nils-herrmann/clean_scirepeval huggingface dataset:
Convex half-quadratic criteria and interacting auxiliary variables for image restoration

This paper deals with convex half-quadratic criteria and associated minimization algorithms for the purpose of image restoration. It brings a number of original elements within a unified mathematical presentation based on convex duality. Firstly, the Geman and Yang's and Geman and Reynolds's constructions are revisited, with a view to establishing the convexity properties of the resulting half-quadratic augmented criteria, when the original nonquadratic criterion is already convex. Secondly, a family of convex Gibbsian energies that incorporate interacting auxiliary variables is revealed as a potentially fruitful extension of the Geman and Reynolds's construction.
Joint K-Step Analysis of Orthogonal Matching Pursuit and Orthogonal Least Squares

Tropp's analysis of orthogonal matching pursuit (OMP) using the exact recovery condition (ERC) is extended to a first exact recovery analysis of orthogonal least squares (OLS). We show that when the ERC is met, OLS is guaranteed to exactly recover the unknown support in at most k iterations where k denotes the support cardinality. Moreover, we provide a closer look at the analysis of both OMP and OLS when the ERC is not fulfilled. The existence of dictionaries for which some subsets are never recovered by OMP is proved. This phenomenon also appears with basis pursuit where support recovery depends on the sign patterns, but it does not occur for OLS. Finally, numerical experiments show that none of the considered algorithms is uniformly better than the other but for correlated dictionaries, guaranteed exact recovery may be obtained after fewer iterations for OLS than for OMP.
Exact Recovery Conditions for Sparse Representations With Partial Support Information

We address the exact recovery of a k-sparse vector in the noiseless setting when some partial information on the support is available. This partial information takes the form of either a subset of the true support or an approximate subset including wrong atoms as well. We derive a new sufficient and worst-case necessary (in some sense) condition for the success of some procedures based on ℓp-relaxation, orthogonal matching pursuit (OMP), and orthogonal least squares (OLS). Our result is based on the coherence μ of the dictionary and relaxes the well-known condition μ <; 1/2k - 1) ensuring the recovery of any k-sparse vector in the noninformed setup. It reads μ <; 1/(2k - g + b - 1) when the informed support is composed of g good atoms and b wrong atoms. We emphasize that our condition is complementary to some restricted-isometry-based conditions by showing that none of them implies the other. Because this mutual coherence condition is common to all procedures, we carry out a finer analysis based on the null space property (NSP) and the exact recovery condition (ERC). Connections are established regarding the characterization of ℓp-relaxation procedures and OMP in the informed setup. First, we emphasize that the truncated NSP enjoys an ordering property when p is decreased. Second, the partial ERC for OMP (ERC-OMP) implies in turn the truncated NSP for the informed ℓ1 problem, and the truncated NSP for p <; 1 .
Resolution enhancement of ultrasonic signals by up-sampled sparse deconvolution

This paper deals with the estimation of the arrival times of overlapping ultrasonic echoes. We focus on approaches based on discrete sparse deconvolution. Such methods are limited by the time resolution imposed by the model discretization, which is usually considered at the data sampling rate. In order to get closer to the continuous-time model, we propose to increase the time precision by introducing an up-sampling factor in the discrete model. The problem is then recast as a Multiple Input Single Output (MISO) deconvolution problem. Then, we propose to revisit standard sparse deconvolution algorithms for MISO systems. Specific and efficient algorithmic implementation is derived in such setting. Algorithms are evaluated on synthetic data, showing improvements in robustness toward discretization errors and competitive computational time compared to the standard approaches.
A single site update algorithm for nonlinear diffraction tomography

We focus on the nonlinear inverse problem of diffraction tomography. We set the problem as one of estimation within the Bayesian framework and define the solution as the maximum a posteriori (MAP) estimate which corresponds to the global minimum of a multimodal criterion. The objective of this paper is to present a new deterministic single site update algorithm specially designed to compute this solution. The term of fidelity to the data, function of one pixel value, can be written as a second order rational fraction. Thus, the 1-D MAP criterion can be evaluated and minimized-at a very low computational cost. Moreover, for certain MRF models the global minimum can even be computed explicitly as roots of a polynomial. The proposed algorithm turns these properties to advantage and moreover performs the updates of intermediate quantities at a particularly low cost compared to the criterion evaluation. Even if not guaranteed to converge towards the global minimum, the algorithm has shown itself to give satisfactory practical results.
A FEM-based nonlinear MAP estimator in electrical impedance tomography

