nils-herrmann/clean_scirepeval huggingface dataset:
Bayesian estimation of a subspace

We consider the problem of subspace estimation in a Bayesian setting. First, we revisit the conventional minimum mean square error (MSE) estimator and explain why the MSE criterion may not be fully suitable when operating in the Grassmann manifold. As an alternative, we propose to carry out subspace estimation by minimizing the mean square distance between the true subspace U and its estimate, where the considered distance is a natural metric on the Grassmann manifold. We show that the resulting estimator is no longer the posterior mean of U but entails computing the principal eigenvectors of the posterior mean of UUT. Illustrative examples involving a linear Gaussian model for the data and a Bingham or von Mises Fisher prior distribution for U are presented. In the former case the minimum mean square distance (MMSD) estimator is obtained in closed-form while, in the latter case, a Markov chain Monte Carlo method is used to approximate the MMSD estimator. The method is shown to provide accurate estimates even when the number of samples is lower than the dimension of U. Finally, an application to hyperspectral imagery is presented.
Bayesian compressed sensing in ultrasound imaging

Following our previous study on compressed sensing for ultrasound imaging, this paper proposes to exploit the image sparsity in the frequency domain within a Bayesian approach. A Bernoulli-Gaussian prior is assigned to the Fourier transform of the ultrasound image in order to enforce sparsity and to reconstruct the image via Bayesian compressed sensing. In addition, the Bayesian approach allows the image sparsity level in the spectral domain to be estimated, a significant parameter in the l1 constrained minimization problem related to compressed sensing. Results obtained with a simulated ultrasound image and an in vivo image of a human thyroid gland show a reconstruction performance similar to a classical compressed sensing algorithm from half of spatial samples while estimating the sparsity level during reconstruction.
ECG denoising using a dynamical model and a marginalized particle filter

The development of robust ECG denoising techniques is important for automatic diagnoses of cardiac diseases. Based on a previously suggested nonlinear dynamic model for the generation of realistic synthetic ECG, we introduce a modified ECG dynamical model with 18 state variables to further include morphology variations. A marginalized particle filter is proposed for tracking this modified nonlinear state-space model which has linear substructures. Quantitative evaluations on the MIT-BIH database show that the proposed algorithm outperforms the extended Kalman filter-based algorithms and can better handle non-Gaussian distributions.
Classification of chirp signals using hierarchical Bayesian learning and MCMC methods

This paper addresses the problem of classifying chirp signals using hierarchical Bayesian learning together with Markov chain Monte Carlo (MCMC) methods. Bayesian learning consists of estimating the distribution of the observed data conditional on each class from a set of training samples. Unfortunately, this estimation requires to evaluate intractable multidimensional integrals. This paper studies an original implementation of hierarchical Bayesian learning that estimates the class conditional probability densities using MCMC methods. The performance of this implementation is first studied via an academic example for which the class conditional densities are known. The problem of classifying chirp signals is then addressed by using a similar hierarchical Bayesian learning implementation based on a Metropolis-within-Gibbs algorithm.
Minimum Mean Square Distance Estimation of a Subspace

We consider the problem of subspace estimation in a Bayesian setting. Since we are operating in the Grassmann manifold, the usual approach which consists of minimizing the mean square error (MSE) between the true subspace U and its estimate U may not be adequate as the MSE is not the natural metric in the Grassmann manifold GN,p, i.e., the set of p-dimensional subspaces in RN. As an alternative, we propose to carry out subspace estimation by minimizing the mean square distance between U and its estimate, where the considered distance is a natural metric in the Grassmann manifold, viz. the distance between the projection matrices. We show that the resulting estimator is no longer the posterior mean of U but entails computing the principal eigenvectors of the posterior mean of UUT. Derivation of the minimum mean square distance (MMSD) estimator is carried out in a few illustrative examples including a linear Gaussian model for the data and Bingham or von Mises Fisher prior distributions for U. In all scenarios, posterior distributions are derived and the MMSD estimator is obtained either analytically or implemented via a Markov chain Monte Carlo simulation method. The method is shown to provide accurate estimates even when the number of samples is lower than the dimension of U. An application to hyperspectral imagery is Anally investigated.
Optimized spatial resampling for microphone array beamforming

Due to the specialty of portable devices, the microphone array configurations usually depend on the device manufacturing constraints, and thus are various and generally irregular. It is then more difficult for the algorithm designers to establish a generic processing. The main contribution of this paper is an optimized spatial resampling procedure for beam-forming with irregular 3-D sensor arrays. Beam pattern analysis show that, via spatial resampling, it is possible to apply beamformer coefficients designed for Uniform Linear Array (ULA) to signals captured by arrays having arbitrary configurations and thus carry out beamforming and spatial filtering in both azimuth and zenith directions. Moreover, this algorithm may benefit to other multi-sensor audio processing methods that require specific sensor array configuration.
On-line model selection of nonstationary time series using Gerschgorin disks

