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The capability of transmission in Wireless sensor networks (WSN) is circumscribed due to the precincts in energy utilization, controlled resources of transmission devices and network components. Information compression is taken into account as the best option, because the major part of energy consumed is for transmission of information. Habitually Lossy compression is adopted, since WSN abides some error in the reconstructed signals subjected to some acceptable tolerance. Lasso based models have been ascertained their capability to effectually compress both multivariate and univariate data. Traditional Lasso considers ℓ1-norm regularization for learning in multi-dimensional data sets and assumes sparsity as model parameters. Lasso prominence on sparsity and deal with the correlation between the data points. However, model sparsity may be constricting and not essentially the foremost applicable assumption in several problem domains. To eliminate this limitation, an enriched lasso (MLasso) is proposed for compression bearing in mind both sparsity and correlation. In specific the strategy can select data that are having strong features to reconstruct the data and are less correlated between each other. Furthermore, an efficient Alternating Direction Method of Multipliers (ADMM) is adopted to resolve the ensuing sparse non-convex optimization problem. Extensive experiments on diverse datasets provides the proof that MLasso outperforms other similar algorithms for signal compression. Thus the proposed method ensures less energy consumption, decreases power loss and improves the operational life and reliability of network components.