nils-herrmann/clean_scirepeval huggingface dataset:
A dual-deconvolution algorithm for radar and communication black-space spectrum sharing

We introduce a dual-deconvolution algorithm for the purpose of black-space spectrum sharing. We consider the case of spectrum sharing between radio-frequency (RF) devices whose data source/scatterers are modeled as a convolution with a pulse-shaping filter. This model encompasses both single-carrier communications as well as pulse-Doppler radars. Preliminary results including the mean-square error (MSE) for the radar system and bit error rate (BER) are provided for a scenario of communications and radar spectrum sharing. These results demonstrate significant improvement in uncoordinated spectrum sharing of radar and wireless communication signals overlapping in time and frequency. The algorithm is implemented using the fast Fourier transform and an iterative procedure that requires no matrix inverse computations. The algorithm also generalizes straightforwardly to multiple-deconvolution scenarios.
Low-pass filters realizable as all-pass sums: design via a new flat delay filter

This paper describes a new class of maximally flat low-pass recursive digital filters. The filters are realizable as a parallel sum of two all-pass filters, a structure for which low-complexity low-noise implementations exist. Note that, with the classical Butterworth filter of degree N which is retrieved as a special case, it is not possible to adjust the delay (or phase linearity). However, with the more general class of filters described in this paper, the adjustment of the delay becomes possible, and the tradeoff between the delay and the phase linearity can be chosen. The construction of these low-pass filters depends upon a new maximally flat delay all-pole filter, for which the degrees of flatness at /spl omega/=0 and /spl omega/=/spl pi/ are not necessarily equal. For the coefficients of this flat delay filter, an explicit solution is introduced, which also specializes to a previously known result.
Polynomial Smoothing of Time Series With Additive Step Discontinuities

This paper addresses the problem of estimating simultaneously a local polynomial signal and an approximately piecewise constant signal from a noisy additive mixture. The approach developed in this paper synthesizes the total variation filter and least-square polynomial signal smoothing into a unified problem formulation. The method is based on formulating an l1-norm regularized inverse problem. A computationally efficient algorithm, based on variable splitting and the alternating direction method of multipliers (ADMM), is presented. Algorithms are derived for both unconstrained and constrained formulations. The method is illustrated on experimental data involving the detection of nano-particles with applications to real-time virus detection using a whispering-gallery mode detector.
The design of approximate Hilbert transform pairs of wavelet bases

Several authors have demonstrated that significant improvements can be obtained in wavelet-based signal processing by utilizing a pair of wavelet transforms where the wavelets form a Hilbert transform pair. This paper describes design procedures, based on spectral factorization, for the design of pairs of dyadic wavelet bases where the two wavelets form an approximate Hilbert transform pair. Both orthogonal and biorthogonal FIR solutions are presented, as well as IIR solutions. In each case, the solution depends on an allpass filter having a flat delay response. The design procedure allows for an arbitrary number of vanishing wavelet moments to be specified. A Matlab program for the procedure is given, and examples are also given to illustrate the results.
Pixel recovery via /spl lscr//sub 1/ minimization in the wavelet domain

This paper uses probability models on expansive wavelet transform coefficients with interpolation constraints to estimate missing blocks in images. We use simple probability models on wavelet coefficients to formulate the estimation process as a linear programming problem and solve it to recover the missing pixels. Our formulation is general and can be augmented with more sophisticated probability models to obtain even better estimates on a variety of image regions. The presented approach has many parallels to recently introduced dictionary based signal representations with which it shares certain optimality properties. We provide simulation examples over edge regions using both critically-sampled and expansive (over-complete) wavelet transforms.
Exchange algorithms for the design of linear phase FIR filters and differentiators having flat monotonic passbands and equiripple stopbands

