A constrained affine-projection (CAP) adaptive-filtering algorithm is proposed. Unlike some other recent CAP algorithms, the new algorithm produces an unbiased output in applications where the desired signal is not available or a desired signal is not required. Simulation results show that the proposed algorithm offers reduced steady-state misalignment relative to the constrained normalized least-mean-squares algorithm as well as some recent CAP algorithms while maintaining their fast convergence.

A new algorithm for the reconstruction of images with sparse gradient is proposed. The algorithm is based on the minimization of the so called total-variation (TV) regularized squared error and is especially suited for image reconstruction from a small number of measurements. The algorithm is developed based on a generalized TV norm and uses a sequential conjugate-gradient method. Simulation results are presented which demonstrate that the proposed algorithm yields significantly improved reconstruction performance for images with sparse gradient and requires significantly reduced computational effort relative to the log-barrier based TV-regularized least-squares algorithm.

A new algorithm for the reconstruction of so called block-sparse signals in a compressive sensing framework is presented. The algorithm is based on minimizing an ℓ2/p-norm regularized l2error. The minimization is carried out by using a sequential conjugate-gradient algorithm where the line search involved is carried out using a technique based on Banach's fixed-point theorem. Simulation results are presented which show that for large-size data the proposed algorithm yields improved reconstruction performance and requires a reduced amount of computation relative to several known algorithms.

A new algorithm for signal reconstruction in a compressive sensing framework is presented. The algorithm is based on minimizing an unconstrained regularized ℓpnorm with p 〈 1 in the null space of the measurement matrix. The unconstrained optimization involved is performed by using a quasi-Newton algorithm in which a new line search based on Banach's fixed-point theorem is used. Simulation results are presented, which demonstrate that the proposed algorithm yields improved reconstruction performance and requires a reduced amount of computation relative to several known algorithms.

A signal recovery method for compressive sensing under noisy measurements is proposed. The problem is formulated as a nonconvex nonsmooth constrained optimization problem that uses the smoothly clipped absolute deviation (SCAD) function to promote sparsity. Relaxation is employed by means of a series of local linear approximations (LLAs) of the SCAD in a constrained formulation. The relaxation is shown to converge to a minimum of the original nonconvex constrained optimization problem. In order to solve each nonsmooth convex relaxation problem, a second-order cone programming (SOCP) formulation is used, which can be applied by using standard state-of-the-art SOCP solvers such as SeDuMi. Experimental results demonstrate that signals recovered using the proposed method exhibit reduced ℓ∞reconstruction error when compared with competing methods such as ℓ1-Magic. Simulations demonstrate that significant reduction in the reconstruction error can be achieved with computational cost that is comparable to that required by the ℓ1-Magic algorithm.

A new robust recursive least-squares (RLS) adaptive filtering algorithm that uses a priori error-dependent weights is proposed. Robustness against impulsive noise is achieved by choosing the weights on the basis of theL1norms of the crosscorrelation vector and the input-signal autocorrelation matrix. The proposed algorithm also uses a variable forgetting factor that leads to fast tracking. Simulation results show that the proposed algorithm offers improved robustness as well as better tracking compared to the conventional RLS and recursive least-M estimate adaptation algorithms.

An optimized numerical mapping scheme for achieving improved location of exons in DNA sequences using digital filters is proposed. Characteristic numerical values for the four nucleotides, referred to as pseudo-EIIP values, are obtained using a training procedure where the location accuracy is maximized using a quasi-Newton algorithm based on the Broyden-Fletcher-Goldfarb-Shanno updating formula. A training set of 80 DNA sequences is chosen from the HMR195 database. The objective function for the optimization procedure is formulated using the so-called receiver operating characteristic (ROC) technique and the procedure is initialized using electron-ion interaction potential (EIIP) values. Unbiased testing of the optimized characteristic values is carried out using a set of DNA sequences that has no overlap with the training set. Simulation results show that the pseudo-EIIP values yield more accurate exon locations than those obtained using the actual EIIP values.

A robust signal recovery approach for compressive sensing using unconstrained minimization is proposed. The ℓ1penalty function of the constrained ℓ1-regularized least-squares recovery problem is replaced by the smoothly clipped absolute deviation (SCAD) sparsity-promoting penalty function. A convex and differentiable local quadratic approximation for the SCAD function is employed to render the computation of the gradient and Hessian tractable. Unconstrained minimization of randomly selected wavelet coefficients is carried out using the Newton method with an inexact line search. Experimental results demonstrate that signals recovered using the proposed approach often exhibit reduced ℓ∞reconstruction error under increasingly additive Gaussian measurement noise when compared with signals recovered using the ℓ1-Magic and gradient projection for sparse reconstruction (GPSR) methods. Conversely, the number of linear measurements required to represent a signal can be reduced. As shown through simulations, significant reduction in the reconstruction error can be achieved although the computational cost is increased.

