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If the resolution of a compressively sensed image is not satisfactory then typically a new acquisition session with more samples needs to be set, and the reconstruction process needs to be run from scratch. Here we present a method to capture LiDAR images by progressively increasing the resolution of the 3D reconstructed image. The method prescribes the additional set of samples required to improve the resolution of a compressively sensed LiDAR. Then, a reconstruction procedure that uses the earlier captured coarser resolution 3D image and the additional samples is applied. The reconstruction process is realized by means of a specially designed deep neural network. This resolution refinement process is efficient in the sense that only the samples needed for the next higher resolution level are captured, and the resolution refinement is performed progressively.