Showing papers in "IEEE Signal Processing Letters in 1996"

Noise reduction using an undecimated discrete wavelet transform

Abstract: A new nonlinear noise reduction method is presented that uses the discrete wavelet transform. Similar to Donoho (1995) and Donohoe and Johnstone (1994, 1995), the authors employ thresholding in the wavelet transform domain but, following a suggestion by Coifman, they use an undecimated, shift-invariant, nonorthogonal wavelet transform instead of the usual orthogonal one. This new approach can be interpreted as a repeated application of the original Donoho and Johnstone method for different shifts. The main feature of the new algorithm is a significantly improved noise reduction compared to the original wavelet based approach. This holds for a large class of signals, both visually and in the l/sub 2/ sense, and is shown theoretically as well as by experimental results.

A fuzzy filter for images corrupted by impulse noise

Abstract: A new operator is presented which adopts a fuzzy logic approach for the enhancement of images corrupted by impulse noise. The proposed operator is based on two-step fuzzy reasoning, and it is able to perform a very strong noise cancellation while preserving image details very well. The new fuzzy filter is favorably compared with other nonlinear operators in the literature.

A DCT-based embedded image coder

Abstract: Since Shapiro (see ibid., vol.41, no.12, p. 445, 1993) published his work on embedded zerotree wavelet (EZW) image coding, there have been increased research activities in image coding centered around wavelets. We first point out that the wavelet transform is just one member in a family of linear transformations, and the discrete cosine transform (DCT) can also be coupled with an embedded zerotree quantizer. We then present such an image coder that outperforms any other DCT-based coder published in the literature, including that of the Joint Photographers Expert Group (JPEG). Moreover, our DCT-based embedded image coder gives higher peak signal-to-noise ratios (PSNR) than the quoted results of Shapiro's EZW coder.

On bandlimited signals with fractional Fourier transform

Abstract: We study bandlimited signals with fractional Fourier transform (FRFT). We show that if a nonzero signal f is bandlimited with FRFT F/sub /spl alpha// for a certain real /spl alpha/, then it is not bandlimited with FRFT F/sub /spl beta// for any /spl beta/ with /spl beta//spl ne//spl plusmn//spl alpha/+n/spl pi/ for any integer n. This is a generalization of the fact that a nonzero signal can not be both timelimited and bandlimited. We also provide sampling theorems for bandlimited signals with FRFT that are similar to the Shannon sampling theorem.

On the relationship between the Fourier and fractional Fourier transforms

Abstract: In recent years, the fractional Fourier transform has been the focus of many research papers. In this letter, we show that the fractional Fourier transform is nothing more than a variation of the standard Fourier transform and, as such, many of its properties, such as its inversion formula and sampling theorems, can be deduced from those of the Fourier transform by a simple change of variable.

Contrasts for multichannel blind deconvolution

Abstract: A class of optimization criteria is proposed whose maximization allows us to carry out blind multichannel deconvolution in the presence of additive noise. Contrasts presented in the paper encompass those related to source separation and independent component analysis problems.

Adaptive matched filter detection in spherically invariant noise

Abstract: The article addresses radar detection of coherent pulse trains embedded in spherically invariant noise with unknown statistics. Starting upon a newly proposed detector, which assumes knowledge of the structure of the clutter covariance matrix, we substitute the actual matrix by a proper estimate based on a set of secondary data vectors. Interestingly, the resulting detector achieves a constant false alarm rate with respect to the texture component of the clutter, and incurs an acceptable loss with respect to the case of a known covariance matrix.

FIR filter design for frequency invariant beamformers

Abstract: Two methods of implementing FIR filters for a frequency invariant beamformer are presented. Each of these methods uses a single underlying set of filter coefficients obtained directly from the desired beamformer response. One method uses multirate processing, and the other is based on a single sampling rate.

Analysis of nonlinear FM signals by pattern recognition of their time-frequency representation

Abstract: The aim is to propose a method for detection and parameter estimation of nonlinear FM signals, mono- or multicomponent, embedded in white Gaussian noise. The proposed approach consists in mapping the signal into the time-frequency plane by a time-frequency distribution with reassignment, and then in applying a pattern recognition technique, like the Hough transform, to the time-frequency representation to recognize specific shapes. The advantages of this method over the conventional maximum likelihood estimator are (1) a simpler implementation, because it reduces the dimension of the search space and (2) a consistent attenuation of the interference terms between different components of a signal or between signal and noise.

The rational filter for image smoothing

Abstract: A nonlinear operator is presented that is able to effectively attenuate the noise that corrupts an image while introducing small distortions on the image details. It is described by a rational function, i.e., by the ratio of two polynomials in the input variables. Notwithstanding its simplicity, this operator proves to be more powerful than conventional methods for many noise distributions.

On a class of computationally efficient, rapidly converging, generalized NLMS algorithms

Abstract: Over the last decade, a certain computationally efficient, rapidly converging adaptive filtering algorithm has been independently discovered many times. The algorithm can be viewed as a generalization of the normalized LMS (NLMS) algorithm that updates on the basis of multiple input signal vectors. This article compares and discusses the different approaches to and embellishments of the basic algorithm, and contrasts the various interpretations from different perspectives.

