Receiver functions (RFs) are derived by deconvolution of the horizontal (radial or transverse) component of ground motion from the vertical component, which segregates the PS phases. Many methods have been proposed to employ deconvolution in frequency as well as in time domain. These methods vary in their approaches to impose regularization that addresses the stability problem. Here, we present application of a new time‐domain deconvolution technique called basis pursuit deconvolution (BPD) that has recently been applied to seismic exploration data. Unlike conventional deconvolution methods, the BPD uses an L1 norm constraint on model reflectivity to impose sparsity. In addition, it uses an overcomplete wedge dictionary based on a dipole reflectivity series to define model constraints, which can achieve higher resolution than that obtained by the traditional methods. We demonstrate successful application of BPD based RF estimation from synthetic data for a crustal model with a near‐surface thin layer of thickness 5, 7, 10, and 15 km. The BPD can resolve these thin layers better with much improved signal‐to‐noise ratio than the conventional methods. Finally, we demonstrate application of the BPD receiver function (BPRF) method to a field dataset from Kutch, India, where near‐surface sedimentary layers are known to be present. The BPRFs are able to resolve reflections from these layers very well.