A new local tomography function g is proposed. It is shown that g still contains non-local artifacts, but their level is an order of magnitude smaller than those of the previously known local tomography function. We also investigate local tomography reconstruction in the dynamic case, i.e. when the object f being scanned is undergoing some changes during the scan. Properties of g are studied, the notion of visible singularities is suitably generalized, and a relationship between the wave fronts of f and g is established. It is shown that the changes in f do not cause any smearing of the singularities of g. Results of numerical experiments are presented.