A novel time-series relationship among four consecutive real-valued single-tone sinusoid samples is proposed based on their linear prediction property. In order to achieve unbiased frequency estimates for a real sinusoid in white noise, based on the proposed four-point time-series relationship, a constrained least squares cost function is minimized based on the unit-norm principle. Closed-form expressions for the variance and the asymptotic expression for the variance of the proposed frequency estimator are derived, facilitating a theoretical performance comparison with the existing three-point counterpart, called as the reformed Pisarenko harmonic decomposer (RPHD). The region of performance advantage of the proposed four-point based constrained least squares frequency estimator over the RPHD is also discussed. Computer simulations are conducted to support our theoretical development and to compare the proposed estimator performance with the RPHD as well as the Cramer-Rao lower bound (CRLB).

In this paper, we propose a localization algorithm that uses the time difference of arrival (TDOA) and the angle of arrival (AOA). The problem is formulated in a hybrid linear matrix equation. TDOA and AOA measurements are used for estimating the target's position. Although it is known that the accuracy of TDOA based localization is superior to that of AOA based localization, TDOA based localization has a poor vertical accuracy in deteriorated geometrical conditions. This paper, therefore, proposes a localization algorithm in which the vertical position is estimated by AOA measurements and the horizontal position is estimated by TDOA measurement in order to achieve high location accuracy in three dimensions. In addition, the Lagrange multipliers are obtained efficiently and robustly. The simulation analysis shows that the proposed constrained linear squares (CLS) algorithm is an unbiased estimator, and that it approaches the Cramer-Rao lower bound (CRLB) when the measurement noise and the sensor's location errors are sufficiently small.

In this paper, we propose a spatially adaptive gradient-projection algorithm for the H.264 video coding standard to remove coding artifacts using local statistics. A hybrid method combining a new weighted constrained least squares (WCLS) approach and the projection onto convex sets (POCS) approach is introduced, where weighting components are determined on the basis of the human visual system (HVS) and projection set is defined by the difference between adjacent pixels and the quantization index (QI). A new visual function is defined to determine the weighting matrices controlling the degree of global smoothness, and a projection set is used to obtain a solution satisfying local smoothing constraints, so that the coding artifacts such as blocking and ringing artifacts can be simultaneously removed. The experimental results show the capability and efficiency of the proposed algorithm.

It is widely known that the family of projection filters includes the generalized inverse filter, and that the family of parametric projection filters includes parametric generalized projection filters. However, relations between the family of parametric projection filters and constrained least squares filters are not sufficiently clarified. In this paper, we consider relations between parameter estimation and image restoration by these families. As a result, we show that the restored image by the family of parametric projection filters is a maximum penalized likelihood estimator, and that it agrees with the restored image by constrained least squares filter under some suitable conditions.

Space-variant approaches subject to local image characteristics are useful in practical image restoration because many natural images are nonstationary. Motivated by the success of denoising approaches in the wavelet domain, we propose a region-adaptive restoration approach which adopts a wavelet denoising technique in flat regions after an under-regularized constrained least squares restoration. Experimental results verify that this approach not only improves image quality in mean square error but also contributes to ringing reduction.

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.