Growth hormone (GH) is secreted by cells in the anterior pituitary on two time scales: discrete pulses over minutes that occur within a 24-hr pattern. Secretion reflects the balance of stimulatory and inhibitory inputs from the hypothalamus and is influenced by gonadal steroids, stress, nutrition, and sleep/wake states. We propose a novel approach for the analysis of GH data and use this approach to quantify (i) the timing, amplitude and the number of GH pulses and (ii) GH infusion, clearance and basal secretion (i.e., time invariant) rates, using serum GH sampled every 10 minutes during an 8-hour sleep study in 18 adolescents. In our method, we approximate hormonal secretory events by deconvolving GH data via a two-step coordinate descent approach. The first step utilizes a sparse-recovery approach to estimate the timing and amplitude of GH secretory events. The second step estimates physiological parameters. Our method identifies the timing and amplitude of GH pulses and system parameters from experimental and simulated data, with a median R2 of 0.93, among experimental data. Recovering GH pulses and model parameters using this approach may improve the quantification of GH parameters under different physiological and pathological conditions and the design and monitoring of interventions.