nils-herrmann/clean_scirepeval huggingface dataset:
Fused lasso with a non-convex sparsity inducing penalty

The fused lasso problem involves the minimization of the sum of a quadratic, a TV term and an ℓ1 term. The solution can be obtained by applying a TV denoising filter followed by soft-thresholding. However, soft-thresholding introduces a certain bias to the non-zero coefficients. In order to prevent this bias, we propose to replace the ℓ1 penalty with a non-convex penalty. We show that the solution can similarly be obtained by applying a modified thresholding function to the result of the TV-denoising filter.
A new complex-directional wavelet transform and its application to image denoising

This paper describes a new complex-directional expansive perfect reconstruction two-dimensional wavelet transform. Each complex wavelet is oriented along one of six possible directions, and the magnitude of each complex wavelet has a smooth bell-shape. The transform is based both on the complex dual-tree wavelet transform introduced by Kingsbury (see Phil. Trans. Royal Society London, A, September 1999 and Applied and Computational Harmonic Analysis, vol.10, no.3, p.234-53, 2001) and on the double-density DWT. It is designed so as to possess simultaneously the properties of the complex dual-tree DWT and the double-density DWT. The paper also describes a simple subband-dependent data-driven denoising algorithm for use with this transform. An example is shown to illustrate the performance of the denoising algorithm and the transform.
Sparsity amplified

The L1 norm is often used as a penalty function to obtain a sparse approximate solution to a system of linear equations, but it often underestimates the true values. This paper proposes a different type of penalty that (1) estimates sparse solutions more accurately and (2) maintains the convexity of the cost function. The new penalty is a multivariate generalization of the minimax-concave (MC) penalty. To define the generalized MC (GMC) penalty we first define a multivariate generalized Huber function. The resulting cost function can be minimized by proximal algorithms comprising simple computations. The effectiveness of the GMC penalty is illustrated in a denoising example.
Wavelet-Domain Soft-Thresholding for Non-Stationary Noise

This paper describes a new wavelet-based denoising algorithm based on a non-stationary noise assumption. Even though stationary noise models can simplify the development and implementation of denoising algorithms, they do not always accurately describe the statistical properties of the noise. The proposed algorithm has been developed to address signal processing problems under environments where the noise is spatially varying. We illustrate two signal denoising examples in order to show the performance of the proposed algorithm.
Sparse Signal Approximation via Nonseparable Regularization

The calculation of a sparse approximate solution to a linear system of equations is often performed using either L1-norm regularization and convex optimization or nonconvex regularization and nonconvex optimization. Combining these principles, this paper describes a type of nonconvex regularization that maintains the convexity of the objective function, thereby allowing the calculation of a sparse approximate solution via convex optimization. The preservation of convexity is viable in the proposed approach because it uses a regularizer that is nonseparable. The proposed method is motivated and demonstrated by the calculation of sparse signal approximation using tight frames. Examples of denoising demonstrate improvement relative to L1 norm regularization.
An iterative algorithm for the construction of notched chirp signals

This paper describes an iterative algorithm for the design of a constant-modulus finite-duration chirp-like signal having a notch in its frequency spectrum. Frequency-notched signals with good pulse compression properties are needed in wide-band radar systems that must avoid radiating into frequency bands assigned to other systems (e.g. communication and navigation systems). The algorithm is computationally efficient and provides explicit control of the notch frequency and notch order.
Wavelet based speckle reduction with application to SAR based ATD/R

The paper introduces a novel speckle reduction method based on thresholding the wavelet coefficients of the logarithmically transformed image. The method is computational efficient and can significantly reduce the speckle while preserving the resolution of the original image. Both soft and hard thresholding schemes are studied and the results are compared. When fully polarimetric SAR images are available, the authors propose several approaches to combine the data from different polarizations to achieve even better performance. Wavelet processed imagery is shown to provide better detection performance for the synthetic-aperture radar (SAR) based automatic target detection/recognition (ATD/R) problem.<<ETX>>
Image Denoising Based on A Mixture of Bivariate Gaussian Models in Complex Wavelet Domain

