Resolution capability of seismic reflection data is becoming more interesting topic to discuss even for today. Several methods and approximations to attempt bandwidth extension of seismic reflection data have been proposed in wide variety. Among them is a non-stationary reflectivity inversion based on basis pursuit decomposition technique. The need of the method is increasing as it can provide realistic resolution of seismic data. The main advantages of the method are consistancy with log data, good lateral continuity, preserve amplitude and capable in denying artificial reflection feature. Nevertheless, its computational process is very expensive thus most pratitioners tend to avoid the method and look for another method that could serve quicker instead of better results.This paper attempt to propose a set of computational scheme which can be used flexibly for any prospective user to reduce the computational cost of the method.