GENERALIZED TOMOGRAPHIC IMAGING FOR RADAR AND LIDAR

IN RADAR, LIDAR, SONAR, AND ULTRASOUND SYSTEMS, RANGE RESOLUTION CAN BE IMPROVED BY INCREASING SIGNAL BANDWIDTH, BUT AZIMUTH (CROSS-RANGE) RESOLUTION IS LIMITED BY ARRAY OR APERTURE SIZE. THE SPACE-TIME TRANSMISSION PATTERN IS TYPICALLY MUCH NARROWER IN RANGE THAN IN AZIMUTH, YIELDING A LINE-LIKE FUNCTION THAT SAMPLES ENVIRONMENTAL REFLECTIVITY AS THE SYSTEM SCANS ITS SURROUNDINGS. OVEMENT OF TRANSMITTER OR TARGET CAUSES THE LINE-LIKE SAMPLING FUNCTION TO ROTATE. IF THE SPACE-TIME TRANSMISSION PATTERN HAS UNBOUNDED LENGTH, THE ENVIRONMENT WOULD BE REPRESENTED BY PROJECTIONS AS IN COMPUTER AIDED TOMOGRAPHY, AND INVERSION OF THE CORRESPONDING RADON TRANSFORM WOULD YIELD AN IMAGE WITH IMPROVED CROSS-RANGE RESOLUTION. FOR ACTUAL TRANSMISSION PATTERNS, A NEW GENERALIZATION OF THE RADON TRANSFORM, VIZ., AN INVERTIBLE LINE SEGMENT TRANSFORM, YIELDS THE DESIRED IMAGE IF THE LINE-LIKE BASIS FUNCTION USED BY THE TRANSFORM IS APPROXIMATED BY THE SPACE-TIME TRANSMISSION PATTERN OF THE RADAR/LIDAR/ULTRASOUND SYSTEM.