You're right that SD cards aren't fast enough. That's why high-end DSLRs support the much faster XQD standard. There are no DSLRs (and precious few if any still cameras, period) that can do 150fps, but 15-20fps isn't at all uncommon in professional lines, and most cameras that support that frame rate also have deep enough buffers and fast enough XQD interfaces that they can shoot raw at full framerate for 10-15 seconds before they fill the buffer and slow down.
Without all those raw images, you won't be able to do this kind of postprocessing after the fact.