  The need for tomographic reconstruction from sparse measurements arises when
the measurement process is potentially harmful, needs to be rapid, or is
uneconomical. In such cases, information from previous longitudinal scans of
the same object helps to reconstruct the current object while requiring
significantly fewer updating measurements. Our work is based on longitudinal
data acquisition scenarios where we wish to study new changes that evolve
within an object over time, such as in repeated scanning for disease
monitoring, or in tomography-guided surgical procedures. While this is easily
feasible when measurements are acquired from a large number of projection
views, it is challenging when the number of views is limited. If the goal is to
track the changes while simultaneously reducing sub-sampling artefacts, we
propose (1) acquiring measurements from a small number of views and using a
global unweighted prior-based reconstruction. If the goal is to observe details
of new changes, we propose (2) acquiring measurements from a moderate number of
views and using a more involved reconstruction routine. We show that in the
latter case, a weighted technique is necessary in order to prevent the prior
from adversely affecting the reconstruction of new structures that are absent
in any of the earlier scans. The reconstruction of new regions is safeguarded
from the bias of the prior by computing regional weights that moderate the
local influence of the priors. We are thus able to effectively reconstruct both
the old and the new structures in the test. In addition to testing on simulated
data, we have validated the efficacy of our method on real tomographic data.
The results demonstrate the use of both unweighted and weighted priors in
different scenarios.
