2-DIMENSIONAL BLOCK ADAPTIVE FILTERING ALGORITHMS WITH OPTIMUM CONVERGENCE FACTORS

In this paper, two new fast gradient algorithms which perform 2-D bloc k adaptive filtering are presented. The 2-D adaptive filter coefficien ts are updated once for every block of input data and error measuremen t. The two algorithms employ variable convergence factors which are op timized in the least-squares (LS) sense to track the variations in an image's local statistics. These 2-D optimal algorithms are obtained fr om the one-dimensional optimal adaptive algorithms, which have been re cently reported. In the first algorithm, the 2-D optimum block adaptiv e algorithm with individual adaptation of parameters (TDOBAI), the con vergence factors are obtained, that are individually tailored for each 2-D filter weight and are updated once per block iteration. The secon d algorithm uses a convergence factor that is the same for all the 2-D coefficients at a particular block iteration, and is determined at ea ch block iteration. This algorithm is called the 2-D optimum block ada ptive algorithm (TDOBA). In both algorithms, the convergence factors a re easily computed from readily available signals. The excellent perfo rmance characteristics of the optimal 1-D algorithms are shown to be r etained in the proposed 2-D optimal algorithms. The convergence proper ties of the TDOBAI and the TDOBA algorithms are investigated and compa red with the 2-D block least-mean-square (TDBLMS) algorithm which uses a convergence factor that is constant for each 2-D coefficient at eac h block iteration, using computer simulations. It is also shown that f or the TDOBAI and TDOBA algorithms, the convergence, speed and accurac y of adaptation are greatly improved at the expense of a modest increa se in computational complexity, as compared to the TDBLMS algorithm. T he effectiveness of the algorithms is demonstrated in 2-D system model ing, restoration (2-D additive noise cancellation), and enhancement of artificially degraded images. Also, it is shown that the TDOBAI algor ithm is a more general formulation, from which several other recently proposed 2-D sequential and block algorithms can be obtained as specia l cases, by trading performance with computational complexity.