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Signal Processing, IEEE Transactions on

Issue 4 • Date April 1998

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Displaying Results 1 - 25 of 35
  • Guest Editorial Special Issue on Theory and Application of Filter Banks and Wavelet Transforms

    Page(s): 829
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    Freely Available from IEEE
  • Wavelet-based statistical signal processing using hidden Markov models

    Page(s): 886 - 902
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    Wavelet-based statistical signal processing techniques such as denoising and detection typically model the wavelet coefficients as independent or jointly Gaussian. These models are unrealistic for many real-world signals. We develop a new framework for statistical signal processing based on wavelet-domain hidden Markov models (HMMs) that concisely models the statistical dependencies and non-Gaussian statistics encountered in real-world signals. Wavelet-domain HMMs are designed with the intrinsic properties of the wavelet transform in mind and provide powerful, yet tractable, probabilistic signal models. Efficient expectation maximization algorithms are developed for fitting the HMMs to observational signal data. The new framework is suitable for a wide range of applications, including signal estimation, detection, classification, prediction, and even synthesis. To demonstrate the utility of wavelet-domain HMMs, we develop novel algorithms for signal denoising, classification, and detection View full abstract»

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  • Analysis of low bit rate image transform coding

    Page(s): 1027 - 1042
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    Calculations based on high-resolution quantizations prove that the distortion rate D(R¯) of an image transform coding is proportional to 2-2R when R¯ is large enough. In wavelet and block cosine bases, we show that if R¯<1 bit/pixel, then D(R¯) varies like R¯1-2γ, where γ remains of the order of 1 for most natural images. The improved performance of embedded codings in wavelet bases is analyzed. At low bit rates, we show that the compression performance of an orthonormal basis depends mostly on its ability to approximate images with a few nonzero vectors View full abstract»

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  • On the least asymmetric wavelets

    Page(s): 1125 - 1130
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    The asymmetry of Daubechies' (1988, 1992) scaling functions and wavelets can be diminished by minimizing a special second moment in time for the wavelet-generating discrete-time filter. The moment is involved in an uncertainty relation for discrete-time signals. Other measures of asymmetry are addressed as well, and corresponding results are compared View full abstract»

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  • A generalized algorithm for linear-phase paraunitary filter banks

    Page(s): 1154 - 1158
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    A new algorithm for a subclass of linear-phase paraunitary filter banks with generalized filter length and symmetry polarity is reported. New properties in the polyphase matrix are derived, and the lattice factorizations for filter banks with an even and odd number of channels are examined in a generalized algorithm View full abstract»

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  • Construction of biorthogonal wavelets starting from any two multiresolutions

    Page(s): 1130 - 1133
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    Starting from any two given multiresolution analyses of L2 , {Vj1}j∈Z and {Vj2}j∈Z, we construct biorthogonal wavelet bases that are associated with this chosen pair of multiresolutions. Thus, our construction method takes a point of view opposite to the one of Cohen-Daubechies-Feauveau (1992), which starts from a well-choosen pair of biorthogonal discrete filters. In our construction, the necessary and sufficient condition is the nonperpendicularity of the multiresolutions View full abstract»

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  • M-channel compactly supported biorthogonal cosine-modulated wavelet bases

    Page(s): 1142 - 1151
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    We generalize the theory of compactly supported biorthogonal two-channel wavelet bases to M-channel. A sufficient condition for the M-channel perfect reconstruction filter banks to construct M-channel biorthogonal bases of compactly supported wavelets is derived. It is shown that the construction of biorthogonal M-channel wavelet bases is equivalent to the design of a M-channel perfect reconstruction filter bank with some added regularity conditions. A family of M-channel biorthogonal wavelet bases based on the cosine-modulated filter bank (CMFB) is proposed. It has the advantages of simple design procedure, efficient implementation, and good filter quality. A new method fur imposing the regularity on the CMFBs is also introduced, and several design examples are given View full abstract»

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  • Least squares approximation of perfect reconstruction filter banks

