This paper unifies commonly used accelerated stochastic gradient methods (Polyak’s Heavy Ball, Nesterov’s Accelerated Gradient and Adaptive Moment Estimation (Adam)) as specific cases of a general lowpass regularized learning framework, the Automatic Stochastic Gradient Method (AutoSGM). For AutoSGM, we derive an optimal iteration-dependent learning rate function and realize an approximation. Adam is also an approximation of this optimal approach that replaces the iteration-dependent learning-rate with a constant. Empirical results on deep neural networks comparing the learning behavior of AutoSGM equipped with this iteration-dependent learning-rate algorithm demonstrate fast learning behavior, robustness to the initial choice of the learning rate, and can tune an initial constant learning-rate in applications where a good constant learning rate approximation is unknown.

This paper presents a new tomography-based anomaly mapping algorithm for composite structures. The system consists of an array of piezoelectric transducers which sequentially excites the structure and collects the resulting waveform at the remaining transducers. Anomaly indices computed from the sensor waveforms are fed as input to the mapping algorithm. The output of the algorithm is a color map indicating the outline of damage on the structure when present. Unlike prior work on this topic, the algorithm of this paper explicitly accounts for both sparsity and cluster pattern structures that are typical of structural anomalies. Hence, the algorithm of this paper provides excellent reconstruction accuracy by incorporating the available prior information on the anomaly map. Experimental results on a unidirectional composite plate confirms that the algorithm of this paper outperforms two competing methods in terms of reconstruction accuracy.

A model-based pre-equalizer for propagation-induced distortion of acoustic waveforms in an air-filled waveguide at high sound pressure levels is developed. The nonlinear distortions introduced by propagation are modeled using Burgers propagation model. This equalizer is stimulus-independent and mitigates nonlinear distortion at some predefined distance in the waveguide. The pre-equalizer digitally propagates the waveform backwards using a sign-inverted propagation model. The output of the pre-equalizer is fed to the waveguide. When the forward model completely characterizes the waveguide, the waveforms arriving at the chosen destination will be identical to a delayed version of the input signal fed to the pre-equalizer. Experimental evaluations employing sinusoidal and multitone stimuli demonstrated approximately a two-fold reduction in the intermodulation distortion and a four-fold reduction in total harmonic distortion at low frequencies. These results represented a two-fold improvement over a model-based method available in the literature.

This paper presents a framework for shared, human-machine control of a prosthetic arm. The method employs electromyogram and peripheral neural signals to decode motor intent, and incorporates a higher-level goal in the controller to augment human effort. The controller derivation employs Markov Decision Processes. The system is trained using a gradient ascent approach in which the policy is parameterized using a Kalman Filter and the goal is incorporated by adapting the Kalman filter output online. Results of experimental performance analysis of the shared controller when the goal information is imperfect are presented in the paper. These results, obtained from an amputee subject and a subject with intact arms, demonstrate that a system controlled by the human user and the machine together exhibit better performance than systems employing machine-only or human-only control.

This paper presents a likelihood-based method for automatically identifying different quadrature amplitude modulations (QAM) and phase-shift keying (PSK) modulations. This algorithm selects the modulation type that maximizes a log-likelihood function based on the known probability distribution associated with the phase or amplitude of the received signals for the candidate modulation types. The approach of this paper does not need prior knowledge of carrier frequency or baud rate. Comparisons of theory and simulation demonstrate good agreement in the probability of successful modulation identification under different signal-to-noise ratios (SNRs). The probability of successful identification results in the simulation results show that under additive white Gaussian noise, the system can identify BPSK, QPSK, 8PSK, and QAMs of order 16, 32, 64, 128, and 256 above 99% accuracy at 4-dB SNR when the two other competing methods available in the literatures cannot for an input signal containing 10 000 symbols and 20 samples per symbol. The simulation results also indicate that when the input signal length decreases, the system needs higher SNRs in order to get accurate identification results. Finally, simulations under different noisy environments indicate that the algorithm is robust to variations of noise environments different from the assumed model in the derivations.

This paper presents a framework for modeling neural decoding using electromyogram (EMG) and electrocorticogram (ECoG) signals to interpret human intent and control prosthetic arms. Specifically, the method of this paper employs Markov Decision Processes (MDP) for neural decoding, parameterizing the policy using an artificial neural network. The system is trained using a modification of the Dataset Aggregation (DAgger) algorithm. The results presented here suggest that the approach of the paper performs better than the state-of-the-art.

This paper reviews technologies and signal processing algorithms for decoding peripheral nerve and electrocorticogram signals to interpret human intent and control prosthetic arms. The review includes a discussion of human motor system physiology and physiological signals that can be used to decode motor intent, electrode technology for acquiring neural data, and signal processing methods including decoders based on Kalman filtering and least-squares regressors. Representative results from human experiments demonstrate the progress that has been made in neural decoding and its potential for developing neuroprosthetic arms that act and feel like natural arms.

Impact location estimation techniques are important components of Structural Health Monitoring systems. This paper considers impact location estimation in composite structures using acoustic emission signals arriving at a passive sensor array attached to the structure. Because composite structures are anisotropic, the wave propagation properties depend both on the direction of propagation and the location on the structures. As a result, this is a substantially more difficult problem than that of impact location estimation in isotropic media. The algorithm presented in this paper uses three sensor clusters and formulates the impact location estimation problem as one of minimizing a quadratic objective function. Unlike many published location estimation algorithms, the algorithm in this paper does not require the waveform velocity profile for the structure. Experimental results demonstrating the ability of the algorithm to accurately estimate the impact location using acoustic emission signals is included in the paper.