Recently, it has been shown that algorithms exploiting dependencies between coefficients for modeling probability density function (pdf) of wavelet coefficients, could achieve better results for image denoising in wavelet domain compared with the ones based on the independence assumption. In this context, we design a bivariate maximum a posteriori (MAP) estimator which relies on a mixture of bivariate Gaussian models. This model not only is bivariate but also is mixture and therefore, using this new statistical model, we are able to better capture heavy-tailed natures of the data as well as the interscale dependencies of wavelet coefficients. The simulation results show that our proposed technique achieves better performance than several published methods both visually and in terms of peak signal-to-noise ratio (PSNR).
Simultaneous Low-Pass Filtering and Total Variation Denoising

This paper seeks to combine linear time-invariant (LTI) filtering and sparsity-based denoising in a principled way in order to effectively filter (denoise) a wider class of signals. LTI filtering is most suitable for signals restricted to a known frequency band, while sparsity-based denoising is suitable for signals admitting a sparse representation with respect to a known transform. However, some signals cannot be accurately categorized as either band-limited or sparse. This paper addresses the problem of filtering noisy data for the particular case where the underlying signal comprises a low-frequency component and a sparse or sparse-derivative component. A convex optimization approach is presented and two algorithms derived: one based on majorization-minimization (MM), and the other based on the alternating direction method of multipliers (ADMM). It is shown that a particular choice of discrete-time filter, namely zero-phase noncausal recursive filters for finite-length data formulated in terms of banded matrices, makes the algorithms effective and computationally efficient. The efficiency stems from the use of fast algorithms for solving banded systems of linear equations. The method is illustrated using data from a physiological-measurement technique (i.e., near infrared spectroscopic time series imaging) that in many cases yields data that is well-approximated as the sum of low-frequency, sparse or sparse-derivative, and noise components.
Convex Denoising using Non-Convex Tight Frame Regularization

This letter considers the problem of signal denoising using a sparse tight-frame analysis prior. The l1 norm has been extensively used as a regularizer to promote sparsity; however, it tends to under-estimate non-zero values of the underlying signal. To more accurately estimate non-zero values, we propose the use of a non-convex regularizer, chosen so as to ensure convexity of the objective function. The convexity of the objective function is ensured by constraining the parameter of the non-convex penalty. We use ADMM to obtain a solution and show how to guarantee that ADMM converges to the global optimum of the objective function. We illustrate the proposed method for 1D and 2D signal denoising.
Nearly symmetric orthogonal wavelets with non-integer DC group delay

This paper investigates the design of Coiflet-like nearly symmetric compactly supported orthogonal wavelets. The group delay is used as the main vehicle by which near symmetry is achieved. By requiring a specified degree of flatness of the group delay at /spl omega/=0 (equivalent to appropriate moment conditions), near symmetry is achieved. The way in which the group delay approximates a constant is a traditional measure of symmetry in filter design. Grobner bases are used to obtain the solutions to the defining nonlinear equations. It is found that the DC group delay that maximizes the group delay flatness at /spl omega/=0 is irrational, and for a length 10 orthogonal wavelet with three vanishing moments, the solution is presented.
Optimization of Symmetric Self-Hilbertian Filters for the Dual-Tree Complex Wavelet Transform

In this letter, we expand upon the method of Tay for the design of orthonormal ldquoQ-shiftrdquo filters for the dual-tree complex wavelet transform. The method of Tay searches for good Hilbert-pairs in a one-parameter family of conjugate-quadrature filters that have one vanishing moment less than the Daubechies conjugate-quadrature filters (CQFs). In this letter, we compute feasible sets for one- and two-parameter families of CQFs by employing the trace parameterization of nonnegative trigonometric polynomials and semidefinite programming. This permits the design of CQF pairs that define complex wavelets that are more nearly analytic, yet still have a high number of vanishing moments.
Three Dimensional Data-Driven Multi Scale Atomic Representation of Optical Coherence Tomography