    Page(s): 968 - 978
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    Designing good causal filters for perfect reconstruction (PR) filter banks is a challenging task due to the unusual nature of the design constraints. We present a new least squares (LS) design methodology for approximating PRFBs that avoids most of these difficult constraints. The designer first selects a set of subband analysis filters from an almost unrestricted class of rational filters. Then, given some desired reconstruction delay, this design procedure produces the causal and rational synthesis filters that result in the best least squares approximation to a PRFB. This technique is built on a multi-input multi-output (MIMO) system model for filter banks derived from the filter bank polyphase representation. Using this model, we frame the LS approximation problem for PRFBs as a causal LS equalization problem for MIMO systems. We derive the causal LS solution to this design problem and present an algorithm for computing this solution. The resulting algorithm includes a MIMO spectral factorization that accounts for most of the complexity and computational cost for this design technique. Finally, we consider some design examples and evaluate their performance View full abstract»

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  • Sampling approximation of smooth functions via generalized coiflets

    Page(s): 1133 - 1138
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    We present the sampling approximation power of a newly constructed class of compactly supported orthonormal wavelets called generalized coiflets. We study the accuracy of generalized coiflets-based sampling approximation of smooth functions by developing convergence rates for the pointwise approximation error as well as its LP-norm. We show: (i) that the L2-error due to the approximation of expansion coefficients by function samples is asymptotically negligible compared with that due to projection and (ii) that generalized coiflets can achieve asymptotically better approximation than the original coiflets View full abstract»

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  • Application of multiscale characterization of edges to motion determination

    Page(s): 1174 - 1178
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    We propose a method based on the study of wavelet transform modulus maxima to characterize signal or image edges from smoothed singularities. This characterization is used to extract robust feature points from object edges. They are tracked along an image sequence to study the motion of unrigid objects. Practical results of edge characterization and motion determination are presented View full abstract»

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  • A robust technique for image descreening based on the wavelet transform

    Page(s): 1179 - 1184
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    In this correspondence, a novel wavelet-based approach to recover continuous-tone (contone) images from halftone images is presented. Wavelet decomposition of the halftone image facilitates a series of spatial and frequency selective processing to preserve most of the original image contents while eliminating the halftone noise. Furthermore, optional nonlinear filtering can be applied as a postprocessing stage to create the final aesthetic contone image. This approach lends itself to practical applications since it is independent of parameter estimation and, hence, universal to all types of halftoned images, including those obtained by scanning printed halftones View full abstract»

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  • High-quality audio compression using an adaptive wavelet packet decomposition and psychoacoustic modeling

    Page(s): 1085 - 1093
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    This paper presents a technique to incorporate psychoacoustic models into an adaptive wavelet packet scheme to achieve perceptually transparent compression of high-quality (34.1 kHz) audio signals at about 45 kb/s. The filter bank structure adapts according to psychoacoustic criteria and according to the computational complexity that is available at the decoder. This permits software implementations that can perform according to the computational power available in order to achieve real time coding/decoding. The bit allocation scheme is an adapted zero-tree algorithm that also takes input from the psychoacoustic model. The measure of performance is a quantity called subband perceptual rate, which the filter bank structure adapts to approach the perceptual entropy (PE) as closely as possible. In addition, this method is also amenable to progressive transmission, that is, it can achieve the best quality of reconstruction possible considering the size of the bit stream available at the encoder. The result is a variable-rate compression scheme for high-quality audio that takes into account the allowed computational complexity, the available bit-budget, and the psychoacoustic criteria for transparent coding. This paper thus provides a novel scheme to marry the results in wavelet packets and perceptual coding to construct an algorithm that is well suited to high-quality audio transfer for Internet and storage applications View full abstract»

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  • Conditions for convergence of a delayless subband adaptive filter and its efficient implementation

