International Journal of Wavelets, Multiresolution and Information Processing

In this paper, a novel statistical test is introduced to compare two locally stationary time series. The proposed approach is a Wald test considering time-varying autoregressive modeling and function projections in adequate spaces. The covariance structure of the innovations may be also time-varying. In order to obtain function estimators for the time-varying autoregressive parameters, we consider function expansions in splines and wavelet bases. Simulation studies provide evidence that the proposed test has a good performance. We also assess its usefulness when applied to a financial time series.

In many image analysis applications, such as image retrieval, the shape of an object is of primary importance. In this paper, a new shape descriptor, namely the Normalized Wavelet Descriptor (NWD), which is a generalization and extension of the Wavelet Descriptor (WD), is introduced. The NWD is compared to the Fourier Descriptor (FD), which in image retrieval experiments conducted by Zhang and Lu, outperformed even the Curvature Scale Space Descriptor (CSSD). Image retrieval experiments have been conducted using a dataset containing 2D-contours of 1400 objects extracted from the standard MPEG7 database. For the chosen dataset, our experimental results show that the NWD outperforms the FD.

Stationary wavelet transform is an efficient algorithm for remote sensing image fusion. In this paper, we investigate the effects of orthogonal/biorthogonal filters and decomposition depth on using stationary wavelet analysis for fusion. Spectral discrepancy and spatial distortion are used as quality measures. Empirical results lead to some recommendations on the wavelet filter parameters for use in remote sensing image fusion applications.

A new approach for designing the Biorthogonal Wavelet Filter Bank (BWFB) for the purpose of image compression is presented in this paper. The approach is broken into two steps. First, an optimal filter bank is designed in the theoretical sense, based on Vaidyanathan's coding gain criterion in the SubBand Coding (SBC) system. Then, the above filter bank is optimized based on the criterion of Peak Signal-to-Noise Ratio (PSNR) in the JPEG2000 image compression system, resulting in a BWFB in practical application sense. With the approach, a series of BWFBs for a specific class of applications related to image compression, such as gray-level images, can be quickly designed. Here, new 7/5 BWFBs are presented based on the above approach for image compression applications. Experiments show that the 7/5 BWFBs not only have excellent compression performance, but also easy computation and are more suitable for VLSI hardware implementations. They perform equally well with respect to 7/5 filters in the JPEG2000 standard.

Construction of rotationally invariant 2D wavelets is important in image processing, but is difficult. In this paper, the discrete form of a 2D rotationally invariant wavelet is constructed by back-projection from a 1D symmetrical wavelet. Such rotationally invariant 2D wavelets allow effective edge detection in any direction. These wavelets are combined with the 2D directional wavelets for the use in non-maximum suppression edge detection. The resulting binary edges are characterized by finer contours, differential detection characteristics and noise robustness compared to other edge detectors in various test images. In particular, where fine binary edges in noisy images are required, this novel approach compares favorably to the classical methods of Canny and Mallat with detection of more edges thanks to the implicit denoising properties and the full rotational invariance of the method.

In this paper, we present a new class of iterative regularization methods in the setting of Besov spaces, which can be seen as generalizations of J. Xu's method. By incorporating translation invariant wavelet transform, minimizers of the new methods can be understood as the alternative to translation invariant wavelet shrinkage with weight that is dependent on the wavelet decomposition scale and the Besov smooth order. And we generalize the iterative regularization methods to a new class of nonlinear inverse scale spaces with scale and Besov smooth order dependent weight. The numerical results show an excellent denoising effect and improvement over J. Xu's method.

This paper presents tight wavelet frames with two compactly supported symmetric generators of more than one vanishing moments in the Unitary Extension Principle. We determine all possible free tension parameters of the quasi-interpolatory subdivision masks whose corresponding refinable functions guarantee our wavelet frame. In order to reduce shift variance of the standard discrete wavelet transform, we use the three times oversampling filter bank and eventually obtain a ternary (low, middle, high) frequency scale. In applications to signal/image denoising and erasure recovery, the results demonstrate reduced shift variance and better performance of our wavelet frame than the usual wavelet systems such as Daubechies wavelets.

We consider irregular sampling in shift invariant spaces V of higher dimensions. The problem that we address is: find ε so that given perturbations (λ_k) satisfying sup|λ_k| < ε, we can reconstruct an arbitrary function f of V as a Riesz basis expansions from its irregular sample values f(k + λ_k). A framework for dealing with this problem is outlined and in which one can explicitly calculate sufficient limits ε for the reconstruction. We show how it works in two concrete situations.