International Journal of Wavelets, Multiresolution and Information Processing

For the three-layer artificial neural networks with trigonometric weights coefficients, the upper bound and lower bound of approximating 2π-periodic pth-order Lebesgue integrable functions are obtained in this paper. Theorems we obtained provide explicit equational representations of these approximating networks, the specification for their numbers of hidden-layer units, the lower bound estimation of approximation, and the essential order of approximation. The obtained results not only characterize the intrinsic property of approximation of neural networks, but also uncover the implicit relationship between the precision (speed) and the number of hidden neurons of neural networks.

In this paper, we show that the space of continuous wavelet transform is a reproducing kernel Hilbert space based on the fundamental theorem of linear transform. An admissible wavelet is got by convolution computation which is made into continuous wavelet transform. By the theory of reproducing kernel we can discuss correlative properties of image space of wavelet transform, which provide theoretic frame for us to study image space of the general wavelet transform.

Secret sharing is an efficient method for transmitting the image securely. This paper proposes an efficient secret sharing scheme for secret image. The protocol allows each participant to share a secret gray image with the rest of participants. In our scheme, a secret digital image is divided into n pieces, which are further distributed into n participants. The secret digital image can be reconstructed if and only if r or more legal participants cooperate together. These schemes have no pixel expansion. It is general in nature and can be applied on any image size. The proposed scheme is based on the chaotic map and the Chinese Remainder theorem. The security of the scheme is analyzed and the protocol is proven to be secure and be able to resist statistic and exhaustive attacks.

Intensity inhomogeneity is a common phenomenon in real-world images and may cause many difficulties in image segmentation. To overcome these difficulties, we propose a new active contour model combining the GVF flow and the directional information about edge location. On one hand, we incorporate the GVF flow into the proposed model to segment the images with intensity inhomogeneity efficiently. On the other hand, we construct an alignment term with the directional information to achieve sub-pixel accuracy and relax the placement of the initial curve. Moreover, a regularization term is also included in our model to ensure accurate computation and avoid time-consuming re-initializations. Experimental results on several synthetic and real images show that the proposed model is effective.

In this paper, a novel super-resolution method for hyperspectral imagery is proposed by using complex ridgelet transform. A Radon transform is first applied to each band image of a datacube to be enhanced to obtain the Radon slices, and then a 1D dual-tree complex wavelet transform is conducted along each Radon slice to generate coefficients of the complex ridgelet transform. The ordinary ridgelet transform or the finite ridgelet transform (FRIT), however, uses the 1D scalar wavelet transform instead of the dual-tree complex wavelet transform along each Radon slice. The reason why the dual-tree complex wavelet is adopted in this paper is because it has the property of approximate shift invariance, which is very important in image super-resolution. Experiments are conducted in this paper to demonstrate the advantages of the proposed method over the wavelet super-resolution, the FRIT image fusion, and the principal component analysis fusion.

In this paper, a non-tensor product method for constructing three-dimension (3D) mother wavelets by back-projecting two dimension (2D) mother wavelets is presented. We have proved that if a 2D mother wavelet satisfies certain conditions, the back-projection of the 2D mother wavelet is a 3D mother wavelet. And the construction instances of 3D Mexican-hat wavelet and 3D Meyer wavelet are given. These examples imply that we can get some new 3D mother wavelets from known 1D or 2D mother wavelets by using back-projecting method. This method inaugurates a new approach for constructing non-tensor product 3D wavelet. In addition, the non-tensor product 3D Mexican-hat wavelet is used for detecting the edge of two 3D images in our experimental section. Compared with the Mallat's maximum wavelet module approach which uses 3D directional wavelets, experimental results show it can obtain better outcome especial for the edge which the orientation is not along the coordinate axis. Furthermore, the edge is more fine, and the computational cost is much smaller. The non-tensor product mother wavelets constructed by using the method of this paper also can be widely used for compression, filtering and denoising of 3D images.

Research on refinable functions in wavelet theory is mostly focused to localized functions. However it is known, that polynomial functions are refinable, too. In our paper we investigate on conversions between refinement masks and polynomials and their uniqueness.

We present a new criterion based on instantaneous frequency (IF) to distinguish mono-components (MCs). We first notice that the "offset of local extremum" caused by low-frequency envelope is often significant on envelope extraction, which determines the calculation of IF for MCs. We estimate the upper and lower bounds of the offset for a general family of signals. Conducted by the offset estimation, we propose a direct and effective algorithm to calculate IF. Our algorithm, which is based on an empirical pursuit of knots and natural splines, provides an accurate estimation of the envelope and derives a well-behaved IF. A theoretical explanation for the good approximation of proposed envelope is also stated. Experiment results show the fast convergence of our algorithm, which leads to a reliable IF and local mean to provide a flexible criterion for MC classification. We emphasize that it is important to pursue a certain balance among different requirements to define MC depending on specific applications.

Varying illumination is a huge challenge of face recognition. The variation caused by varying illumination in the face appearance can be much larger than the variation caused by personal identity. The high frequency signal component in image represents the detail characteristic of the face, and for the reason of being influenced scarcely by varying illumination, this signal component can be used as illumination invariance features in face recognition. However, the definition of the high frequency signal component is blurry, and it is impossible to separate this component from the face image exactly. Because of using the different decomposition methods and different decomposition parameters, high frequency component has been dispersed in decomposed detail images that characterize themselves by containing different scale frequency signal component. This paper proposes a framework to fuse that high frequency signal components in multi-scale detail images using adaptive weight. This novel framework is an open structure, and any method of getting illumination invariance feature can be applied on this framework. The experiment based on three open face databases shows the framework proposed by this paper can get remarkable performance.

Multidimensional scaling (MDS) has been applied in many applications such as dimensionality reduction and data mining. However, one of the drawbacks of MDS is that it is only defined on "training" data without clear extension to out-of-sample points. Furthermore, since that MDS is based on Euclidean distance (which is a dissimilarity measure), it is not suitable for detecting the nonlinear manifold structure embedded in the similarities between data points. In this paper, we extend MDS to the correlation measure space, named correlation MDS (CMDS). CMDS employs an explicit nonlinear mapping between the input and reduced space while MDS using an implicit mapping. As a result, CMDS can directly provide prediction for new samples. In addition, correlation is a similarity measure, CMDS method can effectively capture the nonlinear manifold structure of data embedded in the similarities between the data points. Theoretical analysis also shows that CMDS has some properties similar to kernel methods and can be extended to feature space. The effectiveness of the approach provided in this paper are demonstrated by extensive experiments on various datasets, in comparison with serval existing algorithms.