the past few years. This is of special interest in nuclear imaging where the image resolution is limited by the permissible dosage. Super resolution (SR) techniques based on combination of a set of low resolution images with spatial shifts have been examined for PET and CT images.

Our research is focused on obtaining high quality upsampled tomographic images. The technique we have developed for upsampling uses samples drawn from union of rotated lattices. Both hexagonal and square lattices have been studied. Such a technique has the benefit that the number of images required for deriving the synthetically zoomed output is minimal.