Kalman filters have been used to decode neural signals and estimate hand kinematics in many studies. However, most prior work assumes a linear system model, an assumption that is almost certainly violated by neural systems. In this paper, we show that adding nonlinearities to the decoding algorithm improves the accuracy of tracking hand movements using neural signal acquired via a 32-channel micro-electrocorticographic (μECoG) grid placed over the arm and hand representations in the motor cortex. Experimental comparisons indicate that a Kalman filter with a fifth order polynomial generative model relating the hand kinematics signals to the neural signals improved the mean-square tracking performance in the hand movements over a conventional Kalman filter employing a linear system model. This finding is in accord with the current neurophysiological understanding of the decoded signals.

This paper presents a novel equalizer for nonlinear distortions in direct-radiator loudspeakers in a closed cabinet by constructing an exact inverse of an electro-mechanical model of the loudspeaker. This exact inverse compensates for distortions introduced by excursion and current-dependent nonlin-earities. The equalizer compensates for the nonlinearities in the force factor, voice coil inductance, eddy currents and the stiffness of the loudspeaker. Simulation results demonstrating substantial reduction in the harmonic distortions at the output of the loudspeaker are included in this paper.

This paper presents a phase likelihood-based method for automatically identifying different phase-shift keying (PSK) modulations. This method identifies the PSK signals as the hypothesis for which the likelihood function of phase difference between nearby samples of the received signal is the maximum. This method does not need prior knowledge of carrier frequency or baud rate and can identify modulation types at relatively low signal-to-noise ratio (SNR) and using small number of input samples. Simulation results demonstrate that this algorithm can identify BPSK, QPSK and BPSK signals with 100% accuracy with only 1000 symbols when the SNR of the input signal is better than 7 dB. Additional simulation results demonstrating the robustness of the algorithm to variations of the noise characteristics from the assumed Gaussian model are also included in the paper. Performance comparisons indicate that the approach of this paper can achieve 100% accuracy in modulation identification at 5-7 dB lower SNR than competing methods available in the literature.

This paper describes an adaptive algorithm for selecting perelectrode stimulus intensities and inter-electrode stimulation phasing to achieve desired isometric plantar-flexion forces via asynchronous, intrafascicular multi-electrode stimulation. The algorithm employed a linear model of force production and a gradient descent approach for updating the parameters of the model. The adaptively selected model stimulation parameters were validated in experiments in which stimulation was delivered via a Utah Slanted Electrode Array that was acutely implanted in the sciatic nerve of an anesthetized feline. In simulations and experiments, desired steps in force were evoked, and exhibited short time-to-peak (<; 0.5 s), low overshoot (<; 10%), low steady-state error (<; 4%), and low steady-state ripple (<; 12%), with rapid convergence of stimulation parameters. For periodic desired forces, the algorithm was able to quickly converge and experimental trials showed low amplitude error (mean error <; 10% of maximum force), and short time delay (<; 250 ms).

Digital hearing aids identify acoustic feedback signals and cancel them continuously in a closed loop with an adaptive filter. This scheme facilitates larger hearing aid gain and improves the output sound quality of hearing aids. However, the output sound quality deteriorates as the hearing aid gain is increased. This paper presents two methods to modify the forward path gain in digital hearing aids. The first approach employs a variable, frequency-dependent gain function that is lower at frequencies of the incoming signal where the information is perceptually insignificant. The second method of this paper automatically identifies and suppresses residual acoustical feedback components at frequencies that have the potential to drive the system to instability. The suppressed frequency components are monitored and the suppression is removed when such frequencies no longer pose a threat to drive the hearing aid system into instability. Together, the gain processing methods of this paper provide 8 to 12 dB more hearing aid gain than feedback cancelers with fixed gain functions. Furthermore, experimental results obtained with real world hearing aid gain profiles indicate that the gain processing methods of this paper, individually and combined, provide less distortion in the output sound quality than classical feedback cancelers enabling the use of more comfortable style hearing aids for patients with moderate to profound hearing loss.

The paper discusses computationally efficient NLMS and RLS algorithms for a broad class of nonlinear filters using periodic input sequences. The class comprises all nonlinear filters whose output depends linearly on the filter coefficients. The algorithms presented in the paper are exact, suitable for identification and tracking of every nonlinear system in the class, and require a real-time computational effort of a single multiplication, an addition, and a subtraction per input sample. The transient and steady-state behavior of the algorithms are discussed and the effect of a model mismatch between the unknown system and the adaptive filter is also analyzed. The low computational complexity, good performance, and applicability of the algorithm to a large class of nonlinear systems make the approach of this paper a valuable alternative to the current techniques for nonlinear system identification.

