What recourse would you have if you think that a search warrant was not justified?

The Fourth Amendment protects against unlawful search and seizure. The usual way of enforcing this is to require the police to obtain a search warrant before entering a person’s premises. Search warrants are issued by judges on the basis of what is referred to as probable cause.

Judges are only human and there have been cases of ones who are corrupt. Suppose that a person has been convicted with evidence obtained using a search warrant that the person thinks should not have been issued. What recourse is there? Can the case be appealed? Does a search warrant have documentation associated with it that gives the reasons why it was issued?