Most of the recent classification methods require tuning of the hyper-parameters, such as the kernel function parameter and the regularization parameter. Cross-validation or the leave-one-out method is often used for the tuning, however their computational costs are much higher than that of obtaining a classifier. Quadratically constrained maximum a posteriori (QCMAP) classifiers, which are based on the Bayes classification rule, do not have the regularization parameter, and exhibit higher classification accuracy than support vector machine (SVM). In this paper, we propose a multiple kernel learning (MKL) for QCMAP to tune the kernel parameter automatically and improve the classification performance. By introducing MKL, QCMAP has no parameter to be tuned. Experiments show that the proposed classifier has comparable or higher classification performance than conventional MKL classifiers.

We propose a theory of general frame multiresolution analysis (GFMRA) which generalizes both the theory of multiresolution analysis based on an affine orthonormal basis and the theory of frame multiresolution analysis based on an affine frame to a general frame. We also discuss the problem of perfectly representing a function by using a wavelet frame which is not limited to being of affine type. We call it a "generalized affine wavelet frame." We then characterize the GFMRA and provide the necessary and sufficient conditions for the existence of a generalized affine wavelet frame.

In learning of feed-forward neural networks, so-called 'training error' is often minimized. This is, however, not related to the generalization capability which is one of the major goals in the learning. It can be interpreted as a substitute for another learning which considers the generalization capability. Admissibility is a concept to discuss whether a learning can be a substitute for another learning. In this paper, we discuss the case where the learning which minimizes a training error is used as a substitute for the projection learning, which considers the generalization capability, in the presence of noise. Moreover, we give a method for choosing a training set which satisfies the admissibility.

We propose concepts of Paley-Wiener multiresolution analysis and Paley-Wiener wavelet frame based on general, not limited to dyadic, dilations of functions. Such a wavelet frame is an extension both of the Shannon wavelet basis and the Journe-Meyer wavelet basis. A concept of "natural" Paley-Wiener wavelet frame is also proposed to clarify whether a Paley-Wiener wavelet frame can naturally express functions from the point of view of the multiresolution analysis. A method of constructing a natural Paley-Wiener wavelet frame is given. By using this method, illustrative examples of Paley-Wiener wavelet frames with general scales are provided. Finally, we show that functions can be more efficiently expressed by using a Paley-Wiener wavelet frame with general scales.

We propose a moving picture coding by lapped transform and an edge adaptive deblocking filter to reduce the blocking distortion. We apply subband coding (SBC) with lapped transform (LT) and zero pruning set partitioning in hierarchical trees (zpSPIHT) to encode the difference picture. Effective coding using zpSPIHT was achieved by quantizing and pruning the quantized zeros. The blocking distortion caused by block motion compensated prediction is reduced by an edge adaptive deblocking filter. Since the original edges can be detected precisely at the reference picture, an edge adaptive deblocking filter on the predicted picture is very effective. Experimental results show that blocking distortion has been visually reduced at very low bit rate coding and better PSNRs of about 1.0 dB was achieved.

In this paper, the theory and the design of a new class of orthogonal transforms are presented. The novel transform is derived from a correlation matrix in which an arbitrary orthonormal system is embedded. By embedding an orthonormal system designed empirically, we obtain the transform that is not only adapted for perceptual information but also possess statistical property like the Karhunen-Loeve transform. Our main motivation is the application in block-based adaptive transform coding of images. We show a design example of the transform, which is adapted for directionality such as edges and lines. Using this transform, we perform orientation adaptive coding. Experimental results show that image coding using the transform is effective in rate-distortion sense and subjective quality.

Bandpass filters (BPFs) are very important to extract target signals and eliminate noise from the received signals. A BPF of which frequency characteristics is a sum of Gaussian functions is called the Gaussian mixture BPF (GMBPF). In this research, we propose to implement the GMBPF approximately by the sum of several frequency components of the sliding Fourier transform (SFT) or the attenuated SFT (ASFT). Because a component of the SFT/ASFT can be approximately realized using the finite impulse response (FIR) recursive filters, its calculation complexity does not depend on the length of the impulse response. The property makes GMBPF ideal for narrow bandpass filtering applications. We conducted experiments to demonstrate the advantages of the proposed GMBPF over FIR filters designed by a MATLAB function with regard to the computational complexity.

We propose a set of new algorithms for linear programming. These algorithms are derived by accelerating the method of averaged convex projections for linear inequalities. We provide strict proofs for the convergence of our algorithms. The algorithms are so simple that they can be calculated by super-parallel processing. To this effect, we propose networks for implementing the algorithms. Furthermore, we provide illustrative examples to demonstrate the capability of our algorithms.

A novel class of time-varying subband transforms and its application in image coding are introduced. We construct the framework in which an analysis subband transform is chosen from a given set of analysis transforms and perfect reconstruction is achieved. To this end, we suggest the reconstruction method from the transformed coefficients by applying the theory of convex projections (POCS). We introduce convex sets for perfect reconstruction from the transformed vector. We further propose other convex sets which assure smoothness of plane regions for image coding applications. We show several image coding examples. The proposed coding method is an extension of conventional one with multiple block-based transforms. At each time instance (block), the transform to be applied is chosen from a given set of orthogonal subband transforms according to a certain criterion. Experimental results show that the use of multiple subband transforms leads to the improvement of coding performance compared to the use of single transform even though there exists side information.