Acoustic feedback limits the gain provided by hearing aids. Digital hearing aids identify acoustic feedback signals and cancel them continuously in a closed loop with an adaptive filter in the digital domain. This scheme facilitates larger hearing aid gain and improves the output sound quality of hearing aids. However, the output sound quality of hearing aids deteriorates as the hearing aid gain is increased. This paper automatically identifies and suppresses residual acoustical feedback components at frequencies that have the potential to drive the system to instability. The suppressed frequency components are monitored and the suppression is removed when such frequencies no longer pose a threat to drive the hearing aid system into instability. Experimental results obtained with real world hearing aid gain profiles using speech and music signals indicate that the method of this paper provides less distortion in the output sound quality than classical feedback cancelers enabling the use of more comfortable style hearing aids for patients with moderate to profound hearing loss.

Digital signal processing in modern hearing aids is typically performed in a subband or transform domain that introduces analysis-synthesis delays in the forward path. Long forward-path delays are not desirable because the processed sound combines with the unprocessed sound that arrives at the cochlea through the vent and changes the sound quality. Nonetheless, subband domain processing for digital hearing aids is the most popular choice for hearing aids because of the associated computational simplicity. In this paper, we present an alternative digital hearing aid structure with low-delay characteristics. The central idea in the paper is a low-delay spectral gain shaping method (SGSM) that employs parallel parametric equalization (EQ) filters. The low-delay SGSM provides frequency-dependent amplification for hearing loss compensation with low forward path delays and performs dynamic signal processing such as noise suppression and dynamic range compression. Parameters of the parametric EQ filters and associated gain values are selected using a least-squares approach to obtain the desired spectral response. The low-delay structure also employs an off-the-forward-path, frequency domain adaptive filter to perform acoustic feedback cancellation. Extensive MATLAB simulations and subjective evaluations of the results indicate that the method of this paper is competent with a state-of-the-art digital hearing aid system, but exhibits much smaller forward-path delays.

Adaptive filters are commonly used to cancel acoustic feedback in hearing aids. The sound quality of hearing aids deteriorates as the hearing aid gain is increased. This paper presents a method that increases gain possible in hearing aids by automatically identifying and suppressing residual acoustical feedback components that have the potential to drive the system to instability. The increase in the hearing aid gain over traditional methods and the output sound quality were evaluated using subjective tests. The results indicate that the method of this paper provides 6 to 8 dB more hearing aid gain and less perceptual distortion in the output sound quality than several competing algorithms to improve the performance of adaptive feedback cancellers.

Adaptive filters are commonly used to cancel acoustic feedback in hearing aids. The sound quality of hearing aids deteriorates as the hearing aid gain is increased. This paper presents a method to alter the gain function in digital hearing aids to provide additional amplification and better output sound quality. This approach employs a variable, frequency-dependent gain function that is lower at frequencies of the incoming signal where the information is perceptually insignificant. The increase in stable gain over traditional methods and the output sound quality were evaluated with a psychoacoustic experiment on normal-hearing listeners. The results indicate that the method of this paper provides more hearing aid gain and less distortion in the output sound quality than feedback cancelers with fixed gain functions.

This paper describes a method for jointly designing the crosstalk cancellation filters to facilitate binaural rendering of audio through loudspeakers. The minimax criterion is used to design the immersive audio rendering filters having finite impulse responses for a single listener using loudspeakers. The work presented is applied to the traditional Atal-Schroeder crosstalk canceler structure. The minimax approach provides improved low frequency performance and a better overall separation of the direct path and cross path transfer functions than the conventional least-squares designs.

This paper presents a method for jointly designing immersive audio rendering filters for a single listener using loudspeakers. The filters for crosstalk cancellation are assumed to have finite impulse responses and are designed using the minimax criterion. In addition to the traditional Atal-Schroeder crosstalk canceler structure, this paper explores an alternate topology that requires the approximation of a single filter. In general, the minimax approach provides improved low-frequency performance leading to a better overall separation of the direct-path and cross-path transfer functions than least-squares designs. The performance of the single-filter structure is better than that of the traditional crosstalk cancellation structure.

Howling is a significant problem even in digital hearing aids equipped with adaptive feedback cancellation. Among the many causes of howling is the inability of the adaptive filter to track rapid changes in the feedback path. Many systems use howling detectors to detect the start of howling and reduce the hearing aid gain for several seconds to avoid prolonged howling. Unfortunately the inadequate speech pressure levels (SPL) during times when the gain is reduced causes loss of information and reduced intelligibility of speech signals arriving at the patient's ears. This paper presents a new method that switches to a least-squares adaptation scheme with linear complexity at the onset of howling. The method adapts to the altered feedback path quickly and allows the patient to not lose perceivable information. The complexity of the least-squares estimate is reduced by reformulating the least-squares estimate into a Toeplitz system and solving it with a direct Toeplitz solver. In addition, the gain function is changed immediately after howling detection in such a way that the system operates in a stable manner and the distortions caused are not perceived because of temporal masking. Simulation results comparing with a conventional method is presented in the paper to demonstrate the superior howling suppression capabilities of the method

This paper presents a novel approach for implementing immersive audio rendering filters for a single listener using loudspeakers. We address the problem of crosstalk cancellation inherent in loudspeaker rendering and propose to implement the crosstalk cancellation filters using minimax finite impulse response (FIR) filters. The formulation is based on the Atal-Schroeder crosstalk canceller. The use of the optimal FIR filter design procedure ensures significant amount of separation between the direct path and the cross path. An alternative topology which requires the approximation of just one filter has also been explored using the same design principles. The minimax techniques provides superior solutions as compared to a least-squares design and the alternate structure is shown to be robust in its performance.