    Page(s): 1158 - 1167
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    This article considers the convergence characteristics of the delayless subband adaptive digital filters (ADFs) proposed by Morgan and Thi (see ibid., vol.43, p.1819-30, 1995). We derive a formula for the step-size parameter to ensure the convergence of ADPs and show that the derived formula enables self-adjusting of its value to ensure convergence regardless of the type of analysis filters employed or characteristics of the input signals. Consideration on the efficient implementation of the structure using short-length analysis filters is given through the results of simulations View full abstract»

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  • Balanced multiwavelets theory and design

    Page(s): 1119 - 1125
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    This article deals with multiwavelets, which are a generalization of wavelets in the context of time-varying filter banks and with their applications to signal processing and especially compression. By their inherent structure, multiwavelets are fit for processing multichannel signals. This is the main issue in which we are interested. First, we review material on multiwavelets and their links with multifilter banks and, especially, time-varying filter banks. Then, we have a close look at the problems encountered when using multiwavelets in applications, and we propose new solutions for the design of multiwavelets filter banks by introducing the so-called balanced multiwavelets View full abstract»

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  • Oversampled cosine-modulated filter banks with arbitrary system delay

    Page(s): 941 - 955
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    Design methods for perfect reconstruction (PR) oversampled cosine-modulated filter banks with integer oversampling factors and arbitrary delay are presented. The system delay, which is an important parameter in real-time applications, can be chosen independently of the prototype lengths. Oversampling gives us additional freedom in the filter design process, which can be exploited to find FIR PR prototypes for oversampled filter banks with much higher stopband attenuations than for critically subsampled filter banks. It is shown that for a given analysis prototype, the PR synthesis prototype is not unique. The complete set of solutions is discussed in terms of the nullspace of a matrix operator. For example, oversampling allows the design of PR filter banks having unidentical prototypes (of equal and unequal lengths) for the analysis and synthesis stage. Examples demonstrate the increased design freedom due to oversampling. Finally, it is shown that PR prototypes being designed for the oversampled case can also serve as almost-PR prototypes for critically subsampled cosine-modulated pseudo QMF banks View full abstract»

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  • Theory and design of signal-adapted FIR paraunitary filter banks

    Page(s): 920 - 929
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    We study the design of signal-adapted FIR paraunitary filter banks, using energy compaction as the adaptation criterion. We present some important properties that globally optimal solutions to this optimization problem satisfy. In particular, we show that the optimal filters in the first channel of the filter bank are spectral factors of the solution to a linear semi-infinite programming (SIP) problem. The remaining filters are related to the first through a matrix eigenvector decomposition. We discuss uniqueness and sensitivity issues. The SIP problem is solved using a discretization method and a standard simplex algorithm. We also show how regularity constraints may be incorporated into the design problem to obtain globally optimal (in the energy compaction sense) filter banks with specified regularity. We also consider a problem in which the polyphase matrix implementation of the filter bank is constrained to be DCT based. Such constraints may also be incorporated into our optimization algorithm; therefore, we are able to obtain globally optimal filter banks subject to regularity and/or computational complexity constraints. Numerous experiments are presented to illustrate the main features that distinguish adapted and nonadapted filters, as well as the effects of the various constraints. The conjecture that energy compaction and coding gain optimization are equivalent design criteria is shown not to hold for FIR filter banks View full abstract»

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  • Design of regular nonseparable bidimensional wavelets using Grobner basis techniques

    Page(s): 845 - 856
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    The design of two-dimensional (2-D) filter banks yielding orthogonality and linear-phase filters and generating regular wavelet bases is a difficult task involving the algebraic properties of multivariate polynomials. Using cascade forms implies dealing with nonlinear optimization. We turn the issue of optimizing the orthogonal linear-phase cascade from Kovacevic and Vetterli (1992) into a polynomial problem and solve it using Grobner basis techniques and computer algebra. This leads to a complete description of maximally flat wavelets among the orthogonal linear-phase family proposed by Kovacevic and Vetterli. We obtain up to five degrees of flatness for a 16×16 filter bank, whose Sobolev exponent is 2.11, making this wavelet the most regular orthogonal linear-phase nonseparable wavelet to the authors' knowledge, View full abstract»