Electrical impedance tomography of closed conductive media is an ill-posed inverse problem. Using the finite elements method to solve the corresponding direct problem allows one to preserve the nonlinear dependence of the observation set upon the conductivity distribution. We show that the Bayesian approach presented by Demoment (1989) for linear inverse imaging problems is still valid for such a nonlinear inverse problem. Our contribution is based on an edge-preserving Markov model as a prior for conductivity distribution. Maximum a posteriori reconstruction results from 40-dB noisy measurements (simulated with a finer mesh) yield significant resolution improvement compared to classical methods.
Unsupervised deconvolution of sparse spike trains using stochastic approximation

This paper presents an unsupervised method for restoration of sparse spike trains. These signals are modeled as random Bernoulli-Gaussian processes, and their unsupervised restoration requires (i) estimation of the hyperparameters that control the stochastic models of the input and noise signals and (ii) deconvolution of the pulse process. Classically, the problem is solved iteratively using a maximum generalized likelihood approach despite questionable statistical properties. The contribution of the article is threefold. First, we present a new "core algorithm" for supervised deconvolution of spike trains, which exhibits enhanced numerical efficiency and reduced memory requirements. Second, we propose an original implementation of a hyperparameter estimation procedure that is based upon a stochastic version of the expectation-maximization (EM) algorithm. This procedure utilizes the same core algorithm as the supervised deconvolution method. Third, Monte Carlo simulations show that the proposed unsupervised restoration method exhibits satisfactory theoretical and practical behavior and that, in addition, good global numerical efficiency is achieved.
Single image local blur identification

We present a new approach for spatially varying blur identification using a single image. Within each local patch in the image, the local blur is selected between a finite set of candidate PSFs by a maximum likelihood approach. We propose to work with a Generalized Likelihood to reduce the number of parameters and we use the Generalized Singular Value Decomposition to limit the computing cost, while making proper image boundary hypotheses. The resulting method is fast and demonstrates good performance on simulated and real examples originating from applications such as motion blur identification and depth from defocus.
Joint detection-estimation of brain activity in fMRI using an autoregressive noise model

Different approaches have been considered so far to cope with the temporal correlation of fMRI data for brain activity detection. However, it has been reported that modeling this serial correlation has little influence on the estimate of the hemodynamic response function (HRF). In this paper, we examine this issue when performing a joint detection-estimation of brain activity in a given homogeneous region of interest (ROI). Following the work of Bullmore et al. (1996), we adopt a space-varying AR(1) temporal noise model and assess its influence, on both the estimation of the HRF and the detection of brain activity, using synthetic and real fMRI data. We show that this model yields a significant gain in detection specificity (lower false positive rate)
Sparse Blind Deconvolution Accounting for Time-Shift Ambiguity

Our contribution deals with blind deconvolution of sparse spike trains. More precisely, we examine the problem in the Markov chain Monte-Carlo (MCMC) framework, where the unknown spike train is modeled as a Bernoulli-Gaussian process. In this context, we point out that time-shift and scale ambiguities jeopardize the robustness of basic MCMC methods, in quite a similar manner to the label switching effect studied by Stephens (2000) in mixture model identification. Finally, we propose proper modifications of the MCMC approach, in the same spirit as Stephens' contribution
A Sparsity-Based Method for the Estimation of Spectral Lines From Irregularly Sampled Data

We address the problem of estimating spectral lines from irregularly sampled data within the framework of sparse representations. Spectral analysis is formulated as a linear inverse problem, which is solved by minimizing an l1-norm penalized cost function. This approach can be viewed as a basis pursuit de-noising (BPDN) problem using a dictionary of cisoids with high frequency resolution. In the studied case, however, usual BPDN characterizations of uniqueness and sparsity do not apply. This paper deals with the l1-norm penalization of complex-valued variables, that brings satisfactory prior modeling for the estimation of spectral lines. An analytical characterization of the minimizer of the criterion is given and geometrical properties are derived about the uniqueness and the sparsity of the solution. An efficient optimization strategy is proposed. Convergence properties of the iterative coordinate descent (ICD) and iterative reweighted least-squares (IRLS) algorithms are first examined. Then, both strategies are merged in a convergent procedure, that takes advantage of the specificities of ICD and IRLS, considerably improving the convergence speed. The computation of the resulting spectrum estimator can be implemented efficiently for any sampling scheme. Algorithm performance and estimation quality are illustrated throughout the paper using an artificial data set, typical of some astrophysical problems, where sampling irregularities are caused by day/night alternation. We show that accurate frequency location is achieved with high resolution. In particular, compared with sequential Matching Pursuit methods, the proposed approach is shown to achieve more robustness regarding sampling artifacts.
A new algorithm for iterative deconvolution of sparse spike trains

An iterative algorithm for deconvolution of Bernoulli-Gaussian processes is presented. This detection-estimation problem is formulated as that of a change of initial conditions in linear least-squares estimation. An algorithm with a very simple structure is obtained. It allows the evaluation of either marginal or joint likelihood criteria without any approximation; the resulting method is easy to implement and computationally inexpensive and remains nearly optimal.<<ETX>>
On LARS/Homotopy Equivalence Conditions for Over-Determined LASSO