A new normalized minimum-error entropy (NMEE) algorithm is proposed as an alternative to the minimum-error entropy (MEE) and the minimum-error entropy with self-adjusting step size (MEE-SAS) algorithms. The proposed NMEE algorithm requires fewer iterations and less computation to converge and yields lower misadjustment as compared to those of the MEE and the MEE-SAS algorithms.

A filtering technique for the location of hot spots in proteins proposed recently is applied for the location of exons in DNA sequences. The technique involves conversion of a DNA character sequence into a numerical sequence using the electron-ion interaction potential values and then filtering the numerical sequence using a narrowband bandpass digital filter whose passband is centered at the period-3 frequency, i.e., 2π/3. The strength of the bandpass-filtered signal as a function of nucleotide location is then detected using a lowpass filter. A plot of the signal power versus location reveals the presence of exons as distinct peaks. Simulations have shown that the technique leads to more accurate exon locations than another computational technique based on the short-time discrete Fourier transform. Furthermore, the amount of computation required is reduced by as much as 97 percent thereby rendering the technique suitable for the processing of long DNA sequences, even complete genomes.

An improved technique for the location of hot spots in proteins based on the use of a bandpass notch (BPN) filter is described. The BPN filter is designed by specifying a stability margin and then minimizing the area under the amplitude response so as to achieve maximum selectivity for the chosen stability margin. Preliminary results indicate that the use of a BPN filter leads to improved hot-spot prediction compared to results obtained with classical filters investigated earlier by the authors such as inverse-Chebyshev filters. The results also show that the improved technique yields predictions that are consistent with results based on biological methodologies. In addition, the technique reveals certain new ‘potential’ hot-spot locations which could be investigated further by the biological community.

Multiframe super-resolution algorithms can be used to reconstruct a high-quality high-resolution image from several warped, blurred, undersampled, and possibly noisy images. A widely used means of implementing such algorithms is by optimization-based model inversion. In the past, steepest-descent methods have been applied. While easy to implement, these methods are known for their poor convergence properties and for being sensitive to numerical ill-conditioning. In this paper, we show that the multiframe super-resolution problem can be solved by using quasi-Newton algorithms and propose efficient implementations. Two of these algorithms were applied to a known super-resolution scheme and preliminary results obtained show a significant improvement in terms of convergence speed.

Peak-to-average power-ratio (PAPR) reduction for OFDM systems is investigated in a probabilistic framework. A new constellation extension technique is developed whereby the data for each subcarrier are represented either by points in the original constellation or by extended points. An optimal representation of the OFDM signal is achieved by using a de-randomization algorithm where the conditional probability involved is handled by using the Chernoff bound and the evaluation of the many hyperbolic cosine functions involved is replaced by a tight upper bound for these functions. The proposed algorithm can be used by itself or be combined with a selective rotation technique described in the paper and with other known algorithms such as the coordinate descent optimization and selective mapping algorithms to achieve further performance enhancements at the cost of a slight increase in the computational complexity. When compared with other existing PAPR-reduction algorithms, the enhanced algorithm offers improved PAPR-reduction performance and improved computational complexity although, the transmit power is increased somewhat

An optimization approach for the design of fractional delay (FD) FIR filters based on a genetic algorithm (GA) is presented. The approach exploits the advantages of a global search technique to determine the coefficients of an FD FIR filter based on the Farrow structure. The proposed approach involves a binary encoding scheme and a multiobjective error formulation based on the amplitude response and phase delay. Experimental results show that the GA based approach leads to improved frequency response relative to that achieved by using a least-squares approach

A new constellation extension technique for peak-to-average power-ratio reduction (PAPR) in orthogonal frequency-division multiplexing systems is proposed. Two new algorithms for PAPR reduction are developed by applying the so-called method of conditional probability (MCP) and coordinate descent optimization (CDO). Our simulations demonstrate that the proposed algorithms outperform several existing algorithms and the performance can be further improved by combining the MCP, CDO, and the selective mapping algorithms

A subscriber line is analyzed to estimate the average near-end crosstalk (NEXT) coupling in a twisted pair when all NEXT signals with NEXT couplings greater than a given threshold have been cancelled. The analysis is then used to estimate the expected number of twisted pairs that would require NEXT cancellation in order to reduce the NEXT magnitude on a particular twisted pair to a certain level. The results of the analysis are useful in estimating the feasibility and computational complexity of systems using adaptive filters for NEXT cancellation

A new multiuser detector for direct-sequence code-division multiple-access communication systems is described. The proposed detector divides the received signal stream into a number of overlapping windows and decorrelates them window by window. This scheme is justified by an analysis of the convergence and decay rate of the impulse response. Based on the results, a signal-adapted criterion is developed which enables one to determine the window length according to the near-far situation of a practical system. A performance analysis and simulation results show that a small to moderate window length is usually sufficient to yield a performance that is close to or even better than that of the ideal decorrelating detector.