The paper describes an approach for the identification of static nonlinearities from input-output measurements. The approach is based on a minimax approximation of memoryless nonlinear systems using Chebyshev polynomials. For memoryless nonlinear systems that are finite and continuous with finite derivatives, it is known that the error caused by the Kth order Chebyshev approximation in a specified interval is bounded by a quantity that is proportional to the maximum value of the (K+1)th derivative of the input-output relationship and decays exponentially with K. The described method identifies the system by first estimating the system output at the Chebyshev nodes using a localized linear model around the nodes, and then solving for the coefficients associated with the Chebyshev polynomials of the first kind.

We consider the problem of channel estimation and tracking in OFDM systems and explore the idea of adding pilot symbols to the data symbols as a means of conserving bandwidth. The term pilot embedding (PE) is used to refer to this scheme. Compared to the pilot insertion (PI) scheme, i.e., the conventional pilot symbol assisted modulation (PSAM), PE is more bandwidth efficient since no separate subcarriers/timeslots are allocated to pilots. We formalize this by evaluating the capacity of the two schemes and showing that PE indeed has the potential to transmit at a higher rate. The problem of channel tracking using a decision directed approach is reviewed and found to be unreliable, in the sense that the channel estimator fails to track the channel variations after some iterations because of unavoidable decision errors. We propose an ad hoc channel estimation algorithm that uses the embedded pilots along with the past decisions of data for reliable tracking of the channel.

The paper presents a novel method to predict hypertensive disorders in pregnancy using coherence analysis. Previous studies suggest that there is inadequate secondary trophoblast invasion in hypertensive pregnancies implying that there are differences in the functional relationships between the maternal and fetal circulations. Magnitude squared coherence (MSC) is a function with values between 0 and 1 that indicates how well two waveforms correspond to each other in the frequency domain. The results presented using the MSC of maternal and fetal blood flow velocity waveforms indicate that in complicated hypertensive pregnancies its value is lower than in non-hypertensive controls. With additional validation, this method has the potential to provide an early test for hypertensive obstetric complications.

This paper presents an almost sure (a.s.) mean-square performance analysis of an adaptive Hammerstein filter for the case when the measurement noise in the desired response signal is a martingale difference sequence. The system model consists of a series connection of a memoryless nonlinearity followed by a recursive linear filter. It is shown under the conditions of the analysis that the long-term time average of the squared excess estimation error of the adaptive filter can be made arbitrarily close to zero.

This letter shows that the single frequency approximation for a narrowband lowpass signal embedded in white noise using the Pisarenko harmonic decomposition algorithm is approximately the power-weighted mean frequency of the signal. Experimental results indicate that this method is superior to a commonly used Fourier transform based mean frequency estimation method.

Heart rate variability (HRV) provides important information about the development of the cardiovascular system in fetuses. The paper presents a new measure of fetal HRV that can be estimated using Doppler ultrasound techniques. This measure employs the multiple signal characterization (MUSIC) algorithm which is a high-resolution method for estimating the frequencies of sinusoidal signals embedded in white noise from short-duration measurements. We show that the product of the square-root of the estimated signal-to-noise ratio (SNR) and the variance of the frequency estimates is independent of the noise level in the signal. Since variations in the angle of incidence of the Doppler ultrasound beam effectively changes the input SNR, this measure of HRV is robust to the input noise as well as the angle of incidence. Presented analysis results validate the robustness properties and the usefulness of the HRV measure.

Many applications involving Doppler signals require the accurate estimation of the power-weighted mean frequency over short durations of the signal due to it's nonstationarity. This paper presents a novel algorithm for estimating mean frequencies using the eigenstructure of the covariance matrix of the Doppler data. Experimental results indicate that this method is superior to the competing non-parametric methods.

This paper presents an algorithm that adapts the parameters of a Hammerstein system model. Hammerstein systems are nonlinear systems that contain a static nonlinearity cascaded with a linear system. In this, work, the static nonlinearity is modeled using a polynomial system and the linear filter that follows the nonlinearity is an infinite impulse response system. The adaptation of the nonlinear components is enhanced in the algorithm by orthogonalizing the inputs to the coefficients of the polynomial system. The linear system is implemented as a recursive higher-order filter. The step sizes associated with the recursive components are constrained in such a way as to guarantee bounded-input, bounded-output stability of the overall system. Experimental results included in the paper show that the algorithm performs well and always converges to the global minimum if the input signal is white.

This paper is concerned with the blind identification of bilinear systems excited by higher-order white noise. Unlike prior work that restricted the bilinear system model to simple forms and required the excitation to be Gaussian distributed, the results of this paper are applicable to a more general class of bilinear systems and for the case when the excitation is non-Gaussian. We describe an estimation procedure for the computation of the system parameters using output cumulants of order less than four.

CDMA systems in multipath fading channels need to estimate channel parameters for coherent detection of the transmitted signals. We present a simple but effective channel estimation algorithm that can be incorporated into most types of multiuser receiver to obtain good detection performance. This technique uses a set of correlation filters to independently estimate each of the channel parameters. One advantage our method has over subspace-based algorithms for channel estimation is that it can estimate the channel parameters without phase or amplitude ambiguity. Simulation results demonstrating that our channel estimator is capable of tracking reasonably fast fading channels are also presented.