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  • Formulas for orthogonal IIR wavelet filters

    Page(s): 1138 - 1141
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    Explicit solutions are given for the rational function P(z) for two classes of IIR orthogonal two-band wavelet bases, for which the scaling filter is maximally flat. P(z) denotes the rational transfer function H(z)H(1/z), where H(z) is the (lowpass) scaling filter. The first is the class of solutions that are intermediate between the Daubechies (1992) and the Butterworth wavelets. It is found that the Daubechies, the Butterworth, and the intermediate solutions are unified by a single formula. The second is the class of scaling filters realizable as a parallel sum of two allpass filters (a particular case of which yields the class of symmetric IIR orthogonal wavelet bases). For this class, a closed-form solution is provided by the solution to an older problem in group delay approximation by digital allpole filters View full abstract»

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  • Divide-and-conquer 2-D phase retrieval using subband decomposition and filter banks

    Page(s): 1152 - 1154
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    The two-dimensional (2-D) discrete phase-retrieval problem is to reconstruct a discrete-time signal whose support is known and compact from the magnitude of its discrete Fourier transform. We show how a subband decomposition of this problem can be performed using filter banks. The result is a series of smaller 2-D phase-retrieval problems whose solutions are the phases of the original problem in different frequency bands. The 2-D phase-retrieval problem is first mapped to a one-dimensional (1-D) phase-retrieval problem, and the subband decomposition is applied to this problem to decompose it into smaller 1-D problems, each of which can be viewed as a smaller 2-D problem. This is more flexible than performing the decomposition directly in 2-D. The filter must have finite support, zero phase, and be approximately halfband. While these results can also perform subband decomposition of any 1-D phase-retrieval problem, the general lack of uniqueness for 1-D phase retrieval creates problems in reassembling the solutions to the smaller 1-D problems View full abstract»

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  • Orthogonal multiwavelets with optimum time-frequency resolution

    Page(s): 830 - 844
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    A procedure to design orthogonal multiwavelets with good time-frequency resolution is introduced. Formulas to compute the time-durations and the frequency-bandwidths of scaling functions and multiwavelets are obtained. Parameter expressions for the matrix coefficients of the multifilter banks that generate symmetric/antisymmetric scaling functions and multiwavelets supported in [O,N] are presented for N=2,...,6. Orthogonal multiwavelets with optimum time-frequency resolution are constructed, and some optimal multifilter banks are provided View full abstract»

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  • Orthogonal transmultiplexers in communication: a review

    Page(s): 979 - 995
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    This paper presents conventional and emerging applications of orthogonal synthesis/analysis transform configurations (transmultiplexer) in communications. It emphasizes that orthogonality is the underlying concept in the design of many communication systems. It is shown that orthogonal filter banks (subband transforms) with proper time-frequency features can play a more important role in the design of new systems. The general concepts of filter bank theory are tied together with the application-specific requirements of several different communication systems. Therefore, this paper is an attempt to increase the visibility of emerging communication applications of orthogonal filter banks and to generate more research activity in the signal processing community on these topics View full abstract»

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  • Robust image transmission over energy-constrained time-varying channels using multiresolution joint source-channel coding

    Page(s): 1012 - 1026
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    We explore joint source-channel coding (JSCC) for time-varying channels using a multiresolution framework for both source coding and transmission via novel multiresolution modulation constellations. We consider the problem of still image transmission over time-varying channels with the channel state information (CSI) available at (1) receiver only and (2) both transmitter and receiver being informed about the state of the channel, and we quantify the effect of CSI availability on the performance. Our source model is based on the wavelet image decomposition, which generates a collection of subbands modeled by the family of generalized Gaussian distributions. We describe an algorithm that jointly optimizes the design of the multiresolution source codebook, the multiresolution constellation, and the decoding strategy of optimally matching the source resolution and signal constellation resolution “trees” in accordance with the time-varying channel and show how this leads to improved performance over existing methods. The real-time operation needs only table lookups. Our results based on a wavelet image representation show that our multiresolution-based optimized system attains gains on the order of 2 dB in the reconstructed image quality over single-resolution systems using channel optimized source coding View full abstract»