A new linear multiuser detector for binary signaling in code-division multiple-access communication systems is described. The new detector directly minimizes the bit-error rate (BER) subject to a set of reasonable constraints. It is shown that any local minimum of the constrained BER cost function is a global minimum; hence a robust constrained minimization algorithm always leads to a detector with good performance. Although the proposed detector cannot be shown to be optimal among linear multiuser detectors because of the constraints imposed, our analysis and simulations indicate that it always outperforms the decorrelating detector and is optimal for most realistic systems.

A recursive algorithm for updating linear detectors in code-division multiple-access systems is proposed. Based on this algorithm, a window-based implementation with a signal-based criterion for determining the window length is developed. Performance analysis and numerical experiments are conducted that show the merits of the proposed implementation method.

Two different neural network schemes for the classification of light detection and ranging (LIDAR) waveforms for the LARSEN 500 airborne system and for extraction of ocean information are proposed. The first method employs a single layer of linear neurons for classification of waveforms into various clusters. Both unsupervised and supervised learning algorithms have been employed to demonstrate the spatial distribution of milt in near-shore waters. In the second method, a new multistage multilayer feedforward architecture is used for the classification of the waveforms and for the extraction of various types of ocean information. The stage I networks work in a parallel fashion and map the input waveforms to a set of characteristics. The networks in stage II use these characteristics to assign a signature number to the waveform or extract other information. Both the schemes are used with real-world data collected by the LARSEN 500 system. The paper concludes with experimental results and comparisons.

A new formulation for ocean-depth measurement using a frequency-domain approach is proposed. This technique uses two high-resolution eigensubspace methods to estimate the ocean depth from backscattered noisy data. The problem has been addressed both for real and complex attenuation coefficients by utilizing a double eigenstructure decomposition procedure on a Toeplitz as well as a Hankel matrix structure. The approach is similar to obtaining the best rational approximation that fits the actual measured data in a least-square sense.

To increase the accuracy and the rate of coverage of a given area in shallow coastal waters, light-detection and ranging (lidar) airborne laser ranging systems have been introduced. A new formulation for ocean-depth measurement using the frequency-domain approach as proposed. This technique uses a high-resolution eigensubspace method to estimate the ocean-depth from backscattered noisy data. The problem is addressed for complex attenuation coefficients by utilizing a double eigenstructure decomposition procedure on a Hankel matrix structure. The approach is similar to obtaining the best rational approximation that fits the actual measured data in a least-square sense.

A Hopfield (1986) type neural network for the design of 1-D FIR filters is proposed. Given the frequency or amplitude response, the all-analog network computes the filter coefficients in real time. The network is simulated with HSPICE and examples are included to show that this is an efficient way of solving the approximation problem compared to the standard techniques for FIR filter design.

The application of two-dimensional (2D) signal processing to data collected in airborne laser bathymetry is investigated. Specifically, a type of 2D filter for the suppression of impulsive noise in irregularly-spaced data based on order-statistics filtering is developed. An algorithm which incorporates this type of filter along with a sophisticated 2D interpolation technique is constructed to automate the filtering process. An adaptive 2D filtering technique that can be applied to raw bathymetric profiles to remove wideband noise is then discussed. The results obtained show that each type of filtering enhances the accuracy of bathymetric measurement quite significantly.

Two methods for the design of two-channel perfect reconstruction FIR filter banks with short reconstruction delays are presented. The first method is based on the Lagrange-multiplier method. The method is simple, efficient, flexible, and leads to a closed-form exact solution. The second method is based on a quadratic-constrained least-squares minimization. Design examples are given to illustrate the advantages of the proposed methods. The quality of reconstruction is considered very good and superior to those of existing methods.

A Hopfield-type neural network is proposed for the design of 2-D FIR filters. Given the amplitude response, the all-analog network computes the filter coefficients in real time. The network is simulated with HSPICE and a few examples are included to show that this is an efficient way of solving the approximation problem and has high potential for implementation in analog VLSI.