In this paper, we discuss about applications of different methods for decomposing a signal over elementary waveforms chosen in a family called a dictionary (atomic representations) in optical coherence tomography (OCT). If the representation is learned from the data, a nonparametric dictionary is defined with three fundamental properties of being data-driven, applicability on 3D, and working in multi-scale, which make it appropriate for processing of OCT images. We discuss about application of such representations including complex wavelet based K-SVD, and diffusion wavelets on OCT data. We introduce complex wavelet based K-SVD to take advantage of adaptability in dictionary learning methods to improve the performance of simple dual tree complex wavelets in speckle reduction of OCT datasets in 2D and 3D. The algorithm is evaluated on 144 randomly selected slices from twelve 3D OCTs taken by Topcon 3D OCT-1000 and Cirrus Zeiss Meditec. Improvement of contrast to noise ratio (CNR) (from 0.9 to 11.91 and from 3.09 to 88.9, respectively) is achieved. Furthermore, two approaches are proposed for image segmentation using diffusion. The first method is designing a competition between extended basis functions at each level and the second approach is defining a new distance for each level and clustering based on such distances. A combined algorithm, based on these two methods is then proposed for segmentation of retinal OCTs, which is able to localize 12 boundaries with unsigned border positioning error of 9.22 ±3.05 μm, on a test set of 20 slices selected from 13 3D OCTs.
Image Enhancement Usingwavelet-Domain Mixture Models

We propose a non-linear mapping function for digital image enhancement in the wavelet domain, which amplifies mid-range coefficients more than small and large coefficients. We derive this function based on a statistical model of the wavelet coefficients. This three-component mixture model describes the coefficients in each subband as a mixture of small, medium, and large coefficients to which different amplification factors are assigned. The model parameters are estimated from each subband using the EM algorithm. The algorithm has a small number of user-specified parameters while can obtain good enhancement results
Mitigation of Wind Turbine Clutter for Weather Radar by Signal Separation

This paper addresses the mitigation of wind turbine clutter (WTC) in weather radar data in order to increase the performance of existing weather radar systems and to improve weather analyses and forecasts. We propose a novel approach for this problem based on signal separation algorithms. We model the weather signal as group sparse in the time-frequency domain; in parallel, we model the WTC signal as having a sparse time derivative. In order to separate WTC and the desired weather returns, we formulate the signal separation problem as an optimization problem. The objective function to be minimized combines total variation regularization and time-frequency group sparsity. We also propose a three-window short-time Fourier transform for the time-frequency representation of the weather signal. To show the effectiveness of the proposed algorithm on weather radar systems, the method is applied to simulated and real data from the next-generation weather radar network. Significant improvements are observed in reflectivity, spectral width, and angular velocity estimates.
Image Denoising Employing a Mixture of Circular Symmetric Laplacian Models with Local Parameters in Complex Wavelet Domain

In this paper, we present a new image denoising algorithm. We assume a mixture of bivariate circular symmetric Laplacian probability density functions (pdfs) where for each wavelet coefficients may have different local parameter. This pdf characterizes simultaneously 1) the heavy-tailed nature, 2) the interscale dependencies of the wavelet coefficients and also 3) the empirically observed correlation between the coefficient amplitudes. We employ this local bivariate mixture model to derive a Bayesian image denoising technique. This proposed pdf, potentially can fits better the statistical properties of the wavelet coefficients than several other existing models. Our simulation results reveal that the proposed denoising method is among the best reported in the literature. This is justified since the accuracy of the employed distribution for noise-free data determines the denoising performance.
Artifact-Free Wavelet Denoising: Non-convex Sparse Regularization, Convex Optimization