The authors describe a modification of a technique proposed by Vaidyanathan (1985) for the design of filters having flat passbands and equiripple stopbands. The modification ensures that the passband is monotonic and does so without the use of concavity constraints. Another modification described in this brief adapts the method of Vaidyanathan to the design of low-pass differentiators having a specified degree of tangency at /spl omega/=0.
Group-Sparse Signal Denoising: Non-Convex Regularization, Convex Optimization

Convex optimization with sparsity-promoting convex regularization is a standard approach for estimating sparse signals in noise. In order to promote sparsity more strongly than convex regularization, it is also standard practice to employ non-convex optimization. In this paper, we take a third approach. We utilize a non-convex regularization term chosen such that the total cost function (consisting of data consistency and regularization terms) is convex. Therefore, sparsity is more strongly promoted than in the standard convex formulation, but without sacrificing the attractive aspects of convex optimization (unique minimum, robust algorithms, etc.). We use this idea to improve the recently developed `overlapping group shrinkage' (OGS) algorithm for the denoising of group-sparse signals. The algorithm is applied to the problem of speech enhancement with favorable results in terms of both SNR and perceptual quality.
Constrained least squares design of 2-D FIR filters

We consider the design of 2-D linear phase finite impulse response (FIR) filters according to the least squares (LS) error criterion subject to equality and/or inequality constraints. Since we use a frequency domain formulation, these constraints can be used to explicitly prescribe (frequency-dependent) error tolerances, the maximum, minimum, or fixed values of the frequency response at certain points and/or regions. Our method combines Lagrange multiplier and Kuhn-Tucker theory to solve a much wider class of problems than do standard methods. It allows arbitrary compromises between the LS and the equiripple design.
The dual-tree complex wavelet transform

The paper discusses the theory behind the dual-tree transform, shows how complex wavelets with good properties can be designed, and illustrates a range of applications in signal and image processing. The authors use the complex number symbol C in CWT to avoid confusion with the often-used acronym CWT for the (different) continuous wavelet transform. The four fundamentals, intertwined shortcomings of wavelet transform and some solutions are also discussed. Several methods for filter design are described for dual-tree CWT that demonstrates with relatively short filters, an effective invertible approximately analytic wavelet transform can indeed be implemented using the dual-tree approach.
A bivariate shrinkage function for wavelet-based denoising

Most simple nonlinear thresholding rules for wavelet-based denoising assume the wavelet coefficients are independent. However, wavelet coefficients of natural images have significant dependency. In this paper, a new heavy-tailed bivariate pdf is proposed to model the statistics of wavelet coefficients, and a simple nonlinear threshold function (shrinkage function) is derived from the pdf using Bayesian estimation theory. The new shrinkage function does not assume the independence of wavelet coefficients.
Symmetric nearly shift-invariant tight frame wavelets

K-regular two-band orthogonal filterbanks have been applied to image processing. Such filters can be extended into a case of downsampling by two and more than two filters provided that they satisfy a set of conditions. Such a setup allows for more degrees of freedom but also at the cost of higher redundancy. The latter depends directly on the number of the wavelet filters involved. Tight frame filters allow the design of smooth scaling functions and wavelets with a limited number of coefficients. Moreover, such filters are nearly shift invariant, a desirable feature in many applications. We explore a family of symmetric tight frame finite impulse response (FIR) filters characterized by the relations H/sub 3/(z)=H/sub 0/(-z) and H/sub 2/(z)=H/sub 1/(-z). They are simple to design and exhibit a degree of near orthogonality, in addition to near shift invariance. Both properties are desirable for noise removal purposes.
Simultaneous polynomial approximation and total variation denoising

This paper addresses the problem of smoothing data with additive step discontinuities. The problem formulation is based on least square polynomial approximation and total variation denoising. In earlier work, an ADMM algorithm was proposed to minimize a suitably defined sparsity-promoting cost function. In this paper, an algorithm is derived using the majorization-minimization optimization procedure. The new algorithm converges faster and, unlike the ADMM algorithm, has no parameters that need to be set. The proposed algorithm is formulated so as to utilize fast solvers for banded systems for high computational efficiency. This paper also gives optimality conditions so that the optimality of a result produced by the numerical algorithm can be readily validated.
Convex 1-D Total Variation Denoising with Non-convex Regularization