A new structurally balanced model reduction algorithm that leads to a stable reduced-order system with improved approximation error is proposed. The algorithm is developed by formulating the problem at hand as an unconstrained optimization problem in which the objective function includes a term that depends on the sum of discarded 2-D Hankel singular values. An example is given to illustrate the performance of the reduced-order system obtained using the new algorithm.

An innovative weighted structurally balanced realization of two-dimensional (2-D) discrete systems is proposed. Two auxiliary transfer-function matrices called the weighted-input-to-state and the state-to-weighted-output transfer-function matrices are first introduced. Based on these matrices, the controllability and observability grammians of the weighted system are defined and the existence of the grammians is justified. The resulting 2-D weighted structurally balanced realization method can be applied for the reduction of the system order of 2-D discrete systems.

Results are presented which show the advantages of using a quasi-Newton adaptive filtering algorithm over conventional algorithms in a CDMA indoor wireless system. One of the main impediments in these systems is co-channel interference from users of the same service. Adaptive equalizers of suitable bandwidth can be used to suppress co-channel interference for a CDMA system but the performance of adaptive equalizers depends critically on the algorithm used for their adaptation. Conventional adaptive filtering algorithms are shown to have unsuitable characteristics in these conditions and a recently proposed quasi-Newton algorithm is shown to perform creditably and is recommended for use in a CDMA system.

A new method is proposed for the design of two-channel linear-phase perfect reconstruction QMF banks. The analysis lowpass filter is first designed by a conventional method, and then the synthesis lowpass filter is obtained by using a null-space projection approach. This method is then extended to the design of two-channel perfect reconstruction QMF banks with low reconstruction delay, which are desirable in some applications. Two design examples are given to illustrate the proposed methods.

A new variable forgetting factor RLS adaptive filter is introduced. This algorithm, based on an accurate new measure of RLS performance in a random walk scenario, attempts to achieve the optimal RLS steady-state misadjustment under the assumption that the Wiener filter coefficients vary according to that nonstationarity. Simulations demonstrate that the proposed method is effective in other nonstationary environments and outperforms existing fixed and variable forgetting factor schemes.>

A new adaptive filtering algorithm is developed based on fairly well known off-line optimization techniques. The need for tuning parameters is eliminated through an efficient line search procedure which assures good performance in many practical situations. Simulations are included which demonstrate the algorithm's stability under conditions where other algorithms with fast convergence, e.g., RLS, LMS-Newton, diverge.>

An iterative procedure proposed by Chen and Lee for the design of quadrature mirror filter (QMF) banks is extended to the design of two types of filter banks, i.e., l-D QMF banks with low reconstruction delay and 2-D nonseparable hexagonal QMF banks. Our simulations show that the extended methods are very efficient and yield good designs.>

The application of one-dimensional signal processing techniques for the preprocessing of waveforms obtained in airborne laser bathymetry is investigated. Specifically, a special type of smoothing digital filter is used to remove noise in the waveforms while preserving the information content up to a desired degree. An algorithm, which incorporates a lowpass digital differentiator is then used to detect the bottom reflection. The optimal cutoff frequency of the differentiator is determined on the basis of the spectral content of the bottom reflection. After preprocessing, a waveform-decomposition technique recently described by the authors is used to separate the surface and bottom reflections for sea-depth estimation. In order to evaluate the effectiveness of the techniques developed, sea-depth estimates obtained are compared to corresponding estimates obtained by a local surveying company, and a high degree of agreement is observed between the two sets of results. When the resolution between the surface and bottom returns is low, the proposed techniques together with waveform decomposition offer a significant improvement in the sea-depth estimates.>

The authors describe a method of accurately decomposing a Larsen waveform into the surface and bottom reflections, independently of the degree of their overlap. A mathematical model that can be used to characterize the Larsen waveforms received under diverse circumstances is established. This model is used in conjunction with an optimization technique to facilitate the decomposition of each Larsen waveform into surface and bottom reflections. The optimized parameters of the mathematical model are used to give sea depth estimates. The resolution of Larsen waveforms into two separate components by means of this technique offers two important advantages. First, sea depths can be readily determined from the displacement between the two components without human intervention, that is, the processing can be automated. Second, fairly accurate sea depths can be deduced even in cases where the two reflections strongly overlap.>

A number theoretic transform (NTT) is proposed, which can efficiently be computed by using ternary modular arithmetic. The new NTT relaxes the restriction imposed on the convolution length and, as in other efficient NTT's, its computation can be performed by means of data shifts and additions. A hardware implementation of the new NTT is then described and is compared with the implementation of conventional NTT's based on binary modular arithmetic.