A multiplexed Fourier Ptychographic imaging system comprising: an LED array (112, 212, 312, 412, 714, 814) configured to illuminate a sequence of differing LED patterns, each LED pattern comprising a different plurality of illuminated LEDs, the LED array (112, 212, 312, 412, 714, 814) located to illuminate a sample (20, 21) being imaged; LED circuitry (114, 414) in electrical communication with the LED array (112, 212, 312, 412, 714, 814), wherein the LED circuitry (114, 414) is configured to independently control power to turn on multiple LEDs simultaneously in each LED pattern; a lens (120, 220, 320) configured to collect light issuing from the illuminated sample (20, 21); a light detector (130, 230, 330) configured to receive light from the lens (120, 220, 320) to acquire a first set of lower resolution images associated with the sequence of LED patterns, wherein each lower resolution image of the first set is based on light issued from the sample (20, 21) and received during an exposure time; a processor configured to: perform a weighted sum operation on the first set of lower resolution images to generate a second set of lower resolution images, each image of the second set associated with one LED in the LED array (112, 212, 312, 412, 714, 814); and iteratively update overlapping regions in the Fourier domain with the second set of lower resolution images to generate a higher resolution complex image of the sample (20, 21) using a phase-retrieval operation to recover phase data from the second set of lower resolution images. an LED array (112, 212, 312, 412, 714, 814) configured to illuminate a sequence of differing LED patterns, each LED pattern comprising a different plurality of illuminated LEDs, the LED array (112, 212, 312, 412, 714, 814) located to illuminate a sample (20, 21) being imaged; LED circuitry (114, 414) in electrical communication with the LED array (112, 212, 312, 412, 714, 814), wherein the LED circuitry (114, 414) is configured to independently control power to turn on multiple LEDs simultaneously in each LED pattern; a lens (120, 220, 320) configured to collect light issuing from the illuminated sample (20, 21); a light detector (130, 230, 330) configured to receive light from the lens (120, 220, 320) to acquire a first set of lower resolution images associated with the sequence of LED patterns, wherein each lower resolution image of the first set is based on light issued from the sample (20, 21) and received during an exposure time; a processor configured to: perform a weighted sum operation on the first set of lower resolution images to generate a second set of lower resolution images, each image of the second set associated with one LED in the LED array (112, 212, 312, 412, 714, 814); and iteratively update overlapping regions in the Fourier domain with the second set of lower resolution images to generate a higher resolution complex image of the sample (20, 21) using a phase-retrieval operation to recover phase data from the second set of lower resolution images. perform a weighted sum operation on the first set of lower resolution images to generate a second set of lower resolution images, each image of the second set associated with one LED in the LED array (112, 212, 312, 412, 714, 814); and iteratively update overlapping regions in the Fourier domain with the second set of lower resolution images to generate a higher resolution complex image of the sample (20, 21) using a phase-retrieval operation to recover phase data from the second set of lower resolution images.