For constrained two-dimensional (2-D) finite impulse response (FIR) filters

the computational complexity of the existing design algorithms is very high. Based on the alternating direction method of multipliers (ADMM)

the parallel optimization of constrained least-squares (CLS) 2-D FIR filters was studied. By maximally splitting the problem into univariate subproblems and utilizing a relaxation technique

a maximally split and relaxed ADMM with a highly parallel computing architecture was proposed. The computational complexity and convergence of the algorithm were analyzed

and a practical scheme for selection of the algorithm parameters was provided. Experimental results show that the proposed maximally split and relaxed ADMM converges much faster than the maximally split unrelaxed ADMM. Compared with existing algorithms

the computational efficiency of the proposed algorithm is improved. The large acceleration ratios obtained by GPU demonstrate the high parallelism and scalability of the proposed algorithm

which is very valuable for applications of the algorithm in image processing

computer vision

pattern recognition and machine learning.