Algorithms for signal denoising that combine wavelet-domain sparsity and total variation (TV) regularization are relatively free of artifacts, such as pseudo-Gibbs oscillations, normally introduced by pure wavelet thresholding. This paper formulates wavelet-TV (WATV) denoising as a unified problem. To strongly induce wavelet sparsity, the proposed approach uses non-convex penalty functions. At the same time, in order to draw on the advantages of convex optimization (unique minimum, reliable algorithms, simplified regularization parameter selection), the non-convex penalties are chosen so as to ensure the convexity of the total objective function. A computationally efficient, fast converging algorithm is derived.
A Dual-Tree Rational-Dilation Complex Wavelet Transform

In this correspondence, we introduce a dual-tree rational-dilation complex wavelet transform for oscillatory signal processing. Like the short-time Fourier transform and the dyadic dual-tree complex wavelet transform, the introduced transform employs quadrature pairs of time-frequency atoms which allow to work with the analytic signal. The introduced wavelet transform is a constant-Q transform, a property lacked by the short-time Fourier transform, which in turn makes the introduced transform more suitable for models that depend on scale. Also, the frequency resolution can be as high as desired, a property lacked by the dyadic dual-tree complex wavelet transform, which makes the introduced transform more suitable for processing oscillatory signals like speech, audio and various biomedical signals.
Convex fused lasso denoising with non-convex regularization and its use for pulse detection

We propose a convex formulation of the fused lasso signal approximation problem consisting of non-convex penalty functions. The fused lasso signal model aims to estimate a sparse piecewise constant signal from a noisy observation. Originally, the ℓ1 norm was used as a sparsity-inducing convex penalty function for the fused lasso signal approximation problem. However, the ℓ1 norm underestimates signal values. Non-convex sparsity-inducing penalty functions better estimate signal values. In this paper, we show how to ensure the convexity of the fused lasso signal approximation problem with non-convex penalty functions. We further derive a computationally efficient algorithm using the majorization-minimization technique. We apply the proposed fused lasso method for the detection of pulses.
Balanced GHM-like multiscaling functions

The Geronimo-Bardin-Massopust (see J. Approx. Theory, vol.78, p.373-401, 1994) multiwavelet basis exhibits symmetry, orthogonality, short support, and approximation order K=2, which is not possible for wavelet bases based on a single scaling-wavelet function pair. However, the filterbank associated with this basis does not inherit the zero moment properties of the basis. This work describes a version of the GHM multiscaling functions (constructed with Grobner bases) for which the zero moment properties do carry over to the associated filterbank. That is, the basis is balanced up to its approximation order K=2.
Nonlinear-phase maximally-flat lowpass FIR filter design

This paper reports a new analytic technique for the design of nonlinear-phase maximally-flat lowpass FIR filters. By subjecting the response magnitude and the group delay (individually) to differing numbers of flatness constraints, a new family of filters is obtained. With these filters, the delay can be reduced while maintaining relatively constant group delay in the passband, without significantly altering the response magnitude.
The double-density dual-tree DWT

This paper introduces the double-density dual-tree discrete wavelet transform (DWT), which is a DWT that combines the double-density DWT and the dual-tree DWT, each of which has its own characteristics and advantages. The transform corresponds to a new family of dyadic wavelet tight frames based on two scaling functions and four distinct wavelets. One pair of the four wavelets are designed to be offset from the other pair of wavelets so that the integer translates of one wavelet pair fall midway between the integer translates of the other pair. Simultaneously, one pair of wavelets are designed to be approximate Hilbert transforms of the other pair of wavelets so that two complex (approximately analytic) wavelets can be formed. Therefore, they can be used to implement complex and directional wavelet transforms. The paper develops a design procedure to obtain finite impulse response (FIR) filters that satisfy the numerous constraints imposed. This design procedure employs a fractional-delay allpass filter, spectral factorization, and filterbank completion. The solutions have vanishing moments, compact support, a high degree of smoothness, and are nearly shift-invariant.
Image Denoising Employing a Bivariate Cauchy Distribution with Local Variance in Complex Wavelet Domain

