A transmission mask or cooled aperture is used in spectroscopy to compressively sample an optical signal. The locations of transmissive and opaque elements of the mask are determined by a transmission function. The optical signal transmitted by the mask is detected at each sensor of a plurality of sensors dispersed spatially with respect to the mask. A number of estimated optical signal values is calculated from sensor measurements and the transmission function. The optical signal is compressed by selecting the transmission function so that the number of measurements is less than the number of estimated optical signal values. A reconstructed optical signal is further calculated using signal inference. An imaging system created from plurality of encoded subimaging systems compressively samples an optical signal. Encoding methods include but are not limited to pixel shift coding, birefringent shift coding, transmission mask coding, micro-optic coding, diffractive coding, interferometric coding, and focal plane coding.