A new class of two-channel biorthogonal filter banks and wavelet bases

We propose a novel framework for a new class of two-channel biorthogonal filter banks. The framework covers two useful subclasses: i) causal stable IIR filter banks. ii) linear phase FIR filter banks. There exists a very efficient structurally perfect reconstruction implementation for such a class. Filter banks of high frequency selectivity can be achieved by using the proposed framework with low complexity. The properties of such a class are discussed in detail. The design of the analysis/synthesis systems reduces to the design of a single transfer function. Very simple design methods are given both for FIR and IIR cases. Zeros of arbitrary multiplicity at aliasing frequency can be easily imposed, for the purpose of generating wavelets with regularity property. In the IIR case, two new classes of IIR maximally flat filters different from Butterworth filters are introduced. The filter coefficients are given in closed form. The wavelet bases corresponding to the biorthogonal systems are generated. the authors also provide a novel mapping of the proposed 1-D framework into 2-D. The mapping preserves the following: i) perfect reconstruction; ii) stability in the IIR case; iii) linear phase in the FIR case; iv) zeros at aliasing frequency; v) frequency characteristic of the filters

On the design and multiplierless realization of perfect reconstruction triplet-based FIR filter banks and wavelet bases

This paper proposes new methods for the efficient design and realization of perfect reconstruction (PR) two-channel finite-impulse response (FIR) triplet filter banks (FBs) and wavelet bases. It extends the linear-phase FIR triplet FBs of Ansari et al. to include FIR triplet FBs with lower system delay and a prescribed order of K regularity. The design problem using either the minimax error or least-squares criteria is formulated as a semidefinite programming problem, which is a very flexible framework to incorporate linear and convex quadratic constraints. The K regularity conditions are also expressed as a set of linear equality constraints in the variables to be optimized and they are structurally imposed into the design problem by eliminating the redundant variables. The design method is applicable to linear-phase as well as low-delay triplet FBs. Design examples are given to demonstrate the effectiveness of the proposed method. Furthermore, it was found that the analysis and synthesis filters of the triplet FB have a more symmetric frequency responses. This property is exploited to construct a class of PR M-channel uniform FBs and wavelets with M = 2 L, where L is a positive integer, using a particular tree structure. The filter lengths of the two-channel FBs down the tree are approximately reduced by a factor of two at each level or stage, while the transition bandwidths are successively increased by the same factor. Because of the downsampling operations, the frequency responses of the final analysis filters closely resemble those in a uniform FB with identical transition bandwidth. This triplet-based uniform M-channel FB has very low design complexity and the PR condition and K regularity conditions are structurally imposed. Furthermore, it has considerably lower arithmetic complexity and system delay than conventional tree structure using identical FB at all levels. The multiplierless realization of these FBs using sum-of-power-of-two (SOPOT) coefficients and multiplier block is also studied. © 2004 IEEE.published_or_final_versio

On the application of raised-cosine wavelets for multicarrier systems design

YesNew orthogonal wavelet transforms can be designed by changing the wavelet basis functions or by constructing new low-pass filters (LPF). One family of wavelet may appeal, in use, to a particular application than another. In this study, the wavelet transform based on raisedcosine spectrum is used as an independent orthogonal wavelet to study multicarrier modulation behaviour over multipath channel environment. Then, the raised-cosine wavelet is compared with other well-known orthogonal wavelets that are used, also, to build multicarrier modulation systems. Traditional orthogonal wavelets do not have side-lobes, while the raised-cosine wavelets have lots of side-lobes; these characteristics influence the wavelet behaviour. It will be shown that the raised-cosine wavelet transform, as an orthogonal wavelet, does not support the design of multicarrier application well like the existing well-known orthogonal wavelets

