Accurate detection and quantitative evaluation of defects and damage in metal plates is a crucial task in a range of technological applications, such as maintaining the integrity, enhancing the safety, and assuring the reliability of structures. There is scope for improving eddy current testing methods by incorporating compressive sensing (CS) in the inspection process. The key scientific problems in eddy current imaging of defects of metal plates are sparse representations and transform domain mapping, sparse testing constraints, and sparse image reconstruction. The main research content of this paper is as follows. We first provide basic theory based on research of sparse representations, transform domain mapping, sparse matrices, sparse transform matrices, and signal recovery a priori errors. We then propose information-recovery methods for completing compressive sensing. Third, we establish an experimental system for validating theories and methods. Finally, we establish theories and methods for eddy current imaging of metal plates.