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This paper addresses pilot-assisted channel estimation for wireless orthogonal frequency division multiplexing (OFDM) systems with irregular pilot arrangements. Using nonuniform sampling techniques, we propose a novel channel estimator that is based on conjugate gradient iterations and features very low computational complexity. We investigate the impact of the pilot arrangement on the channel estimation mean square error and we provide a heuristic stopping criterion for early termination of the conjugate gradient iterations. One-dimensional and two-dimensional channel estimator implementations and applications of our method to multiple-antenna and multiuser OFDM systems are discussed. Extensive numerical simulations corroborate that the proposed method performs similarly to computationally much more expensive minimum mean square error estimators.