Transmission microscopy imaging systems include a mask and/or other modulator situated to encode image beams, e.g., by deflecting the image beam with respect to the mask and/or sensor. The beam is modulated/masked either before or after transmission through a sample to induce a spatially and/or temporally encoded signal by modifying any of the beam/image components including the phase/coherence, intensity, or position of the beam at the sensor. For example, a mask can be placed/translated through the beam so that several masked beams are received by a sensor during a single sensor integration time. Images associated with multiple mask displacements are then used to reconstruct a video sequence using a compressive sensing method. Another example of masked modulation involves a mechanism for phase-retrieval, whereby the beam is modulated by a set of different masks in the image plane and each masked image is recorded in the diffraction plane.