Total variation (TV) denoising is an effective noise suppression method when the derivative of the underlying signal is known to be sparse. TV denoising is defined in terms of a convex optimization problem involving a quadratic data fidelity term and a convex regularization term. A non-convex regularizer can promote sparsity more strongly, but generally leads to a non-convex optimization problem with non-optimal local minima. This letter proposes the use of a non-convex regularizer constrained so that the total objective function to be minimized maintains its convexity. Conditions for a non-convex regularizer are given that ensure the total TV denoising objective function is convex. An efficient algorithm is given for the resulting problem.
Sparse Regularization via Convex Analysis

Sparse approximate solutions to linear equations are classically obtained via L1 norm regularized least squares, but this method often underestimates the true solution. As an alternative to the L1 norm, this paper proposes a class of nonconvex penalty functions that maintain the convexity of the least squares cost function to be minimized, and avoids the systematic underestimation characteristic of L1 norm regularization. The proposed penalty function is a multivariate generalization of the minimax-concave penalty. It is defined in terms of a new multivariate generalization of the Huber function, which in turn is defined via infimal convolution. The proposed sparse-regularized least squares cost function can be minimized by proximal algorithms comprising simple computations.
Transient Artifact Reduction Algorithm (TARA) Based on Sparse Optimization

This paper addresses the suppression of transient artifacts in signals, e.g., biomedical time series. To that end, we distinguish two types of artifact signals. We define “Type 1” artifacts as spikes and sharp, brief waves that adhere to a baseline value of zero. We define “Type 2” artifacts as comprising approximate step discontinuities. We model a Type 1 artifact as being sparse and having a sparse time-derivative, and a Type 2 artifact as having a sparse time-derivative. We model the observed time series as the sum of a low-pass signal (e.g., a background trend), an artifact signal of each type, and a white Gaussian stochastic process. To jointly estimate the components of the signal model, we formulate a sparse optimization problem and develop a rapidly converging, computationally efficient iterative algorithm denoted TARA (“transient artifact reduction algorithm”). The effectiveness of the approach is illustrated using near infrared spectroscopic time-series data.
The design of Hilbert transform pairs of wavelet bases via the flat delay filter

This paper describes a simple procedure, based on spectral factorization, for the design of a pair of orthonormal wavelet bases where the two wavelets form a Hilbert transform pair. The two scaling filters respectively have the numerator and denominator of the flat delay all-pass filter as factors. The design procedure allows for an arbitrary number of zero wavelet moments to be specified. A Matlab program for the procedure is given, and examples are also given to illustrate the results.
Bird body and wing-beat radar Doppler signature separation using sparse optimization

Radar bird detection and discrimination has many civilian and non-civilian applications such as collision avoidance, false alarm reduction for detection radars, stealthy target detection, classification of military unmanned aerial vehicles (UAVs) and civilian drones, and conservation ecology. In order to develop new and improve existing detection and discrimination algorithms, this paper proposes a feature extraction technique in which the wing-beat Doppler radar signature of a bird is separated from its respective body signature. More specifically, we propose non-linear morphological component analysis (MCA) using invertible short-time Fourier transform (STFT) for feature extraction. The method is applied to the Peregrine falcon data measured by Alabaster et al. (2012) resulting in successful separation of the aforementioned signatures.
Bivariate shrinkage with local variance estimation

