Selected Wavelet Coefficients Research Articles

Representation of somatosensory evoked potentials using discrete wavelet transform.

Somatosensory evoked potentials (SEP) have been shown to be a useful tool in monitoring of the central nervous system (CNS) during anaesthesia. SEP analysis is usually performed by an experienced human operator. For automatic analysis, appropriate parameter extraction and signal representation methods are required. The aim of this work is to evaluate the discrete wavelet transform (DWT) as such a method for an SEP representation. Median nerve SEP were derived in 52 female patients, scheduled for elective surgery with SEP monitoring, under clinically proven conditions in the awake state. The discrete wavelet transform implemented as the multiresolution analysis was adopted for evaluating SEP. The suitability of the wavelet coefficients was investigated by calculating the error between the averaged response and the corresponding wavelet reconstructions. SEP can be represented by a very small number of wavelet coefficients. Although the individual SEP waveform has an influence on the number and selection of wavelet coefficients, in all subjects more than 84% of the SEP waveform energy can be represented by a set 16 wavelet coefficients. The discrete wavelet transformation provides an efficient tool for SEP representation and parameterisation. Depending on the specific problem the DWT, can be adjusted to the desired accuracy, which is important for the subsequent development of automatic SEP analysers.

A wavelet-based procedure for process fault detection

To detect faults in a time-dependent process, we apply a discrete wavelet transform (DWT) to several independently replicated data sets generated by that process. The DWT can capture irregular data patterns such as sharp jumps better than the Fourier transform and standard statistical procedures without adding much computational complexity. Our wavelet coefficient selection method effectively balances model parsimony against data reconstruction error. The few selected wavelet coefficients serve as the data set to facilitate an efficient decision-making method in situations with potentially large-volume data sets. We develop a general procedure to detect process faults based on differences between the reduced-size data sets obtained from the nominal (in-control) process and from a new instance of the target process that must be tested for an out-of-control condition. The distribution of the test statistic is constructed first using normal distribution theory and then with a new resampling procedure called reversed jackknifing that does not require any restrictive distributional assumptions. A Monte Carlo study demonstrates the effectiveness of these procedures. Our methods successfully detect process faults for quadrupole mass spectrometry samples collected from a rapid thermal chemical vapor deposition process.

WPTER: wavelet packet transform for efficient pattern recognition of signals

In the present work, we propose a novel algorithm based on the Wavelet Packet Transform (WPT) for pattern recognition of signals, which operates both feature selection and classification at the same time: Wavelet Packet Transform for Efficient pattern Recognition of signals (WPTER). The distinctive characteristics of WPTER with respect to the previously proposed algorithms for the WPT-based classification of signals consist mainly of two aspects: (1) a Classification Ability criterion is introduced into the procedure for selection of the best discriminant basis; (2) the signals are reconstructed in the original domain by using only the selected wavelet coefficients, which allow for chemical interpretation of the results. The algorithm was first tested on an artificial (simulated) set of signals, consisting of a number of subsequent peaks, partially overlapped to each other, with added noise and baseline drift, simulating a three-class system. Then, it was applied to a data set consisting of X-ray diffractograms on fired tiles subjected to different firing cycles, aiming at discriminating the different firing methods on the basis of the phase composition. In both cases, satisfactory classifications were achieved.

Context-based lossless image coding using EZW framework

Previous research advances have shown that wavelet-based image-compression techniques offer several advantages over traditional techniques in terms of progressive transmission capability, compression efficiency, and bandwidth utilization. The embedded zerotree wavelet (EZW) coding technique suggested by Shapiro (1992), and its modification-set partitioning in hierarchical trees (SPIHT), suggested by Said and Pearlman (19996)-demonstrate the competitive performance of wavelet-based compression schemes. The EZW-based lossless image coding framework consists of three stages: (1) reversible discrete wavelet transform; (2) hierarchical ordering and selection of wavelet coefficients; and (3) context-modeling-based entropy (arithmetic) coding. The performance of the compression algorithm depends on the choice of various parameters and the implementation strategies employed in all the three stages. This paper proposes different context modeling and selection techniques for efficient entropy encoding of wavelet coefficients, along with the modifications performed to the SPIHT algorithm. The results of several experiments presented in this paper demonstrate the importance of context modeling in the EZW framework. Furthermore, this paper shows that appropriate context modeling improves the performance of compression algorithm after a multilevel subband decomposition is performed.

Image analysis using space-filling curves and 1D wavelet bases

Images are transformed into signals using a Peano-Hilbert space-filling curve: this continuous mapping captures local informations when Hilbert's curve is wandering inside the image. Then the obtained signal is analysed using 1 D (one-dimensional) wavelet orthogonal bases. The spaces of details of smaller and smaller scales are considered. They are built from a scaling function. An image can be computed by selecting wavelet coefficients corresponding to one or several scales and using the inverse Peano-Hilbert procedure. Due to the good localization of wavelet analysis local and global patterns can be detected and global ones can be reinforced. So the edge detection of global edges is prepared and easier with mathematical morphology.