This paper presents a new method for unsharp masking for contrast enhancement of images. The approach employs an adaptive filter that controls the contribution of the sharpening path in such a way that contrast enhancement occurs in high detail areas and little or no image sharpening occurs in smooth areas.

This paper presents a blind adaptive CDMA receiver that requires no knowledge of the spreading codes, the delays, and the energy of the received signals associated with the interfering users. Our receiver is based on linear interference cancellation and adaptive interference signal subspace tracking. It has error control coding embedded in the detector structure and employs "branch processing" to detect the bit stream. Simulation results demonstrating that the receiver suffers negligible performance loss over systems with complete knowledge of the interfering users are presented.

This letter presents some theorems for the exact and pth-order equalization of nonlinear systems described by recursive polynomial input-output relationships. It is shown that the nonlinear equalizers derived on the basis of this theory have simple and computationally efficient structures. Furthermore, the pth-order equalizers can be shown to operate in a stable manner for a finite range of values of the input amplitude when the linear component of the nonlinear system being equalized has minimum phase properties.

This paper presents a theory for the exact and the pth order equalization or linearization of nonlinear systems with known recursive or nonrecursive polynomial input-output relationships. The equalizing and linearizing filters have simple and computationally efficient structures. An experimental result that illustrates the good properties of the technique we propose is also included in this paper.

Parallel-cascade realizations of truncated Volterra systems implement higher-order systems using a parallel connection of multiplicative combinations of lower-order systems. Such realizations are modular and permit efficient approximations of truncated Volterra systems. Frequency-domain realizations of the least-mean-square (LMS) adaptive filter and the normalized LMS adaptive filter that implements the system model using the parallel-cascade structure are presented in this paper. Computational complexity analysis and simulation results show that the normalized frequency-domain, parallel-cascade LMS adaptive quadratic filter has the advantages of computational simplicity and superior performance over direct form realizations.

This paper presents an optimum space-time moving target indication (MTI) processor for the airborne radar. The optimization is based on a stochastic target model, rather than deterministic target models adopted in most space-time MTI processor designs. The optimum solution that maximizes the improvement factor yielded by the processor is shown to be the generalized eigenvector corresponding to the smallest generalized eigenvalue of the signal and clutter covariance matrices. A suboptimal, but computationally simpler solution to this problem is also derived. This approach requires the solution of a linearly constrained minimum variance (LCMV) problem. Unlike typical LCMV problems, our solution also calculates the response vector specifying the frequency response along the look direction. Experimental results demonstrating the usefulness of our methods are included in the paper. The results indicate that the suboptimal solution does not suffer from significant performance loss.

This paper presents an adaptive algorithm for preprocessing document images prior to binarization in character recognition problems. Our method is similar in its approach to the blind adaptive equalization of binary communication channels. The adaptive filter utilizes a quadratic system model to provide edge enhancement for input images that have been corrupted by noise and other types of distortions during the scanning process. Experimental results demonstrating significant improvement in the quality of the binarized images over both direct binarization and a previously available preprocessing technique are also included.

This paper derives sufficient time-varying bounds on the maximum variation of the coefficients of an exponentially stable, linear, time-varying and recursive filter. The stability bound is less conservative than all previously derived bounds for time-varying IIR systems. The bound is then applied to control the step size of output error adaptive IIR filters to achieve exponentially stable operation. Experimental results that demonstrate the good stability characteristics of the resulting algorithms are included in this paper.

This paper introduces a computationally efficient Gauss-Newton type adaptation algorithm for parallel-cascade realizations of truncated Volterra systems with arbitrary, but finite order nonlinearity. Parallel-cascade realizations implement higher-order Volterra systems using parallel and multiplicative combinations of lower-order Volterra systems. The complexity of our system is comparable to the complexity of the system model itself, and is considerably less than that of the fast RLS Volterra filters. Results of experiments comparing the Gauss-Newton method with a competing structure with similar computational complexity as well as demonstrating the capability of parallel-cascade systems to approximate truncated Volterra systems are also included in the paper.

A new scheme of unsharp masking for image contrast enhancement is presented. An adaptive algorithm is introduced so that a sharpening action is performed only in locations where the image exhibits significant dynamics. Hence, the amplification of noise in smooth areas is reduced. An adaptive directional filtering is also performed so as to provide suitable emphasis to the different directional characteristics of the detail. Because it is capable of treating high-detail and medium-detail areas differently, this algorithm also avoids unpleasant overshoot artifacts in regions of sharp transitions. Experimental results demonstrating the usefulness of the adaptive operator in an application involving preprocessing of images for enhancement prior to zooming are also included.

We present some theorems for the exact inversion and the pth-order inversion of a wide class of causal, discrete-time, nonlinear systems. The nonlinear systems we consider are described by the input-output relationship y(n)=g[x(n)]h[x(n-1). y(n-1)]+f[x(n-1). y(n-1)], where g[/spl middot/], h[/spl middot/. /spl middot/], and f[/spl middot/. /spl middot/] are causal, discrete-time and nonlinear operators and the inverse function g/sup -1/[/spl middot/] exists. The exact inverse of such systems is given by z(n)=g/sup -1/[{u(n)-f[z(n-1). u(n-1)]}/h[z(n-1). u(n-1)]]. Similarly, when h[/spl middot/. /spl middot/]=1, the pth-order inverse is given by z(n)=g/sub p//sup -1/[u(n)-f[z(n-1), u(n-1)]] where g/sub p//sup -1/[/spl middot/] is the pth-order inverse of g[/spl middot/].