We revisit the positive cone condition given by Efron for the over-determined least absolute shrinkage and selection operator (LASSO). It is a sufficient condition ensuring that the number of nonzero entries in the solution vector keeps increasing when the penalty parameter decreases, based on which the least angle regression (LARS) and homotopy algorithms yield the same iterates. We show that the positive cone condition is equivalent to the diagonal dominance of the Gram matrix inverse, leading to a simpler way to check the positive cone condition in practice. Moreover, we elaborate on a connection between the positive cone condition and the mutual coherence condition given by Donoho and Tsaig , ensuring the exact recovery of any k -sparse representation using both LARS and homotopy.
An optimal method to segment piecewise poisson distributed signals with application to sequencing data

To analyze the next generation sequencing data, the so-called read depth signal is often segmented with standard segmentation tools. However, these tools usually assume the signal to be a piecewise constant signal and contaminated with zero mean Gaussian noise, and therefore modeling error occurs. This paper models the read depth signal with piecewise Poisson distribution, which is more appropriate to the next generation sequencing mechanism. Based on the proposed model, an opti- mal dynamic programming algorithm with parallel computing is proposed to segment the piecewise signal, and furthermore detect the copy number variation.
Stack algorithm for recursive deconvolution of Bernoulli-Gaussian processes (seismic exploration)

The deconvolution of pulse trains modeled as Bernoulli-Gaussian processes is addressed. The detector presented implements a stack Viterbi algorithm with a parametric level of suboptimality. Simulation results are satisfactory, even in the difficult case of a poor spectral content of the wavelet. The recursive and parallel structure of the method allows fast data processing on modern architectures.
X-ray and ultrasound data fusion

This work deals with three dimensional reconstruction from X-ray and ultrasonic images. Such an issue pertains to the field of data fusion since the data provide complementary information. The two sets of data are independently related to two sets of parameters: X-ray attenuation and ultrasonic reflectivity. The fusion problem is addressed in a Bayesian framework; the kingpin of the task is to define a joint prior model for both attenuation and reflectivity. Dealing with the joint prior model, we propose to correlate the derivative of the attenuation and the reflectivity. Processing examples demonstrate the validity of the fusion approach and the robustness of the proposed method mismatching of the two sets of data.
3-term optimization criterion for faster inversion in microwave tomography

The problem of microwave tomography consists of finding the electrical characteristics (permittivity and conductivity) of a medium using scattered fields measured under various conditions of illumination. Such inversion can be achieved with a variety of techniques based upon the minimization of an appropriate criterion. The popular current source inversion (CSI) technique is one of those. In this paper, the CSI technique is presented and its main limitations are underlined. Then, in order to overcome these limitations, a generalized form of CSI is developed. An analysis of the time consuming operations of this new algorithm is done, and a new technique is proposed; it proves to be faster than the other two methods, the speed increase ranging between factors of 2 and 5. Performance of the algorithms is illustrated with examples based on synthetic data.
Impact of sparse representation on the admissible solutions of spectral unmixing by non-negative matrix factorization

Spectral unmixing in the linear mixing model case can be addressed using non-negative matrix factorization (NMF) algorithms. However, NMF algorithms do not yield a unique solution when the data at hand does not satisfy some uniqueness conditions. Therefore, a set of admissible solutions will be found. The main purpose of this paper is to discuss how much a sparse representation of the data matrix can reduce this set of admissible solutions in the case of spectral unmixing. We propose an algorithm allowing to perform efficiently the sparse representation of data matrix under non-negativity constraints and to assess the admissible solutions when the NMF is performed on the sparse data matrix in the case of reflectance hyperspectral imaging data.
Bayesian Joint Detection-Estimation of Brain Activity Using MCMC With a Gamma-Gaussian Mixture Prior Model

The classical approach of within-subject analysis in event-related functional magnetic resonance imaging (fMRI) first relies on (i) a detection step to localize which parts of the brain are activated by a given stimulus type, and then on (ii) an estimation step to recover the temporal dynamics of the brain response. To date, specially in region-based analysis, the two questions have been addressed separately while intrinsically connected to each other. This situation motivates the need for new methods in neuroimaging that go beyond this unsatisfactory trade-off. In this paper, we propose a generalization of a region based Bayesian detection-estimation approach that addresses (i)-(ii) simultaneously as a bilinear inverse problem. The proposed extension relies on a 2-class Gamma-Gaussian prior mixture modeling to classify the voxels of the brain region either as activated or unactivated. Our approach provides both a spatial activity map and a HRF estimation using Monte Carlo Markov chain (MCMC) techniques. Results show that this novel mixture model yields lower false positive rates and a better sensitivity in comparison with a 2-class Gaussian mixture
Markovian high resolution spectral analysis

