Construction of Hilbert Transform Pairs of Wavelet Bases and Gabor-like Transforms

We propose a novel method for constructing Hilbert transform (HT) pairs of wavelet bases based on a fundamental approximation-theoretic characterization of scaling functions--the B-spline factorization theorem. In particular, starting from well-localized scaling functions, we construct HT pairs of biorthogonal wavelet bases of L^2(R) by relating the corresponding wavelet filters via a discrete form of the continuous HT filter. As a concrete application of this methodology, we identify HT pairs of spline wavelets of a specific flavor, which are then combined to realize a family of complex wavelets that resemble the optimally-localized Gabor function for sufficiently large orders. Analytic wavelets, derived from the complexification of HT wavelet pairs, exhibit a one-sided spectrum. Based on the tensor-product of such analytic wavelets, and, in effect, by appropriately combining four separable biorthogonal wavelet bases of L^2(R^2), we then discuss a methodology for constructing 2D directional-selective complex wavelets. In particular, analogous to the HT correspondence between the components of the 1D counterpart, we relate the real and imaginary components of these complex wavelets using a multi-dimensional extension of the HT--the directional HT. Next, we construct a family of complex spline wavelets that resemble the directional Gabor functions proposed by Daugman. Finally, we present an efficient FFT-based filterbank algorithm for implementing the associated complex wavelet transform.Comment: 36 pages, 8 figure

Distributed video coding for wireless video sensor networks: a review of the state-of-the-art architectures

Distributed video coding (DVC) is a relatively new video coding architecture originated from two fundamental theorems namely, Slepian–Wolf and Wyner–Ziv. Recent research developments have made DVC attractive for applications in the emerging domain of wireless video sensor networks (WVSNs). This paper reviews the state-of-the-art DVC architectures with a focus on understanding their opportunities and gaps in addressing the operational requirements and application needs of WVSNs

A real time classification algorithm for EEG-based BCI driven by self-induced emotions

Background and objective: The aim of this paper is to provide an efficient, parametric, general, and completely automatic real time classification method of electroencephalography (EEG) signals obtained from self-induced emotions. The particular characteristics of the considered low-amplitude signals (a self-induced emotion produces a signal whose amplitude is about 15% of a really experienced emotion) require exploring and adapting strategies like the Wavelet Transform, the Principal Component Analysis (PCA) and the Support Vector Machine (SVM) for signal processing, analysis and classification. Moreover, the method is thought to be used in a multi-emotions based Brain Computer Interface (BCI) and, for this reason, an ad hoc shrewdness is assumed. Method: The peculiarity of the brain activation requires ad-hoc signal processing by wavelet decomposition, and the definition of a set of features for signal characterization in order to discriminate different self-induced emotions. The proposed method is a two stages algorithm, completely parameterized, aiming at a multi-class classification and may be considered in the framework of machine learning. The first stage, the calibration, is off-line and is devoted at the signal processing, the determination of the features and at the training of a classifier. The second stage, the real-time one, is the test on new data. The PCA theory is applied to avoid redundancy in the set of features whereas the classification of the selected features, and therefore of the signals, is obtained by the SVM. Results: Some experimental tests have been conducted on EEG signals proposing a binary BCI, based on the self-induced disgust produced by remembering an unpleasant odor. Since in literature it has been shown that this emotion mainly involves the right hemisphere and in particular the T8 channel, the classification procedure is tested by using just T8, though the average accuracy is calculated and reported also for the whole set of the measured channels. Conclusions: The obtained classification results are encouraging with percentage of success that is, in the average for the whole set of the examined subjects, above 90%. An ongoing work is the application of the proposed procedure to map a large set of emotions with EEG and to establish the EEG headset with the minimal number of channels to allow the recognition of a significant range of emotions both in the field of affective computing and in the development of auxiliary communication tools for subjects affected by severe disabilities

