International Journal of Wavelets, Multiresolution and Information Processing

In earthquake-resistant design of structures, for certain structural configurations and conditions, it is necessary to use accelerograms for dynamic analysis. Accelerograms are also needed to simulate the effects of earthquakes on a building structure in the laboratory. A new method of generating artificial earthquake accelerograms is presented through adroit integration of neural networks and wavelets. A counterpropagation (CPN) neural network model is developed for generating artificial accelerograms from any given design spectrum such as the International Building Code (IBC) design spectrum. Using the IBC design spectrum as network input means an accelerogram may be generated for any geographic location regardless of whether earthquake records exist for that particular location or not. In order to improve the efficiency of the model, the CPN network is modified with the addition of the wavelet transform as a data compression tool to create a new CPN-wavelet network. The proposed CPN-wavelet model is trained using 20 sets of accelerograms and tested with additional five sets of accelerograms available from the U.S. Geological Survey. Given the limited set of training data, the result is quite remarkable.

A Generalized Multiresolution Analysis (GMRA) associated with a wavelet is a sequence of nested subspaces of the function space ℒ²(ℝ), with specific properties, and arranged in such a way that each of the subspaces corresponds to a scale 2^m over all time-shifts n. These subspaces can be expressed in terms of a generating-wandering subspace — of the dyadic-scaling operator — spanned by orthonormal wavelet-functions — generated from the wavelet. In this paper we show that a GMRA can also be expressed in terms of subspaces for each time-shift n over all scales 2^m. This is achieved by means of "elementary" reducing subspaces of the dyadic-scaling operator. Consequently, Time-Shifts GMRA associated with wavelets, as well as "sub-GMRA" associated with "sub-wavelets" will then be introduced.

Image compression will always reduce the image fidelity, especially when the image is compressed at lower bit rates, which cannot be tolerated, especially in medical field. But compression is necessary due to the constraint of transmission bandwidth and the limited storage capacity. In this paper, the bad compression performance of the new JPEG2000 and the more conventional JPEG are studied. Besides, using the common objective measures such as Peak Signal-to-Noise Ratio (PSNR) and Root Mean Square Error (RMSE) as the standard quality measurements, we focus more on the statistical and frequency measures as the image characteristics evaluation. Four types of medical modalities are used: X-ray, Magnetic Resonance Imaging (MRI), Ultrasound and Computed Tomography (CT). From these various measurements, we found the general acceptance compression bit rate for each of the medical modalities.

We present a preliminary investigation of compression of segmented 3D seismic volumes for the rendering purposes. Promising results are obtained on the base of 3D discrete cosine transforms followed by the SPIHT coding scheme. An accelerated version of the algorithm combines 1D discrete cosine transform in vertical direction with the 2D wavelet transform of horizontal slices. In this case the SPIHT scheme is used for coding the mixed sets of cosine-wavelet coefficients.

This paper evaluates the efficacy of directional information of wavelet multi-resolution decomposition to enhance histogram-based classification of human gestures. The gestures are represented by spatio-temporal templates. This template collapses spatial and temporal components of motion into a static gray scale image such that no explicit sequence matching or temporal analysis is required, and it reduces the dimensionality to represent motion. These templates are modified to be invariant to translation and scale. Two-dimensional, 3-level dyadic wavelet transforms have been applied on the template resulting in one lowpass sub-image and nine highpass directional sub-images. Histograms of wavelet coefficients at different scales are used for classification purposes. The experiments demonstrate that while the statistical properties of the template provide high level of classification accuracy, the global detail activity available in highpass decompositions significantly improve the classification accuracy.

This paper presents a new method to monitor machining processes based on a combination of discrete wavelet transform (DWT) and statistical process control (SPC), called a multi-scale statistical approach. First, DWT is applied to decompose the sensor signal onto different scales. Next, the detection limits are formed for each decomposed signal components, called the sub-signals, using Shewhart control charts. Finally, by inverse wavelet transform of the threshold crossing points of the sub-signals, malfunctions can be detected. Based on a test on the tool condition monitoring in turning using acoustic emission (AE) signal, it is shown that the new method is effective and robust.

In this paper, we conduct a series of experiments to evaluate the translation invariant property of a set of discrete wavelet features in a face graph. Using local-area power spectrum estimation based on discrete wavelet transform, we compute a feature vector that possesses both efficient space-frequency structure and translation invariant properties.