One of the main limitations of imaging at high spatial and temporal resolution during in-situ transmission electron microscopy (TEM) experiments is the frame rate of the camera being used to image the dynamic process. While the recent development of direct detectors has provided the hardware to achieve frame rates approaching 0.1 ms, the cameras are expensive and must replace existing detectors. In this paper, we examine the use of coded aperture compressive sensing (CS) methods to increase the frame rate of any camera with simple, low-cost hardware modifications. The coded aperture approach allows multiple sub-frames to be coded and integrated into a single camera frame during the acquisition process, and then extracted upon readout using statistical CS inversion. Here we describe the background of CS and statistical methods in depth and simulate the frame rates and efficiencies for in-situ TEM experiments. Depending on the resolution and signal/noise of the image, it should be possible to increase the speed of any camera by more than an order of magnitude using this approach. Mathematics Subject Classification: (2010) 94A08 · 78A15.