Abstract: This is a constrained optimization type of numerical algorithm for removing noise from images. The L1-norm of total variation of the image is minimized subject to constraints involving the statistics of the noise. The constraints are imposed using Lagrange multipliers. The solution is obtained using the gradient-projection method. This amounts to solving a time dependent partial differential equation on a manifold determined by the constraints. As t →∞ the solution converges to a steady state which is the denoised image. The traditional L2-norm based regularization, which is known to remove high frequency noises in the reconstructed images and make them appear smooth. The recovered contrast in the reconstructed image in these type of methods are typically dependent on the iterative nature of the method employed, in which the non-linear iterative technique is known to perform better in comparison to linear techniques. The usage of non-linear iterative techniques in the real-time, especially in dynamical imaging, becomes prohibitive due to the computational complexity associated with them. This new frame work along with the L1-norm based regularization can provide better robustness to noise and results in better contrast recovery compared to conventionalL2-based techniques. The proposed L1-based technique is computationally efficient.