Underdetermined-order recursive least-squares adaptive filtering: The concept and algorithms

Published versio

Discrete-time variance tracking with application to speech processing

Two new discrete-time algorithms are presented for tracking variance and reciprocal variance. The closed loop nature of the solutions to these problems makes this approach highly accurate and can be used recursively in real time. Since the Least-Mean Squares (LMS) method of parameter estimation requires an estimate of variance to compute the step size, this technique is well suited to applications such as speech processing and adaptive filtering

2-D iteratively reweighted least squares lattice algorithm and its application to defect detection in textured images

In this paper, a 2-D iteratively reweighted least squares lattice algorithm, which is robust to the outliers, is introduced and is applied to defect detection problem in textured images. First, the philosophy of using different optimization functions that results in weighted least squares solution in the theory of 1-D robust regression is extended to 2-D. Then a new algorithm is derived which combines 2-D robust regression concepts with the 2-D recursive least squares lattice algorithm. With this approach, whatever the probability distribution of the prediction error may be, small weights are assigned to the outliers so that the least squares algorithm will be less sensitive to the outliers. Implementation of the proposed iteratively reweighted least squares lattice algorithm to the problem of defect detection in textured images is then considered. The performance evaluation, in terms of defect detection rate, demonstrates the importance of the proposed algorithm in reducing the effect of the outliers that generally correspond to false alarms in classification of textures as defective or nondefective