Regularization techniques for discrete cepstrum estimation

Abstract: Traditional spectral envelope estimation methods suffer from significant drawbacks in (high-pitched) voiced segments: spectral peaks tend to be biased toward pitch harmonics. To alleviate this drawback, discrete modeling techniques have been proposed. The discrete cepstrum method consists in fitting a spectral envelope parameterized by cepstrum coefficients to a discrete set of spectral points using a log-spectral distortion criterion. Unfortunately, this estimation problem is ill conditioned in many cases of interest. The article introduces a simple regularization technique that guarantees that the spectral envelope is well behaved. A modification of the basic regularization criterion is proposed in order to take into account a possible prior knowledge of the spectral tilt of the envelope.

An improved single frequency estimator

Abstract: A new method for estimating the frequency of a complex sinusoid in complex white Gaussian noise is proposed. Its computational complexity is comparable to Kay's method [1989], but it attains the Cramer-Rao bound (CRB) down to lower signal-to-noise ratio (SNR) values. Simulation results are included to demonstrate the performance of the proposed method.

Sampling requirements for Volterra system identification

Abstract: Volterra systems generally produce-due to nonlinearity-an output signal with a higher frequency range when compared with the input signal. Hence, it seems necessary to sample the input and output signals at twice the maximum frequency of the output signal. The article shows that it is sufficient to sample at twice the maximum frequency of the input signal. A discrete-time Volterra system also produces the additional frequency components that appear-due to aliasing-at the sampled output of a continuous-time Volterra system with an equivalent transfer function.

A multichannel affine projection algorithm with applications to multichannel acoustic echo cancellation

Abstract: A straightforward generalization of the so-called affine projection algorithm (APA) to the multichannel (MC) case is easily obtained. However, due to the strong correlation between the input signals of the various channels, the resulting algorithm converges very slowly. The article describes the way to overcome this problem and derives an efficient algorithm that makes use of additional orthogonal projections.

Signal conditioning techniques for robust speech recognition

Abstract: Acoustic mismatch encountered in various training and testing conditions of hidden Markov model (HMM) based systems often causes severe degradation in speech recognition performance. For telephone based speech recognition tasks, acoustic mismatch can arise from various sources, such as variations in telephone handsets, ambient noise, and channel distortions. This paper presents three techniques for blind channel equalization, namely, cepstral mean subtraction (CMS), signal bias removal (SBR) and hierarchical signal bias removal (HSBR). Experimental results on various connected digits databases show a reduction in the digit error rate by 16%, 21%, and 28% when employing CMS, SBR, and HSBR, respectively. Our results also demonstrate that the HSBR technique outperforms SBR and CMS on every sub-data collection and exhibits consistent improvements even for short utterances.

Effect of fractional Fourier transformation on time-frequency distributions belonging to the Cohen class

Abstract: We consider the Cohen (1989) class of time-frequency distributions, which can be obtained from the Wigner distribution by convolving it with a kernel characterizing that distribution. We show that the time-frequency distribution of the fractional Fourier transform of a function is a rotated version of the distribution of the original function, if the kernel is rotationally symmetric. Thus, the fractional Fourier transform corresponds to rotation of a relatively large class of time-frequency representations (phase-space representations), confirming the important role this transform plays in the study of such representations.

Inversion of the Van der Monde matrix

Abstract: We deduce an analytical formula for inversion of a complex Van der Monde matrix. It has applications in signal reconstruction, spectral estimation, system identification, as well as in other important signal processing problems. Previously the inversion of such a matrix has been performed by approximations; we further deduce an exact inversion formula.

Stochastic models for DIV-CURL optical flow methods

Abstract: We consider Suter's (see Proc. CVPR94, Seattle, p.939-948, 1994) DIV-CURL optical flow methods, wherein the problem of computing a velocity field from an image sequence is regularized using smoothness conditions based on the divergence and curl of the field. In particular, we develop stochastic formulations of DIV-CURL splines using the linear smoothing theory of Adams, Willsky, and Levy. Our models are shown to be well posed and thus can be used in both simulating and estimating velocity fields having known stochastic properties. As a special case, our stochastic model reduces to that developed by Rougee, Levy, and Willsky (1984) for the classical Horn and Schunck's (1981) optical flow.

Variable-dimension vector quantization

Abstract: In many signal compression applications, the evolution of the signal over time can be represented by a sequence of random vectors with varying dimensionality. Frequently, the generation of such variable-dimension vectors can be modeled as a random sampling of another signal vector with a large but fixed dimension. Efficient quantization of these variable-dimension vectors is a challenging task and a critical issue in speech coding algorithms based on harmonic spectral modeling. We introduce a simple and effective formulation of the problem and present a novel technique, called variable-dimension vector quantization (VDVQ), where the input variable-dimension vector is directly quantized with a single universal codebook. The application of VDVQ to low bit-rate speech coding demonstrates significant gain in subjective quality as well as in rate-distortion performance over prior indirect methods.