The paper proposes a method for on-line model selection of nonstationary time series. The method is based on computation of the covariance matrix of the data, transformation of the matrix by Housholder's tridiagonalization, and application of a clustering algorithm that can separate the Gerschgorin disks of the transformed covariance matrix into disks that correspond to the signals and noise, respectively. The method is applied to on-line estimation of the the number of harmonic signals in noise. Simulation results are presented that show the performance of the proposed method.
Change Detection in Multisensor SAR Images Using Bivariate Gamma Distributions

This paper studies a family of distributions constructed from multivariate gamma distributions to model the statistical properties of multisensor synthetic aperture radar (SAR) images. These distributions referred to as multisensor multivariate gamma distributions (MuMGDs) are potentially interesting for detecting changes in SAR images acquired by different sensors having different numbers of looks. The first part of this paper compares different estimators for the parameters of MuMGDs. These estimators are based on the maximum likelihood principle, the method of inference function for margins, and the method of moments. The second part of the paper studies change detection algorithms based on the estimated correlation coefficient of MuMGDs. Simulation results conducted on synthetic and real data illustrate the performance of these change detectors.
Tissue motion estimation using dictionary learning: Application to cardiac amyloidosis

Cardiac strain estimation from ultrasound images is an efficient tool for the diagnosis of cardiac diseases. This study focuses on cardiac amyloidosis (CA), a pathology characterized by nonspecific early symptoms such as increased wall thickness. Recent clinical studies have demonstrated that patients with CA present an apex-to-base gradient longitudinal strain pattern, i.e., a normal strain in apex and abnormally lower values for base segments. Existing cardiac motion estimation (ME) methods belong to three categories: optical flow, speckle tracking and elastic registration. To overcome the ill-posedness of ME, they use local parametric models (e.g., affine) or global regularizations (e.g., B-splines). The objective of this study is twofold: i) to propose a novel ME method based on dictionary learning, ii) to evaluate this method on patients subjected to CA.
Hybrid sparse regularization for magnetic resonance spectroscopy

Magnetic resonance spectroscopy imaging (MRSI) is a powerful non-invasive tool for characterising markers of biological processes. This technique extends conventional MRI by providing an additional dimension of spectral information describing the abnormal presence or concentration of metabolites of interest. Unfortunately, in vivo MRSI suffers from poor signal-to-noise ratio limiting its clinical use for treatment purposes. This is due to the combination of a weak MR signal and low metabolite concentrations, in addition to the acquisition noise. We propose a new method that handles this challenge by efficiently denoising MRSI signals without constraining the spectral or spatial profiles. The proposed denoising approach is based on wavelet transforms and exploits the sparsity of the MRSI signals both in the spatial and frequency domains. A fast proximal optimization algorithm is then used to recover the optimal solution. Experiments on synthetic and real MRSI data showed that the proposed scheme achieves superior noise suppression (SNR increase up to 60%). In addition, this method is computationally efficient and preserves data features better than existing methods.
Velocity Dealiased Spectral Estimators of Range Migrating Targets using a Single Low-PRF Wideband Waveform

Wideband radars are promising systems that may provide numerous advantages, like simultaneous detection of slow and fast moving targets, high range-velocity resolution classification, and electronic counter-countermeasures. Unfortunately, classical processing algorithms are challenged by the range- migration phenomenon that occurs then for fast moving targets. We propose a new approach where the range migration is used rather as an asset to retrieve information about target velocities and, subsequently, to obtain a velocity dealiased mode. More specifically three new complex spectral estimators are devised in case of a single low-PRF (pulse repetition frequency) wideband waveform. The new estimation schemes enable one to decrease the level of sidelobes that arise at ambiguous velocities and, thus, to enhance the discrimination capability of the radar. Synthetic data and experimental data are used to assess the performance of the proposed estimators.
Spectral estimation of a Gaussian signal sampled with jitter

This article tackles the problem of a Gaussian band-limited continuous signal with unknown characteristics sampled with jitter. Under this weak assumption, we demonstrate a relation linking the power spectral density of the continuous signal to the second and fourth order statistics of the measured samples. A fundamental point is that this relation does not require a knowledge of the jitter characteristics. This result can be exploited for the derivation of spectral estimation algorithms when the jitter is unknown or jitter detection tests when the sampled signal is unknown. A simulation of spectral estimation confirms the validity of the result.
A Hierarchical Bayesian Model Accounting for Endmember Variability and Abrupt Spectral Changes to Unmix Multitemporal Hyperspectral Images

