The design of a class of perfect reconstruction two-channel FIR linear-phase filterbanks and wavelets bases using semidefinite programming

This paper proposes a new method for designing a class of two-channel perfect reconstruction (PR) linear-phase FIR filterbanks (FBs) and wavelets previously proposed by Phoong et al. By expressing the given K-regularity constraints as a set of linear equality constraints in the design variables, the design problem using the minimax error criterion can be solved using semidefinite programming (SDP). Design examples show that the proposed method is very effective and it yields equiripple stopband response while satisfying the given K-regularity condition.published_or_final_versio

New design and realization techniques for a class of perfect reconstruction two-channel FIR filterbanks and wavelets bases

This paper proposes two new methods for designing a class of two-channel perfect reconstruction (PR) finite impulse response (FIR) filterbanks (FBs) and wavelets with K-regularity of high order and studies its multiplier-less implementation. It is based on the two-channel structural PR FB proposed by Phoong et al. The basic principle is to represent the K-regularity condition as a set of linear equality constraints in the design variables so that the least square and minimax design problems can be solved, respectively, as a quadratic programming problem with linear equality constraints (QPLC) and a semidefinite programming (SDP) problem. We also demonstrate that it is always possible to realize such FBs with sum-of-powers-of-two (SOPOT) coefficients while preserving the regularity constraints using Bernstein polynomials. However, this implementation usually requires long coefficient wordlength and another direct-form implementation, which can realize multiplier-less wavelets with K-regularity condition up to fifth order, is proposed. Several design examples are given to demonstrate the effectiveness of the proposed methods. © 2004 IEEE.published_or_final_versio

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

A state space approach to the design of globally optimal FIR energy compaction filters

We introduce a new approach for the least squared optimization of a weighted FIR filter of arbitrary order N under the constraint that its magnitude squared response be Nyquist(M). Although the new formulation is general enough to cover a wide variety of applications, the focus of the paper is on optimal energy compaction filters. The optimization of such filters has received considerable attention in the past due to the fact that they are the main building blocks in the design of principal component filter banks (PCFBs). The newly proposed method finds the optimum product filter Fopt(z)=Hopt(Z)Hopt (z^-1) corresponding to the compaction filter Hopt (z). By expressing F(z) in the form D(z)+D(z^-1), we show that the compaction problem can be completely parameterized in terms of the state-space realization of the causal function D(z). For a given input power spectrum, the resulting filter Fopt(z) is guaranteed to be a global optimum solution due to the convexity of the new formulation. The new algorithm is universal in the sense that it works for any M, arbitrary filter length N, and any given input power spectrum. Furthermore, additional linear constraints such as wavelets regularity constraints can be incorporated into the design problem. Finally, obtaining Hopt(z) from Fopt(z) does not require an additional spectral factorization step. The minimum-phase spectral factor Hmin(z) can be obtained automatically by relating the state space realization of Dopt(z) to that of H opt(z

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

A System Approach to the Design of Multirate Filter Banks.

This dissertation studies the design of multirate filter banks by adopting a so-called system approach. The design issue of Johnston\u27s method is first investigated in which an explicit expression of the reconstruction error is derived using Lyapunov stability theory, and new convergent iterative algorithms are proposed through non-linear optimization. The results are extended to the two-dimensional filter banks. The design issue of more general multirate filter banks is also investigated through model matching method. Using standard results from modern control theory, new design algorithms are developed which minimize the reconstruction error while completely eliminating the aliasing error. State-space realizations, inner-outer factorizations, and optimal Hankel norm approximation are used to reduce the complexity of computation and improve the accuracy of the proposed design algorithms