A fast regularization parameter selection for regularly sampled 2D inputs

A fast method of computing the regularization parameter is proposed for the case where the radial basis function network is used for image interpolation by putting the regularly sampled pixel as the two-dimensional input and the pixel value as the output. A performance index is minimized by using the steepest descent method to find the optimal regularization parameter. The choice of regularly sampled two-dimensional input data allows a significant reduction in computation time with the properties of a Kronecker product.     

Image interpolation for progressive transmission by using radialbasis function networks

Investigates the application of a radial basis function network (RBFN) to hierarchical image coding for progressive transmission. The RBFN is then used to generate an interpolated image from the subsampled version. An efficient method of computing the network parameters is developed for reduction in computational and memory requirements. The coding method does not suffer from problems of blocking effect and can produce the coarsest image quickly. Quantization error effects introduced at one stage are considered in decoding images at the following stages, thus allowing lossless progressive transmission.     

Interpolation capability of the periodic radial basis function network

A periodic radial basis function (RBF) network based on the regularisation approach is proposed. The periodic RBF network can eliminate the Gibbs phenomenon observed in the conventional RBF network at the boundary of the data. For the evaluation of the interpolation capability, the frequency response of the periodic RBF network is analysed. It is then theoretically shown that the frequency response is asymptotically equivalent to the ideal sinc interpolation, and that the RBF interpolation is closer to the ideal sinc interpolation than the cubic spline and Lanczos interpolations     

A real-time learning algorithm for a multilayered neural networkbased on the extended Kalman filter

A novel real-time learning algorithm for a multilayered neural network is derived from the extended Kalman filter (EKF). Since this EKF-based learning algorithm approximately gives the minimum variance estimate of the linkweights, the convergence performance is improved in comparison with the backwards error propagation algorithm using the steepest descent techniques. Furthermore, tuning parameters which crucially govern the convergence properties are not included, which makes its application easier. Simulation results for the XOR and parity problems are provided     

A nonlinear regulator design in the presence of systemuncertainties using multilayered neural network

The authors present a novel nonlinear regulator design method that integrates linear optimal control techniques and nonlinear neural network learning methods. Multilayered neural networks are used to add nonlinear effects to the linear optimal regulator (LOR). The regulator can compensate for nonlinear system uncertainties that are not considered in the LOR design and can tolerate a wider range of uncertainties than the LOR alone. The salient feature of the regulator is that the control performance is much improved by using a priori knowledge of the plant dynamics as the system equation and the corresponding LOR. Computer simulations are performed to show the applicability and the limitations of the regulator.     

A nonlinear adaptive estimation method based on local approximation

One of the most important problems in signal processing is to estimate the output for a query from the input/output (I/O) data seen so far. This paper presents a nonlinear adaptive estimation method based on the n-nearest neighbor approach. In this method, observed I/O data are stored in a database in the form of a X-dimensional binary digital search trie (k-D trie), and a nonlinear local model to answer each query is derived based on regularization theory. The database contents are efficiently time updated to follow nonstationary data. A storage procedure allowing a simple and efficient update is developed for reduction in processing time and storage requirement. The effectiveness of the proposed method is demonstrated with both simulation data and real speech signals     

Convergence analysis of the adaptive lattice filter for a mixed Gaussian input sequence

The convergence performance of the adaptive lattice filter (ALF) using the stochastic gradient algorithm is measured by the convergence speed and estimated error variance of the PARCOR coefficient. The convergence properties of the ALF are analysed when the filter input has a Gaussian mixture distribution. First, theoretical expressions for the convergence rate and asymptotic error variance of the PARCOR coefficient are derived, and then the theoretical expressions are compared for single and mixed Gaussian input sequences. It is shown that the convergence performance of the ALF improves as the distribution of the input signal approaches a single Gaussian distribution.     

Online recognition of handwritten Hiragana characters based upon acomplex autoregressive model

An online recognition method for handwritten Hiragana characters is developed based upon a complex AR model. The time delay of the AR model is enlarged so that global attributes of handwritten characters are well incorporated into the model, and a character segmentation technique is developed for performance improvement. A good recognition score has been obtained for two different writers     

Convergence properties of an adaptive lattice filter exploitingnonlinear dynamics of a biochemical reaction system

An adaptive lattice filter (ALF) which computes the PARCOR coefficients through a cyclic enzyme system has recently been developed by the author. Using nonlinear dynamics of the cyclic enzyme system, the ALF becomes robust against impulsive noise, and the stability of the estimated AR model can be ensured. The convergence properties of the ALF are studied. First, a theoretical expression for the asymptotic error variance of the PARCOR coefficient is derived. Simulation results are presented, and the theoretical and simulated values show a very good match. Next, the convergence speed of the proposed ALF is compared with that of the simplified ALF. The step sizes are then determined by using the above theoretical expression such that both ALF's achieve the same error variance in steady states. The results show that the proposed ALF has excellent convergence properties than the simplified one     

Hierarchical image coding via cerebellar model arithmetic computers

A hierarchical coding system for progressive image transmission that uses the generalization and learning capability of CMAC (cerebellar model arithmetic computer or cerebellar model articulation controller) is described. Each encoder and decoder includes a set of CMACs having different widths of generalization region. A CMAC with a wider generalization region is used to learn a lower frequency component of the original image. The training signals for each CMAC are progressively transmitted to a decoder. Compression is achieved by decreasing the number of training signals for CMAC with a wider generalization region, and by making quantization intervals wider for CMAC with a smaller generalization region. CMACs in the decoder are trained on the training signals to be transmitted. The output is recursively added to the other so that the quality of image reconstruction is gradually improved. The proposed method, unlike the conventional hierarchical coding methods, uses no filtering technique in both decimation and interpolation processes, and has the following advantages: (i) it does not suffer from problems of blocking effect; (ii) the computation includes no multiplication; (iii) the coarsest reconstructed image is quickly produced; (iv) the total number of transmitted data is equal to the number of the original image pixels; (v) all the reconstructed images are equal to the original image in size; (vi) quantization errors introduced at one level can be taken into account at the next level, allowing lossless progressive image transmission.