International Journal of Wavelets, Multiresolution and Information Processing

We address the problem of similarity search in large multi-dimensional time sequence databases. There has been a lot of attention in similarity search in time sequence databases. However, most of the previous work on time sequences focused on one-dimensional sequences. Many applications such as multimedia databases or weather databases, however, need to handle multi-dimensional time sequences. In this paper, we extend our previous work on the similarity search by considering query types in multi-dimensional time sequence databases and more intensive experimental results that were not reported in the previous paper are illustrated. The proposed method can efficiently reduce the search space and guarantees no false dismissals.

While constructing a dyadic wavelet set through an approach which is purely set-theoretic, Ionascu observed that a dyadic one-dimensional wavelet set W gives rise to a specific measurable, bijective, piecewise increasing selfmap on [0, 1) and termed it to be a wavelet induced isomorphism. Further, he found that such maps provide wavelet sets which, in turn, characterize wavelet sets. In this paper, we consider two-interval, three-interval and symmetric four-interval wavelet sets and determine their wavelet induced isomorphisms. Also, fixed point sets of are determined for these wavelet sets.

Feature extraction plays an important role in brain-computer interface (BCI) systems. In order to characterize the motor imagery related rhythm and higher-order statistics information contained within the EEG signals, a novel feature extraction method based on harmonic wavelet transform and bispectrum is developed and applied to the recognition of right and left motor imageries for developing EEG-based BCI systems. The experimental results on the Graz BCI data set have shown that the separability of the two classes features extracted by the proposed method is notable. Its performance was evaluated by a linear discriminant analysis (LDA) classifier. The recognition accuracy of 90% was obtained. The recognition results have demonstrated the effectiveness of the proposed method. This method provides an effective way for EEG feature extraction in BCI system.

A scale-adaptive edge detection scheme based on wavelet transform is proposed in this paper. This scheme incorporates the edge information in multiple scales of the wavelet domain, and it not only locates the position of each edge point, but also estimates its amplitude and identifies its singularity type, namely, step edge and ridge edge. Moreover, for a ridge edge point, the proposed scheme could estimate the width of the ridge. Unlike traditional edge detectors, this method adaptively selects two optimal scales for each edge point to locate it and estimate its direction. As a result, better performances in localization and edge direction estimation are achieved. Experiments on both synthetic and real images demonstrate the effectiveness of the proposed method.

Due to the large volume required for medical images for transmission and archiving purposes, the compression of medical images is known as one of the main concepts of medical image processing. Lossless compression methods have the drawback of a low compression ratio. In contrast, lossy methods have a higher compression ratio and suffer from lower quality of the reconstructed images in the receiver. Recently, some selective compression methods have been proposed in which the main image is divided into two separate regions: Region of Interest (ROI), which should be compressed in a lossless manner, and Region of Background (ROB), which is compressed in a lossy manner with a lower quality. In this research, we introduce a new selective compression method to compress 3D brain MR images. To this aim, we design an adaptive mesh on the first slice and estimate the gray levels of the next slices by computing the mesh element's deformations. After computing the residual image, which is the difference between the main image and the estimated one, we transform it to the wavelet domain using a region-based discrete wavelet transform (RBDWT). Finally, the wavelet coefficients are coded by an object-based SPIHT coder.

We remove noise from images by solving a parameter depending variational problem. The choice of the parameter is essential for the success of the approach, and in order to compute a solution, the problem must be discretized. It is commonly known that the parameter choice according to the H-curve criterion performs well in combination with discretizations derived from a dyadic orthonormal wavelet basis. However, the concept of orthonormal wavelet bases is restrictive and bears limitations. In order to have a more flexible tool, we construct new nondyadic wavelet bi-frames by convolving scalar wavelets with wavelet vectors. We discretize the variational problem by these new bi-frames, and we verify that the H-curve method performs well for this much more flexible discretization technique.

Navigation and guidance of an autonomous vehicle require determination of the position and velocity of the vehicle. Therefore, fusing the Inertial Navigation System (INS) and Global Positioning System (GPS) is important. Various methods have been applied to smooth and predict the INS and GPS errors. Recently, wavelet de-noising methodologies have been applied to improve the accuracy and reliability of the GPS/INS system. In this work, analysis of real data to identify the optimal wavelet filter for each GPS and INS component for high quality error estimation is presented. A comprehensive comparison of various wavelet thresholding selections with different level of decomposition is conducted to study the effect on GPS/INS error estimation while maintaining the original features of the signal. Results show that while some wavelet filters and thresholding selection algorithms perform better than others on each of the GPS and INS components, no specific parameter selection perform uniformly better than others.

In the current methods of ROI coding methods, after all the pixels have been scanned in order and the ROI is distinguished, an ROI mask is generated. So, to support a dynamic Region-of-Interest (ROI) in JPEG2000, fast ROI mask generation is needed. Our method scans 4 pixels of the corners in one code block and then, based on the information, scans the edges from the corners to get the boundaries of the ROI and background. This information consists of distributed information about the ROI and two coordinates of the pixels, which are the points where the edges and boundaries meet. This information is transmitted to the encoder and supported for fast ROI mask generation. There are no great differences between the proposed method and the existing methods in terms of quality, but the proposed method showed superiority in speed.

A new Bregman iterative regularization method is introduced for wavelet-based image deblurring. By using a suitable sequence of penalty parameters, we solve the issue of solvability of minimization problems arising in each step of the iterative procedure. Moreover, we give a projection-based algorithm to compute the solution. The convergence of the algorithm is also stated. The procedure is very fast and easy to implement. We also show numerical results of image deblurring using the algorithm.