Instantaneous frequency estimation using linear prediction with comparisons to the DESAs

Abstract: Four nonlinear instantaneous frequency estimators are derived by symbolically expressing the output of linear predictive techniques in terms of the input data samples The estimators are similar in form to the instantaneous frequency estimators associated with the discrete energy separation algorithms (DESAs) The mean absolute error and root mean square error (RMSE) of the new frequency estimators compare favorably with those of the DESAs for a specified class of AM-FM/cosine signals The new estimators also require fewer computations than the DESA frequency estimators

Fuzzy statistics of digital images

Abstract: The notion of first- and second-order fuzzy statistics of digital images is presented. Owing to the inherent imprecision in the gray values, fuzzy statistics have been observed to behave better in representing the spatial gray distribution in a digital image.

A note on non-Gaussian adaptive array detection and signal parameter estimation

Abstract: Kelly's (1986) generalized likelihood ratio test (GLRT) statistic is reexamined under a broad class of data distributions known as complex multivariate elliptically contoured (MEC), which include the complex Gaussian as a special case. We show that, mathematically, Kelly's GLRT test statistic is again obtained when the data matrix is assumed to be MEC distributed. The maximum-likelihood (ML) estimate for the signal parameters-alias the sample-covariance-based (SCB) minimum variance distortionless response beamformer output and, in general, the SCB linearly constrained minimum variance beamformer output-is likewise shown to be the same. These results have significant robustness implications for adaptive detection/estimation/beamforming in non-Gaussian environments.

Computing partial DFT for comb spectrum evaluation

Abstract: A comb spectrum evaluation problem arises in the (de)modulation for orthogonal frequency division multiplexing-based (OFDM-based) multichannel communication system. Efficient algorithms for this special type of partial discrete Fourier transform (DFT) computation are studied. For an M-component comb spectrum evaluation with transform length N, it is shown that only O(N+MlogM) multiplications are needed, compared with O(NlogM) multiplications necessary for a narrowband spectrum evaluation. Pruning radix-2 decimation-in-time fast Fourier transform (FFT) requires only (N/4+M/2log/sub 2/M-M) nontrivial complex multiplications. The frequency shift technique has also been applied to allow a modularized mixed-radix structure for the computation of comb spectrum with an initial component not starting from zero frequency point.

Characteristics of band-limited channels unidentifiable from second-order cyclostationary statistics

Abstract: Several works on blind channel identification and equalization rely on a system model with multiple sub-channels driven by a single input. These methods depend on a critical condition that no common zero exists among the sub-channels. We aimed at establishing the physical significance of this critical zero condition and understanding the limitation of methods based on second-order statistics, By deriving a number of sufficient conditions, we characterize several classes of band-limited channels that are not identifiable from only the second-order statistics of the channel output.

Blind phase recovery in QAM communication systems using higher order statistics

Abstract: We present a method for phase recovery in QAM communication systems based on higher order statistics. Under the assumption that the QAM signals have independent, identically distributed (i.i.d.) in-phase and quadrature components, we derive the relation between the phase error and the fourth-order cumulant of the output. Numerical performance of the approach is demonstrated by computer simulation.

Regressive implementations for the forward and inverse MDCT in MPEG audio coding

Abstract: Modified discrete cosine transform (MDCT) and inverse modified discrete cosine transform (IMDCT) are two of the most compute-intensive operations in layer III of the MPEG audio coding standard. We first derive two sinusoidal recursive formulas for the transform kernels of the MDCT and IMDCT. Then we demonstrate that general length of MDCT and IMDCT can be efficiently implemented by using the regressive structure derived from the sinusoidal recursive formulas. The proposed regular structure is particularly suitable for parallel VLSI realization. Besides, it also provides an efficient on-line computation scheme and is especially suitable for the computation of variable length MDCT and IMDCT when involving dynamical window switching in the MPEG audio coding standard.

L-class of time-frequency distributions

Abstract: The L-class of distributions for time-frequency signal analysis is derived and presented, generalizing the L-Wigner distribution. Some particular distributions belonging to this class are introduced.

Effort constraints in adaptive feedforward control

Abstract: Adaptive algorithms are presented for constrained multichannel feedforward control. They minimize the sum of squared error signals while limiting the value of either the sum of squared control signals (total effort) or the mean square value of each individual control signal (individual efforts). It is shown that the exact least squares solutions for these problems have a simple form, which can be approached with an adaptive algorithm. The properties of the resulting algorithm are illustrated by simulation.

Performance analysis of closed-form, ESPRIT based 2-D angle estimator for rectangular arrays

Abstract: The 2D DFT beamspace ESPRIT is an algorithm for use in conjunction with uniform rectangular arrays (URAs) that provides automatically paired azimuth and elevation angle estimates of incident signals via a closed-form procedure. We investigate the statistical performance of 2D DFT beamspace ESPRIT. Expressions for the 2D DFT beamspace ESPRIT estimator variances are obtained. Samples variances of the azimuth and elevation angle estimates obtained through Monte Carlo simulations are shown to be in close agreement with theoretically predicted variances.