Conventional linear prediction based on the 1-2 minimization of the prediction error suffers from the spurious peaks for high orders. SVD truncation which is used to eliminate them requires the knowledge of the number of scattering centers. A wrong choice results in the elimination of the true scattering centers decreasing the accuracy of the model. In this work sparsity constraints are imposed on the AR model coefficients to overcome this drawback. The linear prediction problem is formulated as an optimization problem of BPDN, BPDN with penalty term or LASSO and solved using linear programming. HHR profiles obtained using these sparse coefficients represent less spurious peaks and provide increased classification performance.