In exemplary implementations of this invention, an automultiscopic display device includes (1) one or more spatially addressable, light attenuating layers, and (2) a controller which is configured to perform calculations to control the device. In these calculations, tensors provide sparse, memory-efficient representations of a light field. The calculations include using weighted nonnegative tensor factorization (NTF) to solve an optimization problem. The NTF calculations can be sufficiently efficient to achieve interactive refresh rates. Either a directional backlight or a uniform backlight may be used. For example, the device may have (1) a high resolution LCD in front, and (2) a low resolution directional backlight. Or, for example, the device may have a uniform backlight and three or more LCD panels. In these examples, all of the LCDs and the directional backlight (if applicable) may be time-multiplexed.