In this paper, we propose a normalization method dividing the gradient vector by the sum of the diagonal and two adjoining elements of the matrix expressing the correlation between the components of the discrete Fourier transform (DFT) of the reference signal used for the identification of unknown system. The proposed method can thereby improve the estimation speed of coefficients of adaptive filter.

This paper presents a new hybrid speed function needed to perform image segmentation within the level-set framework. The proposed speed function uses both the boundary and region information of objects to achieve robust and accurate segmentation results. This speed function provides a general form that incorporates the robust alignment term as a part of the driving force for the proper edge direction of an active contour, an active region term derived from the region partition scheme, and the smoothing term for regularization. First, we use an external force for active contours as the Gradient Vector Flow field. This is computed as the diffusion of gradient vectors of a gray level edge map derived from an image. Second, we partition the image domain by progressively fitting statistical models to the intensity of each region. Here we adopt two Gaussian distributions to model the intensity distribution of the inside and outside of the evolving curve partitioning the image domain. Third, we use the active contour model that has the computation of geodesics or minimal distance curves, which allows stable boundary detection when the model's gradients suffer from large variations including gaps or noise. Finally, we test the accuracy and robustness of the proposed method for various medical images. Experimental results show that our method can properly segment low contrast, complex images.

The estimation of the point-spread function (PSF) is one of very important and indispensable tasks for the practical image restoration. Especially, for the motion blur, various PSF estimation algorithms have been developed so far. However, a majority of them becomes useless in the low blurred signal-to-noise ratio (BSNR) environment. This paper describes a new robust PSF estimation algorithm based on Hough transform concerning gradient vectors, which can accurately and robustly estimate the motion blur PSF even in low BSNR case. The effectiveness and validity of the proposed algorithm are verified by applying it to the PSF estimation and the image restoration for noisy and motion blurred images.

The inherent simplicity of the LMS (Least Mean Square) Algorithm has lead to its wide usage. However, it is well known that high speed convergence and low final misadjustment cannot be realized simultaneously by the conventional LMS method. To overcome this trade-off problem, a new adaptive algorithm using Multiple ADF's (Adaptive Digital Filters) is proposed. The proposed algorithm modifies coefficients using multiple gradient vectors of the squared error, which are computed at different points on the performance surface. First, the proposed algorithm using 2 ADF's is discussed. Simulation results show that both high speed convergence and low final misadjustment can be realized. The computation time of this proposed algorithm is nearly as much as that of LMS if parallel processing techniques are used. Moreover, the proposed algorithm using more than 2 ADF's is discussed. It is understood that if more than 2 ADF's are used, further improvement in the convergence speed in not realized, but a reduction of the final misadjustment and an improvement in the stability are realized. Finally, a method which can improve the convergence property in the presence of correlated input is discussed. It is indicated that using priori knowledge and matrix transformation, the convergence property is quite improved even when a strongly correlated signal input is applied.