Recently, a great deal of effort has been devoted to the design problem of "constrained least squares M-D FIR filter" because a significant improvement of the squared error is expected by a slight relaxation of the minimax error condition. Unfortunately, no design method has been reported, which has some theoretical guarantee of the convergence to the optimal solution. In this paper, we propose a class of novel design methods of "constrained least squares M-D FIR filter. " The most remarkable feature is that all of the proposed methods have theoretical guarantees of convergences to the unique optimal solution under any consistent set of prescribed maximal error conditions. The proposed methods are based on "convex projection techniques" that computes the metric projection onto the intersection of multiple closed convex sets in real Hilbert space. Moreover, some of the proposed methods can still be applied even for the problem with any inconsistent set of maximal error conditions. These lead to the unique optimal solution over the set of all filters that attain the least sum of squared distances to all constraint sets.

In the conventional sound field reproduction system with control of the transfer functions from the source to both ears of a listener, a slight shift of the ears caused by movement of the listener inevitably results in sound localization being different from that expected. In this paper, a method for reproducing a sound field by controlling the transfer function from the source to multiple points (called the "method of multiple-points control" hereafter) is applied to a sound reproduction system with the aim of expanding the area which can be controlled. The system is controlled so that the transfer functions from the input of the system to the multiple points adjacent to the original receiving points have the same desired transfer function. By placing the control points at appropriate intervals, a "zone of equalization" is formed. Based on a computer simulation, the intervals between control points is discussed. The configuration of the loundspeakers for sound reproduction is also discussed.

A complex fuzzy adaptive decision feedback equalizer based on the RLS algorithm is proposed. The proposed equalizer not only improves the performance but also reduces the computational complexity compared with the conventional complex fuzzy adaptive equalizers under the assumption of perfect knowledge of the linear and nonlinear channels.

The robust statistics has recently been adopted by the computer vision community. Various robust approaches in the computer vision research have been proposed in the last decade for analyzing the image motion from the image sequence. Because of the frequent violation of the Gaussian assumption of the noise and the motion discontinuities due to multiple motions, the motion estimates based on the straightforward approaches such as the least squares estimator and the regularization often produces unsatisfactory result. Robust estimation is a promising approach to deal with these problems because it recovers the intrinsic characteristics of the original data with the reduced sensitivity to the contamination. Several previous works exist and report some isolated results, but there has been no comprehensive analysis. In this paper robust approaches to the optical flow estimation based on the maximum likelihood estimators are proposed. To evaluate the performance of the M-estimators for estimating the optical flow, comparative studies are conducted for every possible combinations of the parameters of three types of M-estimators, two types of residuals, two methods of scale estimate, and two types of starting values. Comparative studies on synthetic data show the superiority of the M-estimator of redescending ψ-function using the starting value of least absolute residuals estimator using Huber scale iteration, in comparison with the other M-estimators and least squares estimator. Experimental results from the real image experiments also confirm that the proposed combinations of the M-estimators handle the contaminated data effectively and produce the better estimates than the least squares estimator or the least absolute residuals estimator.

The uncertainty involved in the gradient constraint for optical flow detection is often modeled as constant Gaussian noise added to the time-derivative of the image intensity. In this paper, we examine this modeling closely and investigate the error behavior by experiments. Our result indicates that the error depends on both the spatial derivatives and the image motion. We propose alternative uncertainty models based on our experiments. It is shown that the optical flow computation algorithms based on them can detect more accurate optical flow than the conventional least-squares method.

A non-invasive method is proposed to estimate the location of intracranial vascular disease using several sensors placed on the forehead. The advantage of this method over earlier measurements with a single ocular sensor is the abilty to localize the region of abnormal vascular tissue. A weighted least mean square procedure is applied to estimating the time difference between the sensor outputs using the phase distribution in the cross-spectrum. It is possible to estimate time differences shorter than sampling period. Computer simulation and clinical experiments demonstrate that a distance difference of around 20 times shorter than the wavelength can be obtained.

In identification of a finite impulse response (FIR) model using noise-corrupted input and output data, the least squares type of estimation schemes such as the ordinary least squares (LS), the corrected least squares (CLS) and the total least squares (TLS) method become often numerically unstable, when the true input signal to the system is strongly correlated. To overcome this ill-conditioned problem, we propose a regularized CLS estimation method by introducing multiple regularization parameters to minimize the mean squares error (MSE) of the regularized CLS estimate of the FIR model. The asymptotic MSE can be evaluated by considering the third and fourth order cross moments of the input and output measurement noises, and an analytical expression of the optimal regularization parameters minimizing the MSE is also clarified. Furthermore, an effective regularization algorithm is given by using the only accessible input-output data without using any true unknown parameters. The effectiveness of the proposed data-based regularization algorithm is demonstrated and compared with the ordinary LS, CLS and TLS estimates through numerical examples.

In this report, we propose a robust block adaptive digital filter (BADF) which can improve the accuracy of the estimated weights by averaging the adaptive weight vectors. We show that the improvement of the estimated weights is independent of the input signal correlation.

A new gradient type adaptive algorithm is proposed in this paper. It is formulated based on the least squares criteria while the conventional gradient algorithms are based on the least mean square criteria. The proposed algorithm has two variable parameters and by changing them we can adjust the characteristic of the algorithm from the RLS to the LMS depending on the environment. This capability of adjustment achieves the possibility of providing better solutions. However, not only it provides better solutions than the conventional algorithms under some conditions but also it provides a very interesting theoretical view point. It provides a unified view point of the adaptive algorithms including the conventional ones, i.e., the LMS or the RLS, as limited cases and it enables us to analyze the bounds for those algorithms.