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The Eyesafe Ladar Test-bed (ELT) is a experimental ladar system with the capability of digitizing return laser pulse waveforms at 2 GHz. These waveforms can then be exploited o-line in the laboratory to develop signal processing techniques for noise reduction, range resolution improvement, and range discrimination between two surfaces of similar range interrogated by a single laser pulse. This paper presents the results of experiments with new deconvolution algorithms with the hoped for gains of improving the range discrimination of the ladar system. The sparsity of ladar returns is exploited to solve the deconvolution problem in two steps. The rst step is to estimate a point target response using a database of measured calibration data. This basic target response is used to construct a dictionary of target responses with dierent delays/ranges. Using this dictionary ladar returns from a wide variety of surface congurations can be synthesized by taking linear combinations. A sparse linear combination matches the physical reality that ladar returns consist of the overlapping of only a few pulses. The dictionary construction process is a pre-processing step that is performed only once. The deconvolution step is performed by minimizing the error between the measured ladar return and the dictionary model while constraining the coecient vector to be sparse. Other constraints such as the non-negativity of the coecients are also applied. The results of the proposed technique are presented in the paper and are shown to compare favorably with previously investigated deconvolution techniques.