ITC/USA 2013 Conference Proceedings / The Forty-Ninth Annual International Telemetering Conference and Technical Exhibition / October 21-24, 2013 / Bally's Hotel & Convention Center, Las Vegas, NV / Third generation LIDAR full-waveform (FW) based systems collect 1D FW signals of the echoes generated by laser pulses of wide bandwidth reflected at the intercepted objects to construct depth profiles along each pulse path. By emitting a series of pulses towards a scene using a predefined scanning patter, a 3D image containing spatial-depth information can be constructed. Unfortunately, acquisition of a high number of wide bandwidth pulses is necessary to achieve high depth and spatial resolutions of the scene. This implies the collection of massive amounts of data which generate problems for the storage, processing and transmission of the FW signal set. In this research, we explore the recovery of individual continuous-time FW signals at sub-Nyquist rates. The key step to achieve this is to exploit the sparsity in FW signals. Doing this allows one to sub-sample and recover FW signals at rates much lower than that implied by Shannon's theorem. Here, we describe the theoretical framework supporting recovery and present the reader with examples using real LIDAR data.

We propose using overlapping, tapered windows to process seismic data in parallel. This method consists of numerically tight linear operators and adjoints that are suitable for use in iterative algorithms. This method is also highly scalable and makes parallel processing of large seismic data sets feasible. We use this scheme to define the Parallel Windowed Fast Discrete Curvelet Transform (PWFDCT), which we apply to a seismic data interpolation algorithm. The successful performance of our parallel processing scheme and algorithm on a two-dimensional synthetic data is shown.