Two-dimensional block diagonal LMS adaptive filtering

The paper is concerned with the development of two-dimensional (2D) adaptive filters using the block diagonal least mean squared (BDLMS) method. In this adaptive filtering scheme, the image is scanned and processed block by block in a diagonal fashion, and the filter weights are adjusted once per block rather than once per pixel. The diagonal scanning is adopted to avoid the problems inherent in the 1D standard scanning schemes and to account for the correlations in two directions. The weight updating equation for 2D BDLMS is derived, and the convergence properties of the algorithms are investigated. Simulation results that indicate the effectiveness of the 2D BDLMS when used for image enhancement, estimation, and detection applications are presented