David B. H. Tay

Flexible design of multidimensional perfect reconstruction FIR 2-band filters using transformations of variables

An approach to designing multidimensional linear-phase FIR diamond subband filters having the perfect reconstruction property is presented. It is based on a transformation of variables technique and is equivalent to the generalized McClellan transformation. Methods for designing a whole class of transformation are given. The approach consists of two parts; design of the transformation and design of the 1-D filters. The use of Lagrange halfband filters to design the 1-D filters is discussed. The modification of a particular Lagrange halfband filter which gives a pair of simple 1-D filters that are almost similar to each other in their frequency characteristics but still form a perfect reconstruction pair is presented. The design technique is extended to other types of two-channel sampling lattice and subband shapes, in particular, the parallelogram and the diagonally quadrant subband cases. Several numerical design examples are presented to illustrate the flexibility of the design method.

'Generalizability' of a radial-aortic transfer function for the derivation of central aortic waveform parameters.

Objective Arterial transfer functions (TFs) describe the relationship between the pressure waveform at different arterial sites. Generalized TFs are used to reconstruct central aortic waveforms from non-invasively obtained peripheral waveforms and have been promoted as potentially clinically useful. A limitation is the paucity of information on their ‘generalizability’ with no information existing on the number of subjects required to construct a satisfactory TF, nor is adequate prospective validation available. We therefore investigated the uniformity of radial-aortic TFs and prospectively estimated the capacity of a generalized TF to reconstruct individual central blood pressure parameters. Patients and methods Ninety-three subjects (64 male) were studied by simultaneous radial applanation and high-fidelity (Millar Mikro-tip catheter) direct measurement of central aortic BP during elective coronary procedures. Subjects were prospectively randomized to either a derivation or validation group. Results Increasing numbers of individual TFs from the derivation group were averaged to form a generalized TF. There was minimal change with greater than 20 TFs averaged. In the validation group, the error in most reconstructed parameters related to the absolute value of the directly measured parameter [systolic blood pressure (SBP) and pulse pressure, P < 0.05; systolic pressure–time interval, subendocardial viability index, augmentation index, and times to the inflection point, peak and end systole, all P < 0.01]. Aorto-radial delay was related to error in reconstructed central aortic SBP and pulse pressure (negatively) and time to peak systole (positively) (all P < 0.001). Reconstruction of augmentation index was poor. Discussion Inclusion of more than 20 individual TFs in the construction of a generalized TF does not improve ‘generalizability’. There appear to be systematic errors in derived central pressure waveforms and derived aortic augmentation index is inaccurate compared to the directly measured value.

A signal denoising algorithm based on overcomplete wavelet representations and Gaussian models

In this paper, we propose a simple signal estimation algorithm based on multiple wavelet representations and Gaussian observation models. The proposed algorithm has two major steps: a joint-optimum estimation of the wavelet coefficients and an averaging of the denoised images. Experimental results show that the denoising performance of proposed algorithm is comparable to that of the state of the art.

A Fast Watermarking System for H.264/AVC Video

In this paper, we propose a fast watermarking system that works on the H.264/AVC motion vectors. By restricting access to DCT coefficients and pixel information, the computational complexity of the watermark embedder/extractor is kept low and much lower than that of the H.264 decoder. The error propagation due to motion prediction compensation is monitored and its effect is limited by a tracking method that is based solely on the motion information from the bitstream. Although this work focuses on the H.264/AVC standard, the novel watermarking technique is also applicable to the MPEG1-2 and MPEG4 video standards

Orthonormal Hilbert-Pair of Wavelets With (Almost) Maximum Vanishing Moments

An orthonormal Hilbert-pair consists of a pair of conjugate-quadrature-filter (CQF) banks such that the equivalent wavelet function of both banks are approximate Hilbert transforms of each other. We found that the celebrated orthonormal wavelets of Daubechies, which have maximum vanishing-moment (VM), cannot be used to construct good Hilbert-pairs. In this letter, we reduce the number of VM by one and construct a Hilbert-pair with almost maximum VM. Each pair of wavelets are time-reverse versions of each other, and the individual wavelets are of the least asymmetric type (i.e., approximate linear phase CQF)

A novel approach to the design of the class of triplet halfband filterbanks

A new approach is presented for designing the recently introduced class of triplet halfband filterbank which are defined by three kernels. The Parametric Bernstein Polynomial is used to construct the kernels. The filterbanks have the advantage of structural perfect reconstruction and structural regularity. The design of the free parameters of the Bernstein Polynomial is achieved through a least squares method. A novel iterative procedure is employed to optimize the objective function which is a multiquadratic function of the free parameters. The design technique is flexible in that it allows filters with different characteristics to be designed with ease. Filter regularity can be traded for increased sharpness in the frequency response and regular scaling function and wavelets can be readily obtained.

Signal extraction and power spectrum estimation using wavelet transform scale space filtering and Bayes shrinkage

Abstract This paper introduces two novel methods for signal extraction and denoising through the use of the wavelet transform scale space filtering and Bayes shrinkage. In the first method, the noisy signal is decomposed into multiple scales by the dyadic wavelet transform. The scale space filtering algorithm then extracts the original signal modulus maxima by using the properties of the signal and noise modulus maxima across scales. Finally, a “denoised” signal is reconstructed by the alternate projection algorithm. This denoising method can reduce noise to a high degree while preserving most of the important features of the signal such as edges and other singularities. In the second method, we employ a hierarchical Gaussian mixture model for the wavelet coefficients at different scales and we obtain the best signal estimate through the Bayesian posterior analysis technique. In an application example, we implement the algorithm to obtain a smooth and high-resolution power spectral density estimate from the signals periodogram.

Design of approximate Hilbert transform pair of wavelets with exact symmetry [filter bank design]

This paper presents a new technique for designing pairs of filter banks whose corresponding wavelet functions are approximate Hilbert transforms of each other. The filters have exact linear phase which yields biorthogonal wavelets with exact symmetry. The technique is based on matching the frequency response of a given odd-length filter bank with an even-length filter bank. The class of EBFB (even-length Bernstein filter bank) is utilized in the matching design. The EBFB has perfect reconstruction and vanishing moments properties structurally imposed and this simplifies the design process. The design is achieved through a non-iterative least squares method.

A class of lifting based integer wavelet transform

A class of integer wavelet transform (IWT) which are parametrized simply by one free parameter is presented . The class of IWT is obtained by a lifting based factorization on a class of 9/7 filter pair. The class includes the celebrated 9/7 filter pair of Cohen, Daubechies and Feauveau which is adopted in the upcoming JPEG2000 image compression standard. Within this class are lifting filters with simple rational coefficients which are close in characteristics to the irrational coefficient 9/7 pair employed in JPEG2000. By adjusting the free parameter, IWT with different properties and characteristics can be obtained. A study of the non-linearity of this class of IWT is also performed.

Two stage, least squares design of biorthogonal filter banks

A two-stage approach is employed for the design of a class of two-channel biorthogonal filter banks. The filter banks belong to the class of HPFB (Halfband Pair Filter Bank) and are defined by two kernels. The parametric Bernstein polynomial is used to construct the kernels. The design of the free parameters of the Bernstein polynomial is achieved through a least squares method. In the first stage, the analysis low-pass filter is designed and in the second stage, the synthesis low-pass filter is designed. With the two-stage approach, the design process is efficient and involves solving linear equations. The design techniques allows filters with different characteristics to be designed easily.