Hyperspectral unmixing is a blind source separation problem that consists in estimating the reference spectral signatures contained in a hyperspectral image, as well as their relative contribution to each pixel according to a given mixture model. In practice, the process is further complexified by the inherent spectral variability of the observed scene and the possible presence of outliers. More specifically, multitemporal hyperspectral images, i.e., sequences of hyperspectral images acquired over the same area at different time instants, are likely to simultaneously exhibit moderate endmember variability and abrupt spectral changes either due to outliers or to significant time intervals between consecutive acquisitions. Unless properly accounted for, these two perturbations can significantly affect the unmixing process. In this context, we propose a new unmixing model for multitemporal hyperspectral images accounting for smooth temporal variations, construed as spectral variability, and abrupt spectral changes interpreted as outliers. The proposed hierarchical Bayesian model is inferred using a Markov chain Monte Carlo method allowing the posterior of interest to be sampled and Bayesian estimators to be approximated. A comparison with unmixing techniques from the literature on synthetic and real data allows the interest of the proposed approach to be appreciated.
Estimating the Number of Endmembers in Hyperspectral Images Using the Normal Compositional Model and a Hierarchical Bayesian Algorithm

This paper studies a semi-supervised Bayesian unmixing algorithm for hyperspectral images. This algorithm is based on the normal compositional model recently introduced by Eismann and Stein. The normal compositional model assumes that each pixel of the image is modeled as a linear combination of an unknown number of pure materials, called endmembers. However, contrary to the classical linear mixing model, these endmembers are supposed to be random in order to model uncertainties regarding their knowledge. This paper proposes to estimate the mixture coefficients of the Normal Compositional Model (referred to as abundances) as well as their number using a reversible jump Bayesian algorithm. The performance of the proposed methodology is evaluated thanks to simulations conducted on synthetic and real AVIRIS images.
Cardiac motion estimation in ultrasound images using spatial and sparse regularizations

This paper investigates a new method for cardiac motion estimation in 2D ultrasound images. The motion estimation problem is formulated as an energy minimization with spatial and sparse regularizations. In addition to a classical spatial smoothness constraint, the proposed method exploits the sparse properties of the cardiac motion to regularize the solution via an appropriate dictionary learning step. The proposed method is evaluated in terms of motion estimation and strain accuracy and compared with state-of-the-art algorithms using a dataset of realistic simulations. These simulation results show that the proposed method provides very promising results for myocardial motion estimation.
An affine combination of two LMS adaptive filters - statistical analysis of an error power ratio scheme

A recent paper  studied the statistical behavior of an affine combination of two LMS adaptive filters that simultaneously adapt on the same inputs. The filter outputs are linearly combined to yield a performance that is better than that of either filter. Various decision rules can be used to determine the time-varying combining parameter λ(n). A scheme based on the ratio of error powers of the two filters was proposed in . Monte Carlo simulations demonstrated nearly optimum performance for this scheme. The purpose of this paper is to analyze the statistitical behavior of such error power scheme. Expressions are derived for the mean behavior of λ(n) and for the weight mean-square deviation. Monte Carlo simulations show excellent agreement with the theoretical predictions.
Motion Estimation in Echocardiography Using Sparse Representation and Dictionary Learning

This paper introduces a new method for cardiac motion estimation in 2-D ultrasound images. The motion estimation problem is formulated as an energy minimization, whose data fidelity term is built using the assumption that the images are corrupted by multiplicative Rayleigh noise. In addition to a classical spatial smoothness constraint, the proposed method exploits the sparse properties of the cardiac motion to regularize the solution via an appropriate dictionary learning step. The proposed method is evaluated on one data set with available ground-truth, including four sequences of highly realistic simulations. The approach is also validated on both healthy and pathological sequences of in vivo data. We evaluate the method in terms of motion estimation accuracy and strain errors and compare the performance with state-of-the-art algorithms. The results show that the proposed method gives competitive results for the considered data. Furthermore, the in vivo strain analysis demonstrates that meaningful clinical interpretation can be obtained from the estimated motion vectors.
Fast Single Image Super-resolution using a New Analytical Solution for l2-l2 Problems.

This paper addresses the problem of single image super-resolution (SR), which consists of recovering a high resolution image from its blurred, decimated and noisy version. The existing algorithms for single image SR use different strategies to handle the decimation and blurring operators. In addition to the traditional first-order gradient methods, recent techniques investigate splitting-based methods dividing the SR problem into up-sampling and deconvolution steps that can be easily solved. Instead of following this splitting strategy, we propose to deal with the decimation and blurring operators simultaneously by taking advantage of their particular properties in the frequency domain, leading to a new fast SR approach. Specifically, an analytical solution can be obtained and implemented efficiently for the Gaussian prior or any other regularization that can be formulated into an `2-regularized quadratic model, i.e., an `2-`2 optimization problem. Furthermore, the flexibility of the proposed SR scheme is shown through the use of various priors/regularizations, ranging from generic image priors to learning-based approaches. In the case of non-Gaussian priors, we show how the analytical solution derived from the Gaussian case can be embedded into traditional splitting frameworks, allowing the computation cost of existing algorithms to be decreased significantly. Simulation results conducted on several images with different priors illustrate the effectiveness of our fast SR approach compared with the existing techniques.
Bayesian Covariance Matrix Estimation with Non-Homogeneous Snapshots