The performance of various estimators, such as maximum a posteriori (MAP) is strongly dependent on correctness of the proposed model for noise-free data distribution. Therefore, the selection of a proper model for distribution of wavelet coefficients is important in the wavelet based image denoising. This paper presents a new image denoising algorithm based on the modeling of wavelet coefficients in each subband with a bivariate Cauchy probability density functions (pdfs) with local variance. The bivariate pdf takes into account the statistical dependency among wavelet coefficients and the local variance model the empirically observed correlation between the coefficient amplitudes. Therefore, by using this statistical model, we are able to better model statistical property of wavelet coefficients. Within this framework, we propose a novel method for image denoising employing a bivariate MAP estimator, which relies on the bivariate distribution with high local correlation. The simulation results show that our proposed technique outperforms several exiting methods both visually and in terms of peak signal-to-noise ratio (PSNR)
Sparsity-assisted signal smoothing (revisited)

This paper proposes an improved formulation of sparsity-assisted signal smoothing (SASS). The purpose of SASS is to filter/denoise a signal that has jump discontinuities in its derivative (of some designated order) but is otherwise smooth. SASS unifies conventional low-pass filtering and total variation denoising. The SASS algorithm depends on the formulation, in terms of banded Toeplitz matrices, of a zero-phase recursive discrete-time filter as applied to finite-length data. The improved formulation presented in this paper avoids the unwanted end-point transient artifacts which sometimes occur in the original version. For illustration, SASS is applied to ECG signal denoising.
Bivariate shrinkage functions for wavelet-based denoising exploiting interscale dependency

Most simple nonlinear thresholding rules for wavelet-based denoising assume that the wavelet coefficients are independent. However, wavelet coefficients of natural images have significant dependencies. We only consider the dependencies between the coefficients and their parents in detail. For this purpose, new non-Gaussian bivariate distributions are proposed, and corresponding nonlinear threshold functions (shrinkage functions) are derived from the models using Bayesian estimation theory. The new shrinkage functions do not assume the independence of wavelet coefficients. We show three image denoising examples in order to show the performance of these new bivariate shrinkage rules. In the second example, a simple subband-dependent data-driven image denoising system is described and compared with effective data-driven techniques in the literature, namely VisuShrink, SureShrink, BayesShrink, and hidden Markov models. In the third example, the same idea is applied to the dual-tree complex wavelet coefficients.
The slantlet transform

The discrete wavelet transform (DWT) is usually carried out by filterbank iteration; however, for a fixed number of zero moments, this does not yield a discrete-time basis that is optimal with respect to time localization. This paper discusses the implementation and properties of an orthogonal DWT, with two zero moments and with improved time localization. The basis is not based on filterbank iteration; instead, different filters are used for each scale. For coarse scales, the support of the discrete-time basis functions approaches two thirds that of the corresponding functions obtained by filterbank iteration. This basis, which is a special case of a class of bases described by Alpert (1992, 1993), retains the octave-band characteristic and is piecewise linear (but discontinuous). Closed-form expressions for the filters are given, an efficient implementation of the transform is described, and improvement in a denoising example is shown. This basis, being piecewise linear, is reminiscent of the slant transform, to which it is compared.
Sleep spindle detection using time-frequency sparsity

This paper proposes an EEG processor for sleep spindle detection algorithms. It non-linearly separates the raw EEG signal into non-oscillatory transient and sustained rhythmic oscillation components using long and short windows for the short-time Fourier transform. The processor utilizes the fact that sleep spindles can be sparsely represented via the inverse of a short-time Fourier transform. Five sleep spindle detectors were tested on the EEG database with and without the proposed EEG processor. We achieved an improvement of 13.3% in the by-sample F1 score, and 13.9% in the by-sample Matthews Correlation Coefficient score of these algorithms when the processed EEG was used for spindle detection. The processor was able to improve the scores by reducing the number of false positive spindles and increasing the number of true positive spindles detected.