Compressed Sensing for 3D Laser Radar

Abstract: High resolution 3D images are of high interest in military operations, where data can be used to classify and identify targets. The Swedish defence research agency (FOI) is interested in the latest research and technologies in this area. A draw- back with normal 3D-laser systems are the lack of high resolution for long range measurements. One technique for high long range resolution laser radar is based on time correlated single photon counting (TCSPC). By repetitively sending out short laser pulses and measure the time of flight (TOF) of single reflected pho- tons, extremely accurate range measurements can be done. A drawback with this method is that it is hard to create single photon detectors with many pixels and high temporal resolution, hence a single detector is used. Scanning an entire scene with one detector is very time consuming and instead, as this thesis is all about, the entire scene can be measured with less measurements than the number of pixels. To do this a technique called compressed sensing (CS) is introduced. CS utilizes that signals normally are compressible and can be represented sparse in some basis representation. CS sets other requirements on the sampling compared to the normal Shannon-Nyquist sampling theorem. With a digital micromirror device (DMD) linear combinations of the scene can be reflected onto the single photon detector, creating scalar intensity values as measurements. This means that fewer DMD-patterns than the number of pixels can reconstruct the entire 3D-scene. In this thesis a computer model of the laser system helps to evaluate different CS reconstruction methods with different scenarios of the laser system and the scene. The results show how many measurements that are required to reconstruct scenes properly and how the DMD-patterns effect the results. CS proves to enable a great reduction, 85 − 95 %, of the required measurements com- pared to pixel-by-pixel scanning system. Total variation minimization proves to be the best choice of reconstruction method.