In exemplary implementations of this invention, light from a backlight is transmitted through two stacked LCDs and then through a diffuser. The front side of the diffuser displays a time-varying sequence of 2D images. Processors execute an optimization algorithm to compute optimal pixel states in the first and second LCDs, respectively, such that for each respective image in the sequence, the optimal pixel states minimize, subject to one or more constraints, a difference between a target image and the respective image. The processors output signals to control actual pixel states in the LCDs, based on the computed optimal pixel states. The 2D images displayed by the diffuser have a higher spatial resolution than the native spatial resolution of the LCDs. Alternatively, the diffuser may be switched off, and the device may display either (a) 2D images with a higher dynamic range than the LCDs, or (b) an automultiscopic display.