Learning alters theta-nested gamma oscillations in inferotemporal cortex

How coupled brain rhythms influence cortical information processing to support learning is unresolved. Local field potential and neuronal activity recordings from 64- electrode arrays in sheep inferotemporal cortex showed that visual discrimination learning increased the amplitude of theta oscillations during stimulus presentation. Coupling between theta and gamma oscillations, the theta/gamma ratio and the regularity of theta phase were also increased, but not neuronal firing rates. A neural network model with fast and slow inhibitory interneurons was developed which generated theta nested gamma. By increasing N-methyl-D-aspartate receptor sensitivity similar learning-evoked changes could be produced. The model revealed that altered theta nested gamma could potentiate downstream neuron responses by temporal desynchronization of excitatory neuron output independent of changes in overall firing frequency. This learning-associated desynchronization was also exhibited by inferotemporal cortex neurons. Changes in theta nested gamma may therefore facilitate learning-associated potentiation by temporal modulation of neuronal firing

Orthonormal and biorthonormal filter banks as convolvers, and convolutional coding gain

Convolution theorems for filter bank transformers are introduced. Both uniform and nonuniform decimation ratios are considered, and orthonormal as well as biorthonormal cases are addressed. All the theorems are such that the original convolution reduces to a sum of shorter, decoupled convolutions in the subbands. That is, there is no need to have cross convolution between subbands. For the orthonormal case, expressions for optimal bit allocation and the optimized coding gain are derived. The contribution to coding gain comes partly from the nonuniformity of the signal spectrum and partly from nonuniformity of the filter spectrum. With one of the convolved sequences taken to be the unit pulse function,,e coding gain expressions reduce to those for traditional subband and transform coding. The filter-bank convolver has about the same computational complexity as a traditional convolver, if the analysis bank has small complexity compared to the convolution itself

Development of retinal blood vessel segmentation methodology using wavelet transforms for assessment of diabetic retinopathy

Automated image processing has the potential to assist in the early detection of diabetes, by detecting changes in blood vessel diameter and patterns in the retina. This paper describes the development of segmentation methodology in the processing of retinal blood vessel images obtained using non-mydriatic colour photography. The methods used include wavelet analysis, supervised classifier probabilities and adaptive threshold procedures, as well as morphology-based techniques. We show highly accurate identification of blood vessels for the purpose of studying changes in the vessel network that can be utilized for detecting blood vessel diameter changes associated with the pathophysiology of diabetes. In conjunction with suitable feature extraction and automated classification methods, our segmentation method could form the basis of a quick and accurate test for diabetic retinopathy, which would have huge benefits in terms of improved access to screening people for risk or presence of diabetes

Spread spectrum-based video watermarking algorithms for copyright protection

Merged with duplicate record 10026.1/2263 on 14.03.2017 by CS (TIS)Digital technologies know an unprecedented expansion in the last years. The consumer can now benefit from hardware and software which was considered state-of-the-art several years ago. The advantages offered by the digital technologies are major but the same digital technology opens the door for unlimited piracy. Copying an analogue VCR tape was certainly possible and relatively easy, in spite of various forms of protection, but due to the analogue environment, the subsequent copies had an inherent loss in quality. This was a natural way of limiting the multiple copying of a video material. With digital technology, this barrier disappears, being possible to make as many copies as desired, without any loss in quality whatsoever. Digital watermarking is one of the best available tools for fighting this threat. The aim of the present work was to develop a digital watermarking system compliant with the recommendations drawn by the EBU, for video broadcast monitoring. Since the watermark can be inserted in either spatial domain or transform domain, this aspect was investigated and led to the conclusion that wavelet transform is one of the best solutions available. Since watermarking is not an easy task, especially considering the robustness under various attacks several techniques were employed in order to increase the capacity/robustness of the system: spread-spectrum and modulation techniques to cast the watermark, powerful error correction to protect the mark, human visual models to insert a robust mark and to ensure its invisibility. The combination of these methods led to a major improvement, but yet the system wasn't robust to several important geometrical attacks. In order to achieve this last milestone, the system uses two distinct watermarks: a spatial domain reference watermark and the main watermark embedded in the wavelet domain. By using this reference watermark and techniques specific to image registration, the system is able to determine the parameters of the attack and revert it. Once the attack was reverted, the main watermark is recovered. The final result is a high capacity, blind DWr-based video watermarking system, robust to a wide range of attacks.BBC Research & Developmen