A Fast L1 Linear Estimator and Its Application on Predictive Deconvolution

The L₁ linear estimator which is used to solve the linear problem by minimizing the L₁ norm in the data-fitting term does better than traditional least square (LS) methods in applications where the residual vector is super-Gaussian or contains outliers. We propose a fast L₁ linear estimation algorithm by first translating the L₁ norm data-fitting problem into a L₁ norm regularized L₂ norm data-fitting problem and then solving the equivalent problem by fast iterative shrinkage-thresholding algorithm (FISTA). The method of the equivalence is carefully chosen and designed to achieve sufficiently low computational complexity of each FISTA iteration. The commonly used iterative reweighted least square (IRLS) algorithm is used as a benchmark in this letter. In comparison with IRLS, our numerical experiments show that the proposed algorithm is 5-11 times faster when achieving the same estimation accuracy. To demonstrate the performance of the proposed algorithm, we apply it on seismic predictive deconvolution. Both synthetic and real field data examples show that our method outperforms the IRLS-based and the traditional LS-based seismic predictive deconvolution method.