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We develop computationally efficient procedures for solving certain restoration problems in one dimension, including the one-dimensional (1-D) discrete versions of the total variation regularized problem introduced by Sauer and Bouman and the constrained total variation minimization problem introduced by Rudin et al. The procedures are exact and have time complexity ( log ) and space complexity ( ), where is the number of data samples. They are based on a simple nonlinear diffusion equationdoi:10.1109/tsp.2004.840786 fatcat:43i7tuoqhzfn5d3yf6r44gfwte