This paper considers vector quantization of signals using the L/sub /spl infin// distortion measure. The key contribution is a result that allows one to characterize the centroid of a set of vectors for the L/sub /spl infin// distortion measure. A method similar to the Linde-Buzo-Gray (LBG) algorithm for designing codebooks has been developed and tested. The paper also discusses the design of vector quantizers employing the L/sub /spl infin// distortion measure in an application in which the occurrences of quantization errors with larger magnitudes than a preselected threshold must be minimized.

This paper presents a vector quantization system that limits the maximum distortion introduced to a pre-selected threshold value. This system uses a recently introduced variation of the L/sub /spl infin// distortion measure that attempts to minimize the occurrences of quantization errors above a preselected threshold. The vectors are first coded using the new distortion measure. The quantization error vectors in which at least one entry is above the threshold are again coded using a residual vector quantizer. The pixels of the input image where the quantisation errors are still above the threshold are scalar quantized to force all the errors under the specified threshold. An experimental result is included in which all the error magnitudes are constrained to be below fifteen. This image was coded using 0.85 bits per pixel with a relatively simple multiplier-free vector quantizer and without entropy coding.

This paper presents an adaptive maximum likelihood method for estimating the time difference of arrival of a source signal at two spatially separate sensors. It is well-known that the maximum likelihood technique achieves the Cramer-Rao lower bound for time delay estimation error for certain signal conditions. The /spl alpha/-/spl beta/ tracker is a heuristic mechanism that is heavily used in target tracking applications. In this work, we combine an adaptive realization of the maximum likelihood time delay estimator with the /spl alpha/-/spl beta/ tracker to obtain significant improvement in the performance of the tracker, Experimental results showing 2 to 8 dB improvement in the mean-square estimation error over the conventional /spl alpha/-/spl beta/ tracker for various signal-to-noise ratios are also included in the paper.

This paper introduces parallel-cascade realizations of truncated Volterra systems with arbitrary, but finite order of nonlinearity. Parallel-cascade realizations implement higher-order Volterra systems using parallel and multiplicative combinations of lower-order Volterra systems. Such realizations are very modular and therefore well-suited for VLSI implementation. A systematic way of approximating higher-order Volterra systems in parallel-cascade form using a reduced number of branches and a bound on the mean-square error in the output signals caused by such approximate realizations are derived. A variation of the parallel-cascade structure in which a pth order Volterra filter is implemented as a parallel combination of linear filters whose outputs are raised to the pth power is also described.

This paper presents an adaptive Volterra filter that employs a recently developed orthogonalization procedure of Gaussian signals for Volterra system identification. The algorithm is capable of handling arbitrary orders of nonlinearity P as well as arbitrary lengths of memory M for the system model. The adaptive filter consists of a linear lattice predictor of order N, a set of Gram-Schmidt orthogonalizers for N vectors of size P+1 elements each, and a joint process estimator in which each coefficient is adapted individually. The complexity of implementing this adaptive filter is comparable to the complexity of the system model when N is much larger than P, a condition that is true in many practical situations. Experimental results demonstrating the capabilities of the algorithm are also presented in the paper.

This paper discusses the development of a perceptual threshold model for the human visual system. The perceptual threshold functions describe the levels of distortions present at each location in an image that human observers can not detect. Models of perceptual threshold functions are useful in image compression problems because an image compression system that constrains the distortion in the coded images below the levels suggested by the perceptual threshold function performs perceptually lossless compression. Our model involves the decomposition of an input image into its Fourrier components and spatially localized Gabor elementary functions. Data from psychophysical masking experiments are then used to calculate the perceptual detection threshold for each Gabor transform coefficient in the presence of sinusoidal masks. The result of one experiment involving distorting an image using additive noise of magnitudes as suggested by the threshold model is also included in this paper.

This paper introduces output-error LMS bilinear filters with stability monitoring. Bilinear filters are recursive nonlinear systems that belong to the class of polynomial systems. Because of the feedback structure, such models are able to represent many nonlinear systems efficiently. However, the usefulness of adaptive bilinear filters is greatly restricted unless they are guaranteed to perform in a stable manner. A stability monitoring scheme is proposed to overcome the stability problem. The paper concludes with simulation results that demonstrate the usefulness of our technique.

The paper presents an adaptive Volterra filter that employs an orthogonalization procedure of Gaussian signals for Volterra system identification. The algorithm is capable of handling arbitrary orders of nonlinearity P as well as arbitrary lengths of memory N for the system model. The adaptive filter consists of a linear lattice predictor of order N, a set of Gram-Schmidt orthogonalizers for N vectors of size P+1 elements each, and a joint process estimator in which each coefficient is adapted individually. The complexity of implementing this adaptive filter is comparable to the complexity of the system model when N is much larger than P, a condition that is true in many practical situations. Experimental results demonstrating the capabilities of the algorithm are also presented in the paper.

This paper considers vector quantization of signals using the L/sub /spl infin// distortion measure. The key contribution is a result that allows one to characterize the centroid of a set of vectors for the L/sub /spl infin// distortion measure. A method similar to the LEG algorithm for designing codebooks has been developed and tested. The paper also discusses the design of vector quantizers employing the L/sub /spl infin// distortion measure in an application in which the occurrences of quantization errors with larger magnitudes than a pre-selected threshold must be minimized.

