A Monte-Carlo Method for Designing Compressed Sensing Measurement Matrices, with Applications to Robot Path Planning and Environmental Sensing

In recent years, Compressed Sensing (CS) has attracted significant interest in acquiring high-resolution sensory signals while minimizing the amount of signal samples to be measured (so-called sub-Nyquist sampling). At the same time, autonomous robot navigation, such as rovers and drones, is increasingly used for remote data acquisition and environmental data sampling (e.g., temperature, humidity, air quality indicators, etc.). In this context, this paper presents a novel method of preparing the robot data acquisition path that takes advantage of the structure of the measurement matrices used in CS in order to derive robot navigation paths. In particular, we propose a novel Monte-Carlo optimization approach for generating well-suited measurement matrices that jointly lead to short robot path lengths while minimizing the signal recovery error during the CS procedure. Crucially, our method uses Dictionary Learning (DL) to generate a well-suited CS sparsifying transform matrix, enabling high-precision signal recovery while minimizing the number of samples the robot needs to sense. Our proposed method is applied to recover NO2 pollutant maps from the Gulf region. Experimental results demonstrate that our proposed method reduces the length of the robot data acquisition paths to less than 10% of the total path length normally required for total area coverage, while leading to high-precision signal recovery, achieving more than x5 lower signal recovery errors compared to the use of standard DCT- and Polynomial-based CS procedures.