Two-dimensional block diagonal LMS adaptive filtering

The conventional LMS scheme was first extended to the 2-D case by Hadhoud and Thomas [7]. Their 2-D LMS algorithm is particularly useful in various image processing areas such as image enhancement and image data compression where the variations in local statistics of the image must be taken into account. This method processes an image pixel by pixel using a I-D scanning scheme, and consequently, it considers the correlation of pixels in only one direction. Soni et al. [8] used a 2-D adaptive LMS filter to detect and isolate small objects with broad-band spectra from background clutter with a narrow-band spectrum. More recently, several other authors [9]-[11] have developed different 2-D LMS-based adaptive algorithms. In [10], a new 2-D sequential adaptive filtering scheme was proposed which uses variable step-size to improve the convergence behavior. This algorithm was then extended in [11] for block processing using a scalar adaptation rule. This paper is concerned with the development of a 2D block diagonal LMS (BDLMS) algorithm based on the application of the 2-D block processing method [12]. A 2-D diagonal scanning is employed to preserve the local correlational information of pixels in both directions. The convergence behavior of the 2-D BDLMS filter is studied. To consider the nonstationarity inherent in real-world images, a variable step size rule is given. Applications of the 2-D BDLMS in image estimation, filtering, and detection areas are studied. Simulation results for filtering additive noise from a corrupted image are presented, and a comparison is made between the proposed 2-D BDLMS and the standard Wiener Abstract-This paper is concerned with the development of a two-dimensional (2-D) 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 di~gonal fashion, and the filter weights are adjusted o?ce per block rather than once per pixel. The diagonal scanmng is adopted to avoid the problems inherent in the 1-]) standard scanning schemes and to account for the correlations in tw.o directions. The weight updating equation for 2-D BDLMS IS derived and the convergence properties of the algorithms are investig~ted. Simulation results that indicate the etTectiv~nes~ of the 2-D BDLMS when used for image enhancement, estimation, and detection applications are presented.