Fig. 1: Overall structure of the proposed LAPRAN. The CS measurement of a high-dimensional image is performed by a multi-rate random encoder. The LAPRAN takes CS measurements as inputs and progressively reconstructs an original image in multiple hierarchies with incremental resolutions and recov- ery qualities. At each pyramid level, RAN generates an image residual, which is subsequently combined with an upscaled output from the previous level to form a higher-resolution output of the current level (upsampling and upscaling respectively refers to increasing the image resolution with and without new details added).