A Novel Monte-Carlo Compressed Sensing and Dictionary Learning Method for the Efficient Path Planning of Remote Sensing Robots

In recent years, Compressed Sensing (CS) has gained significant attention as a method for acquiring high-resolution sensory data with fewer measurements than traditional Nyquist sampling. Simultaneously, autonomous robotic platforms such as drones and rovers have become valuable tools for remote sensing and environmental monitoring tasks, including temperature, humidity, and air quality measurements. This letter presents, to the best of our knowledge, the first study on exploiting the structure of CS measurement matrices to design optimized sampling trajectories for robotic environmental data collection. We introduce a Monte Carlo optimization framework that generates measurement matrices minimizing both the robot's path length and the CS reconstruction error. Central to our approach is Dictionary Learning (DL), which provides a data-driven sparsifying transform to enhance reconstruction accuracy and further reduce the number of required samples. Experiments on $NO_{2}$ pollution and temperature map reconstruction across two geographical areas demonstrate that our method can cut robot travel distance to under 10% of a full-coverage path while improving reconstruction accuracy by over fivefold compared to traditional CS methods and twofold compared to prior Informative Path Planning (IPP) techniques.