The performance of image-denoising algorithms using wavelet transforms can be improved significantly by taking into account the statistical dependencies among wavelet coefficients as demonstrated by several algorithms presented in the literature. In two earlier papers by the authors, a simple bivariate shrinkage rule is described using a coefficient and its parent. The performance can also be improved using simple models by estimating model parameters in a local neighborhood. This letter presents a locally adaptive denoising algorithm using the bivariate shrinkage function. The algorithm is illustrated using both the orthogonal and dual tree complex wavelet transforms. Some comparisons with the best available results are given in order to illustrate the effectiveness of the proposed algorithm.
Narrowband lowpass digital differentiator design

This paper describes a simple formulation for the non-iterative design of narrowband FIR linear-phase low-pass digital differentiators. The frequency response of the filters is flat around dc and have equally spaced nulls in the stopband. The design problem is formulated so as to avoid the complexity or ill conditioning of standard methods for the design of similar filters when those methods are used to design narrowband filters with long impulse responses.
Signal decomposition for wind turbine clutter mitigation

This paper addresses the problem of dynamic clutter mitigation by focusing on the mitigation of the wind turbine clutter from the radar data. The basis pursuit and morphological component analysis approach are used to decompose the radar returns into the sum of oscillatory and transient components. The success of the morphological component analysis rely on sparsity, thus different transform domains needs to be identified correctly to represent each component sparsely. The method is illustrated on a radar data collected from a small custom built radar system to show the success of the proposed algorithm for wind turbine clutter mitigation.
The Estimation of Laplace Random Vectors in Additive White Gaussian Noise

This paper develops and compares the maximum a posteriori (MAP) and minimum mean-square error (MMSE) estimators for spherically contoured multivariate Laplace random vectors in additive white Gaussian noise. The MMSE estimator is expressed in closed-form using the generalized incomplete gamma function. We also find a computationally efficient yet accurate approximation for the MMSE estimator. In addition, this paper develops an expression for the MSE for any estimator of spherically contoured multivariate Laplace random vectors in additive white Gaussian noise (AWGN), the development of which again depends on the generalized incomplete gamma function. The estimators are motivated and tested on the problem of wavelet-based image denoising.
Generalized digital Butterworth filter design

This correspondence introduces a new class of infinite impulse response (IIR) digital filters that unifies the classical digital Butterworth filter and the well-known maximally flat FIR filter. New closed-form expressions are provided, and a straightforward design technique is described. The new IIR digital filters have more zeros than poles (away from the origin), and their (monotonic) square magnitude frequency responses are maximally flat at /spl omega/=0 and at /spl omega/=/spl pi/. Another result of the correspondence is that for a specified cutoff frequency and a specified number of zeros, there is only one valid way in which to split the zeros between z=-1 and the passband. This technique also permits continuous variation of the cutoff frequency. IIR filters having more zeros than poles are of interest because often, to obtain a good tradeoff between performance and implementation complexity, just a few poles are best.
Lowpass filters realizable as coupled allpasses: design via a new flat delay filter

This paper describes a new class of maximally flat lowpass recursive digital filters. The filters are realizable as a parallel sum of two allpass filters, a structure for which low-complexity low-noise implementations exist. Note that, with the classical Butterworth filter of degree N, which can be retrieved as a special case, it is not possible to adjust the delay (or phase-linearity). However, with the more, general class of filters described in this paper, the adjustment of the delay becomes possible, and the trade-off between the delay and the phase-linearity can be chosen. The construction of these lowpass filters depends upon a new maximally flat delay allpole filter, for which the degrees of flatness at /spl omega/=0 and /spl omega/=/spl pi/ are not necessarily equal. For the coefficients of this flat delay filter, an explicit solution is introduced, which also specializes to a previously known result.
Multivariate shrinkage functions for wavelet-based denoising

The first nonlinear rules for wavelet based image denoising assume wavelet coefficients are independent. However it is well known that there are strong dependencies between coefficients such as interscale and intrascale dependencies. We have introduced a non-Gaussian bivariate pdf that exploits the interscale dependencies between a coefficient and its parent. In this paper, how to extend this pdf in order to include the other dependencies will be discussed and in one example, a multivariate shrinkage rule will be derived. The good performance of this new rule will be illustrated on an image denoising algorithm which captures also interscale dependencies.
Bayesian Estimation of Bessel K Form Random Vectors in AWGN

