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The total variability i-vector based speaker verification system is one of the most successful systems in the recent NIST evaluations. It achieves significant improvement in performance over the conventional GMM-UBM based systems by using the projections of the GMM mean shifted supervectors to a low dimensional space for representation. This low dimensional projections are commonly referred to as the total variability i-vector features. In our recent works we have explored the use of sparse representation of the GMM mean shifted supervectors derived using a learned redundant dictionary as a feature for the speaker verification. This approach resulted in a performance comparable to that of the similar complexity i-vector based system. In this work, we explore a fusion of these two approaches in which the GMM mean supervectors are smoothed using the total variability space prior to creating dictionary for sparse representation. The proposed method is found to give a relative improvement of 19% in EER compared to that of the i-vector based system for the experiments done using the NIST 2003 SRE database.