Accurate detection and quantitative evaluation of defects and damages in conductive structures is an essential and 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 the current methods by incorporating compressive sensing in the inspection process. In conductive structures eddy current imaging, scientific key problems are sparse representations and transform domain mapping, sparse testing constraints, and sparse image reconstruction. The main research contents are as follows: firstly, constructing the model of conductive structures eddy current imaging and researching on sparse representations, transform domain mapping, sparse matrix, sparse transform matrix, and signal recovery priori errors, for providing basic theory; secondly, using a coil probe to do C scan, and researching on the mapping relationship between the specimen and sparse data acquisition, and the methods of data acquisition, for establishing the theoretical framework of data acquisition; thirdly, proposing the information recovery methods for completing the compressive sensing; fourthly, establishing the experimental system for validating theories and methods. Finally, currently urgent need theories and methods of conductive structures eddy current imaging are established. It will promote the theories and technologies development of eddy current testing. The study and application of conductive structures are also accelerated.