We have developed a Computer Assisted Tomography (CAT) program that modifies a time‐dependent three‐dimensional kinematic heliospheric model to fit interplanetary scintillation (IPS) observations. The tomography program iteratively changes this global model to least‐squares fit IPS data. The short time intervals of the kinematic modeling (∼1 day) force the heliospheric reconstructions to depend on outward solar wind motion to give perspective views of each point in space accessible to the observations, allowing reconstruction of interplanetary Coronal Mass Ejections (CMEs) as well as corotating structures. We show these models as velocity or density Carrington maps and remote views. We have studied several events, including the July 14, 2000 Bastille‐day halo CME. We check our results by comparison with additional remote‐sensing observations, and observations from near‐Earth spacecraft. © 2003 American Institute of Physics