IEEE Transactions on Signal Processing

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 p... View full abstract»

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 inform... View full abstract»

We investigate improved detectors for transmultiplexer-based high bit rate transmission over dispersive channels like telephone wires. The transmitter is based on a synthesis stage. For the receiver, we design fractionally spaced single-input/multiple-output linear detectors, possibly upgraded with a multiple-input/multiple-output decision-feedback section, for an MMSE criterion. The performance o... View full abstract»

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 d... View full abstract»

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 desig... View full abstract»

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 reconstruct... View full abstract»

This article describes efficient schemes for the computation of a large number of differently scaled/oriented filtered versions of an image. We generalize the well-known steerable/scalable (“deformable”) filter bank structure by imposing X-Y separability on the basis filters. The resulting systems, designed by an iterative projections technique, achieve substantial reduction of the com... View full abstract»

A new approach for recognizing the iris of the human eye is presented. Zero-crossings of the wavelet transform at various resolution levels are calculated over concentric circles on the iris, and the resulting one-dimensional (1-D) signals are compared with model features using different dissimilarity functions View full abstract»

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... View full abstract»

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, ... View full abstract»

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 implementatio... View full abstract»

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... View full abstract»

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 employ... View full abstract»

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 postpro... View full abstract»

We present a new approach to filtering and reconstruction of periodic signals. The tool that proves to handle these tasks very efficiently is the discrete Zak transform. The discrete Zak transform can be viewed as the discrete Fourier transform performed on the signal blocks. It also can be considered the polyphase representation of periodic signals. Fast filtering-decimation-interpolation-reconst... View full abstract»

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 th... View full abstract»

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 ti... View full abstract»

This paper describes a new motion estimation algorithm that is potentially useful for both computer vision and video compression applications. It is hierarchical in structure, using a separable two-dimensional (2-D) discrete wavelet transform (DWT) on each frame to efficiently construct a multiresolution pyramid of subimages. The DWT is based on a complex-valued pair of four-tap FIR filters with G... View full abstract»

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 a... View full abstract»

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 prope... View full abstract»

New lapped transforms are introduced. The lapped biorthononal transform (LBT) and hierarchical lapped biorthogonal transform (HLBT) are appropriate for image coding, and the modulated HLBT biorthogonal transform (MMLBT) and nonuniform modulated lapped biorthogonal transform (NMLBT) are appropriate for audio coding. The HLBT has a significantly lower computational complexity than the lapped orthogo... View full abstract»

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»

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»

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 polynom... View full abstract»