Introduction: Local activation times (LATs) of atrial electrograms recorded during high resolution atrial mapping, are used to represent depolarization wave-front propagation in atrial tissue. The LATs is mostly marked as the steepest decent of a unipolar electrogram. This does not provide reliable LAT estimations for fractionated electrograms. To improve LAT estimation, we focus on trans-membrane currents estimation, which are more local activities and provide better LAT estimations than electrograms. Methods: Each electrogram is the result of spatial convolution of an appropriate distance kernel with the cells' trans-membrane currents. To estimate these currents, we can deconvolve the electrograms with the appropriate distance kernel, however, this is an ill-posed problem. To overcome this issue, we add sparsity as an appropriate regularization term to the problem. Further, to assure the maximum sparsity, we use the electrograms’ first temporal derivative in the deconvolution problem. The LATs are then determined by the minimum of the deconvolved data which are the first temporal derivative of the trans-membrane currents. For an efficient implementation, we use ADMM and present detailed solutions for each of its steps. Moreover, for faster computations, we perform all large matrix multiplications in the frequency domain. Results: As the true LATs for clinical electrograms are unknown, we use simulated data to evaluate the performance of the proposed approach. Electrograms are simulated for three two-dimensional rectangular grids of cells with different patterns of slow conduction and/or blocks. Finally, we estimate the LATs of fractionated electrograms using the proposed approach and two reference methods: the steepest decent and the maximum of the spatial derivative. In all cases, the proposed approach outperforms the two references in terms of mean square error. In general, the deconvolution intensifies the amplitude of the true deflection in a fractionated electrogram which subsequently improves the performance of LAT estimation.