Snapshot compressive sensing refers to compressive imaging systems where  multiple frames are mapped into a single measurement frame. Each pixel in the  acquired frame is  a linear combination of the corresponding pixels in the  frames that are combined together.  While the problem can be cast as a  compressive sensing problem,  due to the very special  structure of the sensing  matrix,  standard compressive sensing theory cannot be employed to study such systems. 
In this work, two novel, efficient and theoretically-analyzable snapshot compressive sensing recovery algorithms are proposed.  The algorithms are  iterative and  employ  compression codes to impose structure on the recovered frames. The algorithms are validated in simulation results and their performances are shown to be comparable with the  performances of  state-of-the-art heuristic algorithms.