Two-dimensional joint process lattice for adaptive restoration of images

Abstract

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.

Design of a multichannel two-dimensional delta-domain lattice filter for noise removal

“…1. The 2-D joint process lattice used for each channel is the same structure used in [11][12][13]. However, the joint process estimator is also modified to handle multichannel data during the simulations.…”

“…The application areas for multichannel adaptive algorithms are wide and diverse, and the following are just a few examples to indicate: Synthetic aperture radar (SAR) imaging, color image processing, multichannel equalization, multidimensional (NLMS) algorithm has been developed by Youlal et.al. [11] The four-field, three-parameter lattice structure has been applied to 2-D AR modelling [10], and to image restoration and noise cancellation in images in the form of joint process estimator [11,13].…”

2-D Iteratively Reweighted Least Squares Lattice Algorithm and Its Application to Defect Detection in Textured Images

“…2-D lattice filter is a digital filter that has been developed extending the structure of 1-D lattice filter to 2-D. With the attractive features stated [1][2][3][4][5][6][7][8], the 2-D lattice filter has been the center of interest in this study as an effective tool for modeling the input data as an AR process.…”

“…Each stage is a multi-input/multi-output structure defined in terms of reflection coefficients. The reflection coefficients can be calculated either directly solving normal equations [1][2][3] or recursively by adaptive methods [4][5][6][7][8]. The algorithms developed for the adaptation of the lattice parameters are either gradient-based [4][5][6] or ________________________________________________________________________________ *This work has been partially supported by Turkish Technology Development Foundation under contract number recursive least squares (RLS) type [7][8] algorithms.…”

“…(3.6). Alternatively, the reflection coefficients can be calculated adaptively [4][5][6][7][8]. There have been a number of adaptive algorithms developed to update the reflection coefficients of the 2-D lattice filter.…”