We address the problem of estimating the covariance matrix Mp of an observation vector, using K groups of training samples {Zk}Kk=1, of respective size Lk, whose covariance matrices Mk may differ from Mp. A Bayesian model is formulated where we assume that Mp and the matrices Mk are random, with some prior distribution. Within this framework, we derive the minimum mean-square error (MMSE) estimator of Mp which is implemented using a Gibbs-sampling strategy. Moreover, we consider simpler estimators based on a weighted sum of the sample covariance matrices of Zk. We derive an expression for the weights that result in minimum mean square error (MSE), within this class of estimators. Numerical simulations are presented to illustrate the performances of the different estimation schemes.
Multivariate Markovian gamma distributions for multitemporal sequences of SAR images

This paper introduces a family of multivariate gamma distributions characterized by a Markovian correlation structure. These distributions are interesting for detecting changes between multi-temporal sequences of synthetic aperture radar images. The parameters of these distributions can be estimated by using the maximum likelihood principle. This estimation procedure allows one to obtain a change indicator between each pair of images. A performance comparison with maximum likelihood estimators derived from a bivariate gamma distribution model is conducted. The gain of performance provided by the Markovian multivariate model with respect to a bivariate model is emphasized on synthetic and real images.
Bayesian fusion of hyperspectral and multispectral images

This paper presents a Bayesian fusion technique for multi-band images. The observed images are related to the high spectral and high spatial resolution image to be recovered through physical degradations, e.g., spatial and spectral blurring and/or subsampling defined by the sensor characteristics. The fusion problem is formulated within a Bayesian estimation framework. An appropriate prior distribution related to the linear mixing model for hyperspectral images is introduced. To compute Bayesian estimators of the scene of interest from its posterior distribution, a Gibbs sampling algorithm is proposed to generate samples asymptotically distributed according to the target distribution. To efficiently sample from this high-dimensional distribution, a Hamiltonian Monte Carlo step is introduced in this Gibbs sampler. The efficiency of the proposed fusion method is evaluated with respect to several state-of-the-art fusion techniques.
Computing the Cramer–Rao Bound of Markov Random Field Parameters: Application to the Ising and the Potts Models

This letter considers the problem of computing the Cramer-Rao bound for the parameters of a Markov random field. Computation of the exact bound is not feasible for most fields of interest because their likelihoods are intractable and have intractable derivatives. We show here how it is possible to formulate the computation of the bound as a statistical inference problem that can be solve approximately, but with arbitrarily high accuracy, by using a Monte Carlo method. The proposed methodology is successfully applied on the Ising and the Potts models.
A new model for peaky altimetric waveforms

Coastal altimetric waveforms may be corrupted by peaks. A simple parametric model was recently introduced to model peaky altimetric waveforms. This model assumes that the received altimetric waveform is the sum of a Brown echo and a Gaussian peak. This model has provided interesting results for symmetric peaks affecting altimetric signals. However, it is not appropriate for altimetric signals corrupted by asymmetric peaks. This paper introduces a Brown with asymmetric Gaussian peak model for altimetric waveforms. The parameters of this model are estimated by a maximum likelihood estimator. The performance of the proposed model and the resulting estimation strategy is evaluated via simulations conducted on synthetic and real data.
Singular ARMA signals

Singular random signals are collections of singular random variables indexed over time. Singular random variables have continuous distribution with derivatives equal to zero almost everywhere. Such random variables do not seem interesting in signal processing. On the contrary, the paper shows that simple signals can be singular. This is especially the case of ARMA signals generated from discrete white noise with poles located inside a so-called singularity circle. The origin of singularity and its relations to a fractal structure are presented along with various simulations illustrating the theoretical results.
An NCM-based Bayesian algorithm for hyperspectral unmixing

This paper studies a new Bayesian algorithm to unmix hyperspectral images. The algorithm is based on the recent normal compositional model introduced by Eismann. Contrary to the standard linear mixing model, the endmember spectra are assumed to be random signatures with know mean vectors. Appropriate prior distributions are assigned to the abundance coefficients to ensure the usual positivity and sum-to-one constraints. However, the resulting posterior distribution is too complex to obtain a closed form expression for the Bayesian estimators. A Markov chain Monte Carlo algorithm is then proposed to generate samples distributed according to the full posterior distribution. These samples are used to estimate the unknown model parameters. Several simulations are conducted on synthetic and real data to illustrate the performance of the proposed method.