Design of efficient M-band coders with linear-phase andperfect-reconstruction properties

This paper presents a new design technique for obtaining M-band orthogonal coders where M=2ⁱ. The structures obtained using the proposed technique have the perfect reconstruction property. Furthermore, all filters that constitute the subband coder are linear-phase FIR-type filters. In contrast with conventional design techniques that attempt to find a unitary alias-component matrix in the frequency domain, we carry out the design in the time domain, based on time-domain orthonormality constraints that the filters must satisfy. The M-band design problem is reduced to the problem of finding a suitable lowpass filter h₀(n). Once a suitable lowpass filter is found, the remaining (M-1) filters of the coder are obtained through the use of shuffling operators on the lowpass filter. This approach leads to a set of filters that use the same numerical coefficient values in different shift positions, allowing very efficient numerical implementation of the subband coder. In addition, by imposing further constraints on the lowpass branch impulse response h₀(n), we are able to construct continuous bases of M-channel wavelets with good regularity properties. Design examples are presented for four-, eight-, and 16-band coders, along with examples of continuous wavelet bases that they generate     

A Novel Scheme for the Design of Approximate Hilbert Transform Pairs of Orthonormal Wavelet Bases

In designing the Hilbert transform pairs of orthonormal wavelet bases, several authors have shown that the requirements of the equal magnitude responses and the half-sample phase offset are the necessary and sufficient conditions on the scaling filters of conjugate quadrature filter (CQF) banks. In this paper, we first show that the scaling filters of CQF banks with equal magnitude responses cannot approach the half-sample phase offset in the high-frequency range properly. Then, a new design scheme, making a tradeoff between the requirements of the equal magnitude responses and the half-sample phase offset, is presented. The design scheme can make the scaling filter pairs approximately satisfy the requirement of the half-sample phase offset over the full frequency range while the magnitude responses of each pair remain nearly equal. As a result, the corresponding orthonormal wavelet bases can approximate to Hilbert transform pairs better. Some orthogonal wavelet bases we designed demonstrate the superiority of our scheme.     

双通道RSPUDT声表面波滤波器优化设计

介绍了一种利用分布声反射换能器 (DART)结构的双通道谐振单相单向换能器(RSPUDT)滤波器的设计方法.滤波器中2个通道的4个换能器结构完全不同,分别对它们进行优化设计,使结构具有更大的自由度,因而获得更好的性能.在与单通道RSPUDT滤波器相同指标下,双通道结构可实现小的长度和体积.采用随机优化算法找到换能函数和反射函数的全局最优解,从而避免了结构收敛到局部最小点.实验分析表明,模拟结果和实验结果相吻合.     

Implementation of Digital Unbiased FIR Filters with Polynomial Impulse Responses

This paper addresses the design and implementation of digital unbiased finite impulse response (FIR) filters with polynomial impulse response functions. The transfer function, its fundamental properties, and a general block-diagram are discussed for the impulse response represented with the l-degree Taylor series expansion. As a particular results, we show a fundamental identity uniquely featured to such filters in the transform domain. For low-degree impulse responses, the transfer functions are found in simple closed forms and represented in compact block-diagrams. The magnitude and phase responses are also analyzed along with the group delays. A comparison with predictive FIR filters is given. As examples of applications, filtering of time errors of local clocks is discussed along with the low-pass filter design employing a cascade of the unbiased FIR filters.     

Parametric least squares approximation using gamma bases

We study the problem of linear approximation of a signal using the parametric gamma bases in L² space. These bases have a time scale parameter, which has the effect of modifying the relative angle between the signal and the projection space, thereby yielding an extra degree of freedom in the approximation. Gamma bases have a simple analog implementation that is a cascade of identical lowpass filters. We derive the normal equation for the optimum value of the time scale parameter and decouple it from that of the basis weights. Using statistical signal processing tools, we further develop a numerical method for estimating the optimum time scale     

Multidimensional multichannel FIR deconvolution using Gr?bner bases.