We present new Bayesian estimators for spherically-contoured Bessel K form (BKF) random vectors in additive white Gaussian noise (AWGN). The derivations are an extension of existing results for the scalar BKF and multivariate Laplace (MLAP) densities. MAP and MMSE estimators are derived. We show that the MMSE estimator can be written in exact form in terms of the generalized incomplete Gamma function. Computationally efficient approximations are given. We compare the proposed exact and approximate MMSE estimators with recent results using the BKF density, both in terms of the shrinkage rules and the associated mean-square error.
On the Dual-Tree Complex Wavelet Packet and $M$-Band Transforms

The two-band discrete wavelet transform (DWT) provides an octave-band analysis in the frequency domain, but this might not be ldquooptimalrdquo for a given signal. The discrete wavelet packet transform (DWPT) provides a dictionary of bases over which one can search for an optimal representation (without constraining the analysis to an octave-band one) for the signal at hand. However, it is well known that both the DWT and the DWPT are shift-varying. Also, when these transforms are extended to 2-D and higher dimensions using tensor products, they do not provide a geometrically oriented analysis. The dual-tree complex wavelet transform , introduced by Kingsbury, is approximately shift-invariant and provides directional analysis in 2-D and higher dimensions. In this paper, we propose a method to implement a dual-tree complex wavelet packet transform , extending the as the DWPT extends the DWT. To find the best complex wavelet packet frame for a given signal, we adapt the basis selection algorithm by Coifman and Wickerhauser, providing a solution to the basis selection problem for the . Lastly, we show how to extend the two-band to an -band (provided that ) using the same method.
Dynamic clutter mitigation using sparse optimization

The impact of wind farms on radar systems, such as air traf-fc control (ATC), air defense (AD), and weather radars, is a signifcant issue, especially considering that demand for wind power and wind farms is increasing dramatically. According to the American Wind Energy Association, more than 51,630 MW of wind power capacity are installed in the United States . There are also more than 8,900 MW of wind power capacity under construction, involving more than 90 separate projects spanning 31 states and Puerto Rico .
Constrained least square design of FIR filters without specified transition bands

This paper puts forth the notion that explicitly specified transition bands have been introduced in the filter design literature in part as an indirect approach for dealing with discontinuities in the desired frequency response. We suggest that the use of explicitly specified transition bands is sometimes inappropriate because to satisfy a meaningful optimality criterion, their use implicitly assumes a possibly unrealistic assumption on the class of input signals. This paper also presents an algorithm for the design of peak constrained lowpass FIR filters according to an integral square error criterion that does not require the use of specified transition bands. This rapidly converging, robust, simple multiple exchange algorithm uses Lagrange multipliers and the Kuhn-Tucker conditions on each iteration. The algorithm will design linear- and minimum-phase FIR filters and gives the best L/sub 2/ filter and a continuum of Chebyshev filters as special cases. It is distinct from many other filter design methods because it does not exclude from the integral square error a region around the cut-off frequency, and yet, it overcomes the Gibbs' phenomenon without resorting to windowing or 'smoothing out' the discontinuity of the ideal lowpass filter.
Multidimensional mapping techniques for convolution

It is shown that the Winograd approach, nesting algorithms, and multidimensional interpolation methods for circular convolution are conveniently described using similarity transforms and companion matrices. Using the notion of similarity, it is further shown that the one-dimensional to multidimensional mapping techniques employed by the nesting algorithms can be extended to some noncircular convolutions. This increases the flexibility in the design of algorithms which employ both the Chinese remainder theorem and the multidimensional techniques. The use of multidimensional mappings for noncircular convolutions in multidimensional interpolation methods is also described.<<ETX>>