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

A statistical multiresolution approach for face recognition using structural hidden Markov models

This paper introduces a novel methodology that combines the multiresolution feature of the discrete wavelet transform (DWT) with the local interactions of the facial structures expressed through the structural hidden Markov model (SHMM). A range of wavelet filters such as Haar, biorthogonal 9/7, and Coiflet, as well as Gabor, have been implemented in order to search for the best performance. SHMMs perform a thorough probabilistic analysis of any sequential pattern by revealing both its inner and outer structures simultaneously. Unlike traditional HMMs, the SHMMs do not perform the state conditional independence of the visible observation sequence assumption. This is achieved via the concept of local structures introduced by the SHMMs. Therefore, the long-range dependency problem inherent to traditional HMMs has been drastically reduced. SHMMs have not previously been applied to the problem of face identification. The results reported in this application have shown that SHMM outperforms the traditional hidden Markov model with a 73% increase in accuracy

A Wavelet Transform Module for a Speech Recognition Virtual Machine

This work explores the trade-offs between time and frequency information during the feature extraction process of an automatic speech recognition (ASR) system using wavelet transform (WT) features instead of Mel-frequency cepstral coefficients (MFCCs) and the benefits of combining the WTs and the MFCCs as inputs to an ASR system. A virtual machine from the Speech Recognition Virtual Kitchen resource (www.speechkitchen.org) is used as the context for implementing a wavelet signal processing module in a speech recognition system. Contributions include a comparison of MFCCs and WT features on small and large vocabulary tasks, application of combined MFCC and WT features on a noisy environment task, and the implementation of an expanded signal processing module in an existing recognition system. The updated virtual machine, which allows straightforward comparisons of signal processing approaches, is available for research and education purposes

Wavelet-based voice morphing

This paper presents a new multi-scale voice morphing algorithm. This algorithm enables a user to transform one person's speech pattern into another person's pattern with distinct characteristics, giving it a new identity, while preserving the original content. The voice morphing algorithm performs the morphing at different subbands by using the theory of wavelets and models the spectral conversion using the theory of Radial Basis Function Neural Networks. The results obtained on the TIMIT speech database demonstrate effective transformation of the speaker identity

Eye Detection Using Wavelets and ANN

A Biometric system provides perfect identification of individual based on a unique biological feature or characteristic possessed by a person such as finger print, hand writing, heart beat, face recognition and eye detection. Among them eye detection is a better approach since Human Eye does not change throughout the life of an individual. It is regarded as the most reliable and accurate biometric identification system available. In our project we are going to develop a system for ‘eye detection using wavelets and ANN’ with software simulation package such as matlab 7.0 tool box in order to verify the uniqueness of the human eyes and its performance as a biometric. Eye detection involves first extracting the eye from a digital face image, and then encoding the unique patterns of the eye in such a way that they can be compared with preregistered eye patterns. The eye detection system consists of an automatic segmentation system that is based on the wavelet transform, and then the Wavelet analysis is used as a pre-processor for a back propagation neural network with conjugate gradient learning. The inputs to the neural network are the wavelet maxima neighborhood coefficients of face images at a particular scale. The output of the neural network is the classification of the input into an eye or non-eye region. An accuracy of 81% is observed for test images under different environment conditions not included during training

Reduce The Noise in Speech Signals Using Wavelet Filtering

 تنخفض قدرة قنوات البيانات غالبا ما بسبب الضوضاء وتشوه الإشارات المرسلة . يستخدم تخفيض الضوضاء في مجالات  مختلفة (حيث لا يمكن عزل الإشارات المرسلة من الضوضاء والتشويه): في التعرف على الكلام ومعالجة الصور وأنظمة الاتصالات المتنقلة ومعالجة الإشارات الطبية والأنظمة الراديوية والرادارية وما إلى ذلك. توضح هذه الورقة مشكلة وجود ضوضاء في إشارات الكلام. ويتم النظر في نموذج ضوضاء غوسية بيضاء مضافة وإضافته إلى إشارة الكلام - نمذجة عملية الضوضاء. حيث تم   دراسة الميزات الاساسية للمويجات المستخدمة لتقليل الضوضاء. وتم النظر في الخوارزمية الاساسية لعميلة  ازالة الضوضاء باستخدام تقنيات تحليل المويجات. تم بناء التنفيذ العملي للحد من الضوضاء. تم رسم الاشارة الاصلية والاشاره المشوهة  والاشاره المستخلصه بعد تقليل الضوضاء. تم تحليل نتائج إلغاء الضوضاء باستخدام أسر مختلفة من المويجات، حيث تم رسم الاشكال للصلات المتبادلة بين إشارات الكلام المشوهة والنظيفة.تقليل الضوضاء نفذ باستخدام برنامج ماتلاب.The capacity of the data channels is often reduced due to noise and distortion of the transmitted signals. Noise reduction is used in various areas (where from noise and distortion the transmitted signals cannot be isolated): speech / speaker recognition, image processing, mobile communication systems, medical signal processing, radio and radar systems, etc. This paper illustrates the problem of the presence of noise in speech signals. A model of additive white Gaussian noise is considered and adding it to the speech signal – modeling of noise process. The main features of wavelets, which used in noise reduction, are described. The main algorithm of the noise cancellation process using wavelet analysis techniques is considered. Carried out the practical implementation of noise reduction. The graphs of the original, noisy and cleaned signals are plotted. An analysis of the results of noise cancellation was carried out using different families of wavelets, graphs of the cross correlation of noisy and clean speech signals are plotted. Noise reduction carried out using Matlab programing

The development of the quaternion wavelet transform

The purpose of this article is to review what has been written on what other authors have called quaternion wavelet transforms (QWTs): there is no consensus about what these should look like and what their properties should be. We briefly explain what real continuous and discrete wavelet transforms and multiresolution analysis are and why complex wavelet transforms were introduced; we then go on to detail published approaches to QWTs and to analyse them. We conclude with our own analysis of what it is that should define a QWT as being truly quaternionic and why all but a few of the “QWTs” we have described do not fit our definition

Integrodifferential equations for multiscale wavelet shrinkage : the discrete case

We investigate the relations between wavelet shrinkage and integrodifferential equations for image simplification and denoising in the discrete case. Previous investigations in the continuous one-dimensional setting are transferred to the discrete multidimentional case. The key observation is that a wavelet transform can be understood as derivative operator in connection with convolution with a smoothing kernel. In this paper, we extend these ideas to the practically relevant discrete formulation with both orthogonal and biorthogonal wavelets. In the discrete setting, the behaviour of the smoothing kernels for different scales is more complicated than in the continuous setting and of special interest for the understanding of the filters. With the help of tensor product wavelets and special shrinkage rules, the approach is extended to more than one spatial dimension. The results of wavelet shrinkage and related integrodifferential equations are compared in terms of quality by numerical experiments