Abstract
One of the main challenges for optimal designs of two-dimensional (2D) finite impulse response (FIR) filters is their heavy computational load due to the large number of filter coefficients and the high dimensions of the data for model fitting. The alternating direction method of multipliers (ADMM) is a powerful technique appropriate for optimization for big data. In this paper, a relaxed ADMM is presented and then applied in the weighted least-squares (WLS) design of linear-phase 2D FIR filters. It is shown that the relaxed ADMM algorithm converges much faster than the standard ADMM algorithm. In addition, a salient feature of the relaxed ADMM is its highly parallel structure which makes it very efficient if implemented in parallel. Simulation examples and comparisons demonstrate the fast convergence and high efficiency of the relaxed ADMM algorithm.
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