When short data records are available, spectral analysis is basically an undetermined linear inverse problem. One usually considers the theoretical setting of regularization to solve such ill-posed problems. In this paper, we first show that "nonparametric" and "high resolution" are not incompatible in the field of spectral analysis. To this end, we introduce non-quadratic convex penalization functions, like in low level image processing. The spectral amplitudes estimate is then defined as the unique minimizer of a compound convex criterion. An original scheme of regularization to simultaneously retrieve narrow-band and wide-band spectral features is finally proposed.
Efficiency of line search strategies in interior point methods for linearly constrained signal restoration

We discuss in this paper the influence of line search on the performances of interior point algorithms applied for constrained signal restoration. Interior point algorithms ensure the fulfillment of the constraints through the minimization of a criterion augmented with a barrier function. However, the presence of the barrier function can slow down the convergence of iterative descent algorithms when general-purpose line search procedures are employed. We recently proposed a line search algorithm, based on a majorization-minimization approach, which allows to handle the singularity introduced by the barrier function. We present here a comparative study of various line search strategies for the resolution of a sparse signal restoration problem with both primal and primal-dual interior point algorithms.
Joint detection-estimation of brain activity in functional MRI: a Multichannel Deconvolution solution

Analysis of functional magnetic resonance imaging (fMRI) data focuses essentially on two questions: first, a detection problem that studies which parts of the brain are activated by a given stimulus and, second, an estimation problem that investigates the temporal dynamic of the brain response during activations. Up to now, these questions have been addressed independently. However, the activated areas need to be known prior to the analysis of the temporal dynamic of the response. Similarly, a typical shape of the response has to be assumed a priori for detection purpose. This situation motivates the need for new methods in neuroimaging data analysis that are able to go beyond this unsatisfactory tradeoff. The present paper raises a novel detection-estimation approach to perform these two tasks simultaneously in region-based analysis. In the Bayesian framework, the detection of brain activity is achieved using a mixture of two Gaussian distributions as a prior model on the "neural" response levels, whereas the hemodynamic impulse response is constrained to be smooth enough in the time domain with a Gaussian prior. All parameters of interest, as well as hyperparameters, are estimated from the posterior distribution using Gibbs sampling and posterior mean estimates. Results obtained both on simulated and real fMRI data demonstrate first that our approach can segregate activated and nonactivated voxels in a given region of interest (ROI) and, second, that it can provide spatial activation maps without any assumption on the exact shape of the Hemodynamic Response Function (HRF), in contrast to standard model-based analysis.
Three-dimensional edge-preserving image enhancement for computed tomography

Computed tomography (CT) images exhibit a variable amount of noise and blur, depending on the physical characteristics of the apparatus and the selected reconstruction method. Standard algorithms tend to favor reconstruction speed over resolution, thereby jeopardizing applications where accuracy is critical. In this paper, we propose to enhance CT images by applying half-quadratic edge-preserving image restoration (or deconvolution) to them. This approach may be used with virtually any CT scanner, provided the overall point-spread function can be roughly estimated. In image restoration, Markov random fields (MRFs) have proven to be very flexible a priori models and to yield impressive results with edge-preserving penalization, but their implementation in clinical routine is limited because they are often viewed as complex and time consuming. For these practical reasons, we focused on numerical efficiency and developed a fast implementation based on a simple three-dimensional MRF model with convex edge-preserving potentials. The resulting restoration method provides good recovery of sharp discontinuities while using convex duality principles yields fairly simple implementation of the optimization. Further reduction of the computational load can be achieved if the point-spread function is assumed to be separable. Synthetic and real data experiments indicate that the method provides significant improvements over standard reconstruction techniques and compares well with convex-potential Markov-based reconstruction, while being more flexible and numerically efficient.
Statistical Linear Destriping of Satellite-Based Pushbroom-Type Images

This paper introduces a new self-calibration destriping technique for pushbroom-type satellite imaging systems. Self-calibration means that no specific training data are required. It is based on the statistical estimation of each detector gain from the observed image, assuming a linear response. Both theoretical and practical behaviors are studied. Our technique is shown to outperform simpler techniques based on column averages in terms of gain estimation precision while keeping the computational cost within admissible limits.
Joint Reconstruction Strategy for Structured Illumination Microscopy With Unknown Illuminations

The blind structured illumination microscopy strategy proposed by Mudry et al. is fully re-founded in this paper, unveiling the central role of the sparsity of the illumination patterns in the mechanism that drives super-resolution in the method. A numerical analysis shows that the resolving power of the method can be further enhanced with optimized one-photon or two-photon speckle illuminations. A much improved numerical implementation is provided for the reconstruction problem under the image positivity constraint. This algorithm rests on a new preconditioned proximal iteration faster than existing solutions, paving the way to 3D and real-time 2D reconstruction.