3-D models of environments can be very useful and are commonly employed in areas such as robotics, art and architecture, environmental planning and documentation. A 3-D model is typically comprised of a large number of measurements. When 3-D models of environments need to be transmitted or stored, they should be compressed efficiently to use the capacity of the communication channel or the storage medium effectively. In this thesis, we propose a novel compression technique based on compressive sampling, applied to sparse representations of 3-D laser range measurements. The main issue here is finding highly sparse representations of the range measurements, since they do not have such representations in common domains, such as the frequency domain. To solve this problem, we develop a new algorithm to generate sparse innovations between consecutive range measurements acquired while the sensor moves. We compare the sparsity of our innovations with others generated by estimation and filtering. Furthermore, we compare the compression performance of our lossy compression method with widely used lossless and lossy compression techniques. The proposed method offers small compression ratio and provides a reasonable compromise between reconstruction error and processing time.