Is it deemed perjury if police lie on a police report to secure an arrest warrant against you for a crime you did not commit and then you are found to be innocent and if so can I sue?

Yes you can get a lawyer and take up legal action. It is called false arrest, and something to do with lieing on the report with there signature and defrauding the system. It happens all the time and people sue for this reason all the time. Not saying they win, just saying they sue.