Traditional methods in seismic acquisition require sources and geophones that are uniformly located along a spatial line, using the Nyquist sampling rate. Depending on the area to be explored, it can be necessary to use seismic surveys with large offsets, or decrease the separation between adjacent geophones to improve the resolution, which generates very high volumes of data. It makes the exploration process more difficult and particularly expensive. This work presents the reconstruction of a compressive set of seismic traces acquired using the compressive sensing paradigm where the pair of sources and geophones are randomly located along the spatial line. The recovery of the wavefield from compressive measurements is feasible due to the capabilities of Curvelets on representing wave propagators with only a small set of coefficients. The method first uses the compressive samples to find a sparse vector representation of each pixel in a 2-D Curvelet dictionary. The sparse vector representation is estimated by solving a sparsity constrained optimization problem using the Gradient Projection for Sparse Reconstruction (GPSR) method. The estimated vector is then used to compute the seismic velocity profiles via acoustic Full Waveform Inversion (FWI). Simulations of the reconstructed image gathers and the resulting seismic velocity profiles illustrate the performance of the method. An improvement in the resulting images is obtained in comparison with traditional F-K filtering used in seismic data processing when traces are missing.