We present a new method for general multidimensional multichannel deconvolution with finite impulse response (FIR) convolution and deconvolution filters using Gr?bner bases. Previous work formulates the problem of multichannel FIR deconvolution as the construction of a left inverse of the convolution matrix, which is solved by numerical linear algebra. However, this approach requires the prior information of the support of deconvolution filters. Using algebraic geometry and Gr?bner bases, we find necessary and sufficient conditions for the existence of exact deconvolution FIR filters and propose simple algorithms to find these deconvolution filters. The main contribution of our work is to extend the previous Gr?bner basis results on multidimensional multichannel deconvolution for polynomial or causal filters to general FIR filters. The proposed algorithms obtain a set of FIR deconvolution filters with a small number of nonzero coefficients (a desirable feature in the impulsive noise environment) and do not require the prior information of the support. Moreover, we provide a complete characterization of all exact deconvolution FIR filters, from which good FIR deconvolution filters under the additive white noise environment are found. Simulation results show that our approaches achieve good results under different noise settings.     

Multidimensional Multichannel FIR Deconvolution Using GrÖbner Bases

We present a new method for general multidimensional multichannel deconvolution with finite impulse response (FIR) convolution and deconvolution filters using GrÖbner bases. Previous work formulates the problem of multichannel FIR deconvolution as the construction of a left inverse of the convolution matrix, which is solved by numerical linear algebra. However, this approach requires the prior information of the support of deconvolution filters. Using algebraic geometry and GrÖbner bases, we find necessary and sufficient conditions for the existence of exact deconvolution FIR filters and propose simple algorithms to find these deconvolution filters. The main contribution of our work is to extend the previous GrÖbner basis results on multidimensional multichannel deconvolution for polynomial or causal filters to general FIR filters. The proposed algorithms obtain a set of FIR deconvolution filters with a small number of nonzero coefficients (a desirable feature in the impulsive noise environment) and do not require the prior information of the support. Moreover, we provide a complete characterization of all exact deconvolution FIR filters, from which good FIR deconvolution filters under the additive white noise environment are found. Simulation results show that our approaches achieve good results under different noise settings.     

Adaptive alpha-trimmed mean filters under deviations from assumed noise model

Alpha-trimmed mean filters are widely used for the restoration of signals and images corrupted by additive non-Gaussian noise. They are especially preferred if the underlying noise deviates from Gaussian with the impulsive noise components. The key design issue of these filters is to select its only parameter, alpha, optimally for a given noise type. In image restoration, adaptive filters utilize the flexibility of selecting alpha according to some local noise statistics. In the present paper, we first review the existing adaptive alpha-trimmed mean filter schemes. We then analyze the performance of these filters when the underlying noise distribution deviates from the Gaussian and does not satisfy the assumptions such as symmetry. Specifically, the clipping effect and the mixed noise cases are analyzed. We also present a new adaptive alpha-trimmed filter implementation that detects the nonsymmetry points locally and applies alpha-trimmed mean filter that trims out the outlier pixels such as edges or impulsive noise according to this local decision. Comparisons of the speed and filtering performances under deviations from symmetry and Gaussian assumptions show that the proposed filter is a very good alternative to the existing schemes.     

Subpixel rendering for diamond-shaped PenTile displays using patch-based adaptive filters

We propose a novel subpixel rendering algorithm for diamond-shaped PenTile displays, which reduces color distortions while improving apparent resolutions. We develop two types of subpixel rendering filters: main filter and color distortion reduction (CDR) filters. To derive the filters, we formulate a quadratic program to minimize the difference between an original input image and a virtual image that the human visual system perceives. By imposing two constraints for filter size and coefficients, we obtain the main filter, which has a suitable size and is normalized. Then, we design the CDR filters based on the analysis of various patch patterns for image areas. We define the patch patterns to classify local areas with possible color distortions. By imposing additional constraints according to the patch patterns, we derive the CDR filters. Lastly, by matching local areas in the input image into the pre-defined patch patterns, we render the image using the main filter and the CDR filters, which are applied adaptively to the local areas. Experimental results demonstrate that the proposed subpixel rendering algorithm improves apparent resolutions and suppresses color distortions effectively, thereby outperforming conventional algorithms.     

On fast FIR filters implemented as tail-canceling IIR filters

We have developed an algorithm based on synthetic division for deriving the transfer function that cancels the tail of a given arbitrary rational (IIR) transfer function after a desired number of time steps. Our method applies to transfer functions with repeated poles, whereas previous methods of tail-subtraction cannot. We use a parallel state-variable technique with periodic refreshing to induce finite memory in order to prevent accumulation of quantization error in cases where the given transfer function has unstable modes. We present two methods for designing linear-phase truncated IIR (TIIR) filters based on antiphase filters. We explore finite-register effects for unstable modes and provide bounds on the maximum TIIR filter length. In particular, we show that for unstable systems, the available dynamic range of the registers must be three times that of the data. Considerable computational savings over conventional FIR filters are attainable for a given specification of linear-phase filter. We provide examples of filter design. We show how to generate finite-length polynomial impulse responses using TIIR filters. We list some applications of TIIR filters, including uses in digital audio and an algorithm for efficiently implementing Kay's optimal high-resolution frequency estimator     