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  • Wavelet functions to estimate velocity in spatiotemporal signals

    Page(s): 1105 - 1118
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    This paper establishes a framework to estimate velocity from spatiotemporal signals using the wavelet transform and multiresolution techniques. Initial theory is derived with the assumption that the spatiotemporal signal can be represented by a polynomial of order M. Wavelet functions are derived for polynomials of different degree from which the velocity can be estimated as the ratio of two of the four components of a two dimensional (2-D) wavelet transform of the signal. We have characterized two classes of wavelet and scaling functions: one with nonuniform support and another with symmetry and uniform support. For a wavelet function of order M, the velocity estimates are exact if the signal can be represented by a polynomial of the same order or less. In many cases, the velocity error is very low, even when there is no match. We also present the error estimates for three different signals: a polynomial of degree four, a sinusoid (polynomial of degree infinity), and a function with analytical value for the velocity. The paper also demonstrates how error in the velocity estimates can be reduced by using multiresolution techniques. Even though results are presented using one-dimensional (1-D) signals, the extension to higher dimensions (images) is straightforward and uses the same wavelet functions derived in this paper View full abstract»

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  • FIR principal component filter banks

    Page(s): 930 - 940
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    Two-dimensional (2-D) principal component filter banks (PCFBs) of finite impulse response (FIR) are proposed. For 2-D signals, among all uniform paraunitary FIR analysis/synthesis filter banks, the FIR PCFBs have the most energy compaction and maximize the arithmetic mean to geometric mean ratio (AM/GM ratio) of subband variances, which is the theoretic coding gain (TCC) of the systems under proper assumptions. The theoretic proof and design techniques are provided. Several special cases are discussed. Experimental results show the potential power of the FIR PCFBs View full abstract»

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  • Design of hybrid filter banks for analog/digital conversion

    Page(s): 956 - 967
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    This paper presents design algorithms for hybrid filter banks (HFBs) for high-speed, high-resolution conversion between analog and digital signals. The HFB is an unconventional class of filter bank that employs both analog and digital filters. When used in conjunction with an array of slower speed converters, the HFB improves the speed and resolution of the conversion compared with the standard time-interleaved array conversion technique. The analog and digital filters in the HFB must be designed so that they adequately isolate the channels and do not introduce reconstruction errors that limit the resolution of the system. To design continuous-time analog filters for HFBs, a discrete-time-to-continuous-time (“Z-to-S”) transform is developed to convert a perfect reconstruction (PR) discrete-time filter bank into a near-PR HFB; a computationally efficient algorithm based on the fast Fourier transform (FFT) is developed to design the digital filters for HFBs. A two-channel HFB is designed with sixth-order continuous-time analog filters and length 64 FIR digital filters that yield -86 dB average aliasing error. To design discrete-time analog filters (e.g., switched-capacitors or charge-coupled devices) for HFBs, a lossless factorization of a PR discrete-time filter bank is used so that the reconstruction error is not affected by filter coefficient quantization. A gain normalization technique is developed to maximize the dynamic range in the finite-precision implementation. A four-channel HFB is designed with 9-bit (integer) filter coefficients. With internal precision limited to the equivalent of 15 bits, the maximum aliasing error is -70 dB, and with the equivalent of 20 bits internal precision, maximum aliasing is -100 dB. The 9-bit filter coefficients degrade the stopband attenuation (compared with unquantized coefficients) by less than 3 dB View full abstract»

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Aims & Scope

IEEE Transactions on Signal Processing covers novel theory, algorithms, performance analyses and applications of techniques for the processing, understanding, learning, retrieval, mining, and extraction of information from signals

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Meet Our Editors

Editor-in-Chief
Zhi-Quan (Tom) Luo
University of Minnesota