This article presents a simple method for orthogonalizing correlated Gaussian input signals for identification of truncated Volterra systems of arbitrary order of nonlinearity P and memory length N. The procedure requires a Gram-Schmidt orthogonalizer for a vector containing N elements and some nonlinear processing of the output elements of the Gram-Schmidt processor. However, the nonlinear processors do not depend on the statistics of the input signals and, consequently, are easy to design and implement.>

Subband coding with vector quantization is addressed in this paper. Forming the data vectors from both between and within the subbands is considered. The former of these two schemes is referred to as interband coding and the latter as intraband coding. Interband coder design is relatively straightforward since the design of the single codebook involved follows readily from a representative set of interband data vectors. Intraband coder design is more complicated since it entails the selection of a vector dimension and a bit-rate for each subband. The main contribution of this work is an optimal methodology for intraband subband vector quantizer design. The problem formulation includes constraints on the bit-rate and the encoding complexity and is solved with nonlinear programming methods. Subband vector quantization image coding in conjunction with a human visual system model is thoroughly investigated. Results of a large number of experiments indicate that the optimal intraband coder yields superior results from quantitative as well as subjective points of view than the interband coder for comparable bit-rates. This improvement becomes more pronounced as the computational complexity of the intraband encoder is allowed to increase.>

This paper considers an extended recursive least squares (RLS) adaptive bilinear predictor. It is shown that the extended RLS adaptive bilinear predictor is guaranteed to be stable in the sense that the time average of the squared a-posteriori prediction error signal is bounded whenever the input signal is bounded in the same sense. It also shows that the a-priori prediction error itself is bounded whenever the desired signal is bounded. This paper also contains simulation results to demonstrate the usefulness of the extended RLS adaptive bilinear predictor.>

This paper introduces a nonlinear recursive least squares decision feedback equalizer (DFE). The nonlinearity is modeled using a bilinear system. Bilinear models are attractive because of its ability to approximate a large class of nonlinear systems efficiently. Results of computer simulation experiments that compare the performance of the bilinear DFE to two other alternatives, viz., a conventional DFE and a truncated Volterra DFE, in eliminating the intersymbol interference caused by a nonlinear channel are presented. The results demonstrate the superior performance of the bilinear DFE over the competing structures at least for the cases considered.>

The article considers recursive least squares (RLS) adaptive nonlinear filtering using bilinear system models. It is shown that the extended RLS adaptive bilinear filter, as well as the equation-error RLS adaptive bilinear filter, are guaranteed to be stable in the sense that the time average of the squared estimation error is bounded whenever the underlying process that generates the input signals is stable in the same sense.>

Results of psychophysical experiments on human vision conducted in the last three decades indicate that the eye performs a multichannel decomposition of the incident images. The paper presents a subband vector quantization algorithm that employs hexagonal filter banks. The hexagonal filter bank provides an image decomposition similar to what the eye is believed to do. Consequently, the image coder is able to make use of the properties of the human visual system and produce compressed images of high quality at low bit rates. A systematic approach is presented for optimal allocation of available bits among the subbands and also for the selection of the size of the vectors in each of the subbands.>

An image compression technique that incorporates visual masking functions in vector quantizer schemes is presented. Visual masking functions provide a description of the maximum amount of noise that can be present in an image, while remaining undetected when the image is viewed by an observer. The basic idea used in this work is that of a spatially varying distortion measure which is defined to be zero where the error involved is below a threshold level defined by the visual masking function. A gradient based algorithm is used to generate the vector quantizer codebooks. Experimental results involving subband vector quantization and a perceptual masking function recently proposed by R.J. Safranek and J.D. Johnston (1989,1990) are presented.>

An efficient algorithm that jointly estimates differential time delays and frequency offsets between two signals is introduced. The approach is a two-step procedure. First, the differential frequency offsets are estimated from measurement of the autocorrelation functions of the received and transmitted signals. The time delays are estimated from estimates of the higher-order statistics of the two signals involved. The major advantage of the approach is its remarkably reduced computational complexity over traditional approaches. The experimental results indicate that the algorithm performs better than the traditional methods in most cases of interest in spite of its reduced computational complexity.>

The author considers vector quantization that uses the L (1) distortion measure for its implementation. A gradient-based approach for codebook design that does not require any multiplications or median computation is proposed. Convergence of this method is proved rigorously under very mild conditions. Simulation examples comparing the performance of this technique with the LBG algorithm show that the gradient-based method, in spite of its simplicity, produces codebooks with average distortions that are comparable to the LBG algorithm. The codebook design algorithm is then extended to a distortion measure that has piecewise-linear characteristics. Once again, by appropriate selection of the parameters of the distortion measure, the encoding as well as the codebook design can be implemented with zero multiplications. The author applies the techniques in predictive vector quantization of images and demonstrates the viability of multiplication-free predictive vector quantization of image data.

