Tomographic Imaging of Surface Deformation From Scarce Measurements via Sinogram Recovery

Imaging from limited data is a common practice in many industrial tomography applications where sensor design often assumes an irregular approach with low number of measurements. In this paper, we propose a novel algorithm that reduces the task of hard-field imaging from incomplete data to a sinogram recovery problem. The algorithm utilises a novel angular interpolation scheme, employing the sinusoidal Hough transform, to identify sinusoidal traces in the sinogram and estimate missing sinogram samples along such traces. Together with the detailed theory behind the algorithm, we present its performance with experimental data obtained from a photonic guided path tomography system. The targeted subject function is the induced deformation in the quasi-planar surface of a flexible ~1 m² sensor, fixed to an underlying soft-foam mat. The set of 32 independent measurements generated by the system are presented in a severely sparse 91times180 sinogram image. The sinogram is then recovered to a degree suitable for standard tomographic algorithms for hard-field data inversion, such as filtered back-projection.