Two-dimensional joint process lattice for adaptive restoration of images

The two dimensional (2D) joint process lattice (TDJPL) and its implementations for image restoration applications are examined. A 2D adaptive lattice algorithm (TDAL) is first developed. Convergence properties of the algorithm are covered for the 2D adaptive lattice least mean squares (TDAL-LMS) case. The complexity of the normalized algorithm is slightly more than that of the TDAL-LMS, but it is a faster-converging algorithm. Implementations of the proposed TDJPL estimator as a 2D adaptive lattice noise canceler and as a 2D adaptive lattice line enhancer are then considered. The performance of both schemes is evaluated using artificially degraded image data at different signal-to-noise ratios (SNRs). The results show that substantial noise reduction has been achieved, and the high improvement in the mean square error, even at very low input SNR, is ensured. The results obtained consistently demonstrate the efficacy of the proposed TDJPL implementations, and illustrate the success in its use for adaptive restoration of images