Improving the lifetime of Wireless Sensor Networks (WSNs) is directly related with the energy efficiency of computation and communication operations in the sensor nodes. By employing the concepts of Compressive Sensing (CS) theory it is possible to reconstruct a signal with a certain number of random linear measurements, which is much less than the number of measurements necessary in conventional signal reconstruction techniques. In this study, communication and computation energy dissipation models for CS and conventional signal processing techniques are built in order to investigate impact of CS based signal reconstruction on WSN lifetime with Linear Programming (LP) based on the data flow optimization.