The authors present two fast least-squares lattice algorithms for adaptive nonlinear filters equipped with system models involving nonlinear feedback. Such models can approximate a large class of nonlinear systems adequately, and usually with considerable parsimony in the number of coefficients required. For simplicity of presentation, the authors consider the bilinear system model, even though the results are applicable to more general models. The computational complexity of the algorithms is an order of magnitude smaller than that of previously available methods. Results of several experiments that demonstrate the properties of the adaptive bilinear filters are presented. Their performance is compared with that of two other algorithms that are computationally more expensive.>

A direct approach to the estimation of the parameters associated with a bilinear time series model is presented. The approach depends critically on the expressions for certain higher-order statistics of the signals that satisfy the bilinear model. These expressions are linear in most of the parameters of the model. The parameters are then estimated from an overdetermined set of equations. Results of an experiment that employs this technique and demonstrates its good properties are included.>

Two adaptive step-size gradient adaptive filters are presented. The step sizes are changed using a gradient descent algorithm designed to minimize the squared estimation error. The first algorithm uses the same step-size sequence for all the filter coefficients, whereas the second algorithm uses different step-size sequences for different adaptive filter coefficients. An analytical performance analysis of the first algorithm is also presented. Analyses and experiments indicate that (1) the algorithms have fast convergence rates and small midadjustment errors and (2) in nonstationary environments, the algorithms tend to adjust the step sizes so as to give close to the best possible performance. Several simulation examples demonstrating the good properties of the adaptive filters are also presented.>

The authors first consider vector quantization that uses the L/sub 1/ distortion measure for its implementation. The L/sub 1/ distortion measure is very attractive from an implementational point of view, since no multiplication is required for computing the distortion measure. Unfortunately, the traditional Linde-Buzo-Gray method (1980) for designing the codebook for the L/sub 1/ distortion measure can become extremely time-consuming, since it involves several computations of medians of very large arrays. The authors propose a gradient-based approach for codebook design that does not require any multiplications or median computations. The codebook design algorithm is then extended to a distortion measure that has piecewise-linear characteristics. By appropriate selection of the parameters of the distortion measure, the encoding as well as the codebook design can be implemented with zero multiplications. The authors apply the proposed techniques in predictive vector quantization of images and demonstrate the viability of multiplication-free predictive vector quantization of image data.>

A new approach is presented to the digitization and compression of a class of voiceband modem signals. The approach, baseband residual vector quantization (BRVQ), relies heavily on the simple structure present in a modem signal. After the signal is converted to baseband, the magnitude sequence and the sequence of residuals obtained when the phase within each baud of the baseband signals is modeled by a straight line are separately vector quantized. Carrier frequency estimation and baud-rate classification schemes that were designed to carry out these operations are described. Experimental results show that the performance of the BRVQ system at and below 16 kb/s is better than that of a previously developed vector quantization scheme that has itself been shown to outperform traditional speech-compression techniques such as adaptive predictive coding, adaptive transform coding, and subband coding when these techniques are used to compress modem signals.>

Convergence analyses of two adaptive filter structures that require no multiplications for their implementation are presented. Under the assumption that primary and reference inputs to the adaptive filters are zero mean, wide-sense stationary, and Gaussian random processes, expressions are derived for the mean and mean-squared behavior of the filter weight vector using a variety of simplifying assumptions. Results of some computer simulation experiments are presented.>

A fast, recursive least-squares (RLS) adaptive nonlinear filter is presented. The nonlinearity is modeled using a second-order Volterra-series expansion. The structure makes use of the ideas of fast RLS multichannel filters and has a computational complexity of O(N/sup 3/) multiplications. This compares with O(N/sup 6/) multiplications required for direct implementation. Simulation examples in which the filter is employed to identify nonlinear systems using noisy output observations are also presented. Further simplification to the structure through a simplified model is discussed.>

A novel carrier frequency estimation scheme for a relatively broad class of voiceband data signals (modem signals) is presented. The class of signals being studied includes different types of phase-shift-keyed (PSK) and frequency-shift-keyed (FSK) signals. The frequency estimates are obtained averaging the estimates of the derivative of the instantaneous signal phase after discarding the estimates at the baud boundaries. Experimental results illustrate that the frequency estimates obtained are unbiased and have small variances. Results also show that the carrier frequency estimation scheme presented is superior to two other techniques in terms of both the mean and variance of the carrier frequency estimates.>

A novel approach to image compression using vector quantization of linear (one-step) prediction errors is presented in this paper. In order to minimize the image reconstruction error, we choose the optimum predictor coefficients (in a least-squares sense) that satisfy the additional constraint that the energy of the impulse response function of the inverse reconstruction filter is bounded by a small constant c. Further, the code vectors are selected such that the reconstruction error is minimized, rather than the quantization noise for the prediction error sequences. Examples demonstrating the excellent quality of the reconstructed images using our approach at bit rates below 0.65 bit/pixel are presented.

An efficient method for updating the lattice filter/predictor coefficients using the sign algorithm is introduced. The pertinent coefficients are updated using only the signs of the estimation errors at each stage. This method requires less number of multiplications than other adaptive lattice filter algorithms. The performance of this method is compared with that of the lattice filter using the LMS algorithm for the problems of spectrum estimation and adaptive interference cancellation.

This paper introduces two recursive realizations of the Phase Transform (PHAT) processor for time delay estimation (TDE), using a simple one-pole lowpass filter and the least mean square (LMS) adaptive filter, respectively. It is shown that these adaptive methods are very effective in reducing the effect of interfering tonals. The performances of these methods are compared with those of other existing adaptive TDE algorithms via computer simulations.