Development of Multirate Filter – Based Region Features for Iris Identification

The emergence of biometric system is seen as the next-generation technological solution in strengthening the social and national security. The evolution of biometrics has shifted the paradigm of authentication from classical token and knowledge-based systems to physiological and behavioral trait based systems. R & D on iris biometrics, in last one decade, has established it as one of the most promising traits. Even though, iris biometric takes high resolution near-infrared (NIR) images as input, its authentication accuracy is very commendable. Its performance is often influenced by the presence of noise, database size, and feature representation. This thesis focuses on the use of multi resolution analysis (MRA) in developing suitable features for non-ideal iris images. Our investigation starts with the iris feature extraction technique using Cohen −Daubechies − Feauveau 9/7 (CDF 9/7) filter bank. In this work, a technique has been proposed to deal with issues like segmentation failure and occlusion. The experimental studies deal with the superiority of CDF 9/7 filter bank over the frequency based techniques. Since there is scope for improving the frequency selectivity of CDF 9/7 filter bank, a tunable filter bank is proposed to extract region based features from non-cooperative iris images. The proposed method is based on half band polynomial of 14th order. Since, regularity and frequency selectivity are in inverse relationship with each other, filter coefficients are derived by not imposing maximum number of zeros. Also, the half band polynomial is presented in x-domain, so as to apply semidefinite programming, which results in optimization of coefficients of analysis/synthesis filter. The next contribution in this thesis deals with the development of another powerful MRA known as triplet half band filter bank (THFB). The advantage of THFB is the flexibility in choosing the frequency response that allows one to overcome the magnitude constraints. The proposed filter bank has improved frequency selectivity along with other desired properties, which is then used for iris feature extraction. The last contribution of the thesis describes a wavelet cepstral feature derived from CDF 9/7 filter bank to characterize iris texture. Wavelet cepstrum feature helps in reducing the dimensionality of the detail coefficients; hence, a compact feature presentation is possible with improved accuracy against CDF 9/7. The efficacy of the features suggested are validated for iris recognition on three publicly available databases namely, CASIAv3, UBIRISv1, and IITD. The features are compared with other transform domain features like FFT, Gabor filter and a comprehensive evaluation is done for all suggested features as well. It has been observed that the suggested features show superior performance with respect to accuracy. Among all suggested features, THFB has shown best performance

Design and Analysis of A New Illumination Invariant Human Face Recognition System

In this dissertation we propose the design and analysis of a new illumination invariant face recognition system. We show that the multiscale analysis of facial structure and features of face images leads to superior recognition rates for images under varying illumination. We assume that an image I ( x,y ) is a black box consisting of a combination of illumination and reflectance. A new approximation is proposed to enhance the illumination removal phase. As illumination resides in the low-frequency part of images, a high-performance multiresolution transformation is employed to accurately separate the frequency contents of input images. The procedure is followed by a fine-tuning process. After extracting a mask, feature vector is formed and the principal component analysis (PCA) is used for dimensionality reduction which is then proceeded by the extreme learning machine (ELM) as a classifier. We then analyze the effect of the frequency selectivity of subbands of the transformation on the performance of the proposed face recognition system. In fact, we first propose a method to tune the characteristics of a multiresolution transformation, and then analyze how these specifications may affect the recognition rate. In addition, we show that the proposed face recognition system can be further improved in terms of the computational time and accuracy. The motivation for this progress is related to the fact that although illumination mostly lies in the low-frequency part of images, these low-frequency components may have low- or high-resonance nature. Therefore, for the first time, we introduce the resonance based analysis of face images rather than the traditional frequency domain approaches. We found that energy selectivity of the subbands of the resonance based decomposition can lead to superior results with less computational complexity. The method is free of any prior information about the face shape. It is systematic and can be applied separately on each image. Several experiments are performed employing the well known databases such as the Yale B, Extended-Yale B, CMU-PIE, FERET, AT&T, and LFW. Illustrative examples are given and the results confirm the effectiveness of the method compared to the current results in the literature

Fractional wavelet transform using an unbalanced lifting structure

In this article, we introduce the concept of fractional wavelet transform. Using a two-channel unbalanced lifting structure it is possible to decompose a given discrete-time signal x[n] sampled with period T into two sub-signals x1[n] and x2[n] whose average sampling periods are pT and qT, respectively. Fractions p and q are rational numbers satisfying the condition: 1/p + 1/q = 1. The low-band sub-signal x 1[n] comes from [0, π/p] band and the high-band wavelet signal x 2[n] comes from (π/p, π] band of the original signal x[n]. Filters used in the liftingstructure are designed using the Lagrange interpolation formula. It is straightforward to extend the proposed fractional wavelet transform to two or higher dimensions in a separable or non separable manner. © 2011 Copyright Society of Photo-Optical Instrumentation Engineers (SPIE)

Balanced Multiwavelets Theory and Design

This paper deals with multiwavelets which are a recent generalization of wavelets in the context of multirate filter banks and with their applications to signal processing and especially compression. By their inherent structure, multiwavelets are fit for processing multi-channel signals. First, we will recall some general results on multifilters by looking at them as time-varying filters. Then, we will link this to multiwavelets, looking closely at the convergence of the iterated matrix product leading to them and the typical properties we can expect. Then, we will define under what conditions we can apply systems based on multiwavelets to one-dimensional signals in a simple way. That means we will give some natural and simple conditions that should help in the design of new multiwavelets for signal processing. Finally, we will provide some tools in order to construct multiwavelets with the required properties, the so-called `balanced multiwavelets'