Constrained Least Mean Square Research Articles

A new adaptive constrained LMS time delay estimation algorithm

In this paper, a new adaptive constrained LMS time delay estimation (TDE) algorithm is devised. It is known that in the TDE problem, the time differences between relevant sensors can be modeled as a finite impulse response (FIR) filter whose weight coefficients are samples of a sinc function. Moreover, in case of non-integer TDE, the performance of estimation result is highly dependent upon the convergence rate of weight coefficients of the FIR filter. To speed up the convergence rate of the weight coefficients, in this paper, we propose a new constrained LMS TDE algorithm by making use of the constraint that the sum of the squares of the weight coefficients of the FIR filter equals unity. Here, we show that the constrained optimum solution is identical to the true weights solution which is the error free optimum solution. Also, to document the advantage of the proposed algorithm, the statistical analysis of the steady-state weight-error vector as well as the mean square error of the estimator, using the proposed algorithm, are derived. As confirmed by the theoretical and simulation results, the new proposed algorithm for non-integer TDE outperform the conventional LMS TDE algorithm.

Inverse halftoning using binary permutation filters

The problem of reconstructing a continuous-tone image given its ordered dithered halftone or its error-diffused halftone image is considered. We develop a modular class of nonlinear filters that can reconstruct the continuous-tone information preserving image details and edges that provide important visual cues. The proposed nonlinear reconstruction algorithms, denoted as binary permutation filters, are based on the space and rank orderings of the halftone samples provided by the multiset permutation of the "on" pixels in a halftone observation window. For a given window size, we obtain a wide range of filters by varying the amount of space-rank ordering information utilized in the estimate. For image reconstructions from ordered dithered halftones, we develop periodically space-varying filters that can account for the periodical nature of the underlying screening process. A class of suboptimal but simpler space-invariant reconstruction filters are also proposed and tested. Constrained LMS type algorithms are employed for the design of reconstruction filters that minimize the reconstruction mean squared error. We present simulations showing that binary permutation filters are modular, robust to image source characteristics, and that they produce high visual quality image reconstruction.

Constrained adaptive LMS L-filters

Two novel adaptive nonlinear filter structures are proposed which are based on linear combinations of order statistics. These adaptive schemes are modifications of the standard LMS algorithm and have the ability to incorporate constraints imposed on coefficients in order to permit location-invariant and unbiased estimation of a constant signal in the presence of additive white noise. The convergence in the mean and in the mean square of the proposed adaptive nonlinear filters is studied. The rate of convergence is also considered. It is verified by simulations that the independence theory provides useful bounds on the rate of convergence. The extreme eigenvalues of the matrix which controls the performance of the location-invariant adaptive LMS L-filter are related to the extreme eigenvalues of the correlation matrix of the ordered noise samples which controls the performance of other adaptive LMS L-filters proposed elsewhere. The proposed filters can adapt well to a variety of noise probability distributions ranging from the short-tailed ones (e.g. uniform distribution) to long-tailed ones (e.g. Laplacian distribution).