Symmetry Study for Delta- Operator-Based 2-D Digital Filters

The complexity in the design and implementation of two-dimensional (2-D) filters can be considerably reduced if we utilize the symmetries that might be present in the frequency response of these filters. As the delta-operator formulation of digital filters offers better numerical accuracy and lower coefficient sensitivity in narrowband filter designs when compared to the traditional shift-operator formulation, it is desirable to have efficient design and implementation techniques in$gamma$-domain which utilize the various symmetries in filter specifications. With this motivation, we comprehensively establish the theory of constraints for delta-operator formulated discrete-time real-coefficient polynomials and functions, arising out of the many types of symmetries in their magnitude responses. We also show that as sampling time tends to zero, the$gamma$-domain symmetry constraints merge with those of$s$-domain symmetry constraints. We then present a least square error criterion based procedure to design 2-D digital filters in$gamma$-domain that utilizes the symmetry properties of the magnitude specification. A design example is provided to illustrate the savings in computational complexity resulting from the use of the$gamma$-domain symmetry constraints.     

On two-channel filter banks with directional vanishing moments.

The contourlet transform was proposed to address the limited directional resolution of the separable wavelet transform. One way to guarantee good approximation behavior is to let the directional filters in the contourlet filter bank have sharp frequency response. This requires filters with large support size. We seek to isolate the key filter property that ensures good approximation. In this direction, we propose filters with directional vanishing moments (DVM). These filters, we show, annihilate information along a given direction. We study two-channel filter banks with DVM filters. We provide conditions under which the design of DVM filter banks is possible. A complete characterization of the product filter is, thus, obtained. We propose a design framework that avoids 2-D factorization using the mapping technique. The filters designed, when used in the contourlet transform, exhibit nonlinear approximation comparable to the conventional filters while being shorter and, therefore, providing better visual quality with less ringing artifacts. Furthermore, experiments show that the proposed filters outperform the conventional ones in image approximation and denoising.     

A subspace matching color filter design methodology for a multispectral imaging system.

In this paper, we present a methodology to design filters for an imaging system to improve the accuracy of the spectral measurements for families of reflective surfaces. We derive the necessary and sufficient conditions that the sensor space of the system must obey in order to measure the spectral reflectance of the surfaces accurately. Through simulations, we show how these conditions can be applied to design filters using a set of sample spectral data acquired from extracted teeth. For this set of data, we also compare our results to those of Wolski's method, a conventional filter design method which produces filters that recover tristimulus values of surfaces accurately under several illuminants. We show that our method produces filters that capture the spectral reflectance better given the same number of measurements. The errors in predicting the color of the sample data are much lower under every test illuminant when the filters designed with our method are used.     

Wavelet Packets Analysis Based on IIR Two-channel Bi-orthogonal Filter Banks

1IntroductionAccordingtoitSrelationwithwaveletanalysis,tWo-channelfilterbankscanbeusednotonlyintheimplementationofwavelettransformandinversetransform,butalsoinwavelet'sconsmichon.AndIIRfiltersarewellknowntohaveshadertransihonregions,lowcomplexity,lowreconstrUctionermrandaPPro~lylinearphase.Weconstr'UctIIRhi-orthogonalPerfectreconstructionfilterbanksusinganallpassfunchonA(z)whoseamplitUdecharacterishcsisallpassandwhosephasecharacterishcsisanapproximatelylinearPhaseinthepass-band.Andweacc…     

Balanced multiwavelet bases based on symmetric FIR filters

This paper describes a basic difference between multiwavelets and scalar wavelets that explains, without using zero moment properties, why certain complications arise in the implementation of discrete multiwavelet transforms. Assuming we wish to avoid the use of prefilters in implementing the discrete multiwavelet transform, it is suggested that the behavior of the iterated filter bank associated with a multiwavelet basis of multiplicity r is more fully revealed by an expanded set of r² scaling functions φ_i,j. This paper also introduces new K-balanced orthogonal multiwavelet bases based on symmetric FIR filters. The nonlinear design equations arising in this work are solved using the Grobner basis. The minimal-length K-balanced multiwavelet bases based on even-length symmetric FIR filters are better behaved than those based on odd-length symmetric FIR filters, as illustrated by special relations they satisfy and by examples constructed     

Precision of morphological-representation estimators for translation-invariant binary filters: Increasing and nonincreasing

Mean-absolute-error-optimal, finite-observation, translations, invariant, binary-image filters have previously been characterized in terms of morphological representations: increasing filters as unions of erosions and nonincreasing filters as unions of hit-or-miss operators. Based on these characterizations, (sub)optimal filters have been designed via image-process realizations. The present paper considers the precision of filter estimation via realizations. The following problems are considered: loss of performance owing to employing erosion filters limited by basis size, precision in the estimation of erosion bases, and precision in the estimation of union-of-hit-or-miss filters. A key point: while precision deteriorates for both erosion and hit-or-miss filters as window size increases, the number of image realizations required to obtain good estimation in erosion-filter design can be much less than the number required for hit-or-miss-filter design. Thus, while in theory optimal hit-or-miss filtering is better because the unconstrained optimal hit-or-miss filter is the conditional expectation, owing to estimation error it is very possible that estimated optimal erosion filters are better than estimated optimal hit-or-miss filters.     

A Globally Optimal Bilinear Programming Approach to the Design of Approximate Hilbert Pairs of Orthonormal Wavelet Bases

It is understood that the Hilbert transform pairs of orthonormal wavelet bases can only be realized approximately by the scaling filters of conjugate quadrature filter (CQF) banks. In this paper, the approximate FIR realization of the Hilbert transform pairs is formulated as an optimization problem in the sense of the lp (p=1, 2, or infinite) norm minimization on the approximate error of the magnitude and phase conditions of the scaling filters. The orthogonality and regularity conditions of the CQF bank pairs are taken as the constraints of such an optimization problem. Whereafter the branch and bound technique is employed to obtain the globally optimal solution of the resulting bilinear program optimization problem. Since the orthogonality and regularity conditions are explicitly taken as the constraints of our optimization problem, the attained solution is an approximate Hilbert transform pair satisfying these conditions exactly. Some orthogonal wavelet bases designed herein demonstrate that our design scheme is superior to those that have been reported in the literature. Moreover, the designed orthogonal wavelet bases show that minimizing the l ₁ norm of the approximate error should be advocated for obtaining better approximated Hilbert pairs.     

Multispectral Filter-Wheel Cameras: Geometric Distortion Model and Compensation Algorithms

Multispectral image acquisition considerably improves color accuracy in comparison to RGB technology. A common multispectral camera design concept features a filter-wheel consisting of six or more optical bandpass filters. By shifting the filters sequentially into the optical path, the electromagnetic spectrum is acquired through the channels, thus making an approximate reconstruction of the spectrum feasible. However, since the optical filters exhibit different thicknesses, refraction indices and may not be aligned in a perfectly coplanar manner, geometric distortions occur in each spectral channel: The reconstructed RGB images thus show rainbow-like color fringes. To compensate for these, we analyze the optical path and derive a mathematical model of the distortions. Based on this model we present two different algorithms for compensation and show that the color fringes vanish completely after application of our algorithms. We also evaluate our compensation algorithms in terms of accuracy and execution time.      

Biorthogonal nearly coiflet wavelets for image compression

Filter bank design for wavelet compression is crucial; careful design enables superior quality for broad classes of images. The Bernstein basis for frequency-domain construction of biorthogonal nearly coiflet (BNC) wavelet bases forms a unified design framework for high-performance medium-length filters. A common filter bandwidth is characteristic of widely favoured BNC filter pairs: the classical CDF 9/7, the Villasenor 6/10, and the Villasenor 10/18. Based on this observation, we construct previously unknown BNC 17/11 and BNC 16/8 wavelet filters. Key filter-quality evaluation metrics, due to Villasenor, demonstrate these filters to be well suited for image compression. Also studied are the biorthogonal coiflet 17/11 (half-band), 18/10 and 10/6 filter pairs, which have not previously been formally evaluated for image coding. Simulation results confirm that the BNC 17/11 and BNC 16/8 wavelet bases are outstanding for compression of natural and medical images, and particularly for images with significant high-frequency detail, such as fingerprints. The BNC 17/11 pair recommends itself for international standardization for the compression of still images; the BNC 16/8 pair for high-quality compression of production quality video. Experimental evidence suggests biorthogonal filters achieve good compression if, subject to a filter bandwidth constraint, maximum vanishing moments are obtained for a given filter support.