nils-herrmann/clean_scirepeval huggingface dataset:
On the Superresolution Capacity of Imagers Using Unknown Speckle Illuminations

Speckle-based imaging consists of forming a super-resolved reconstruction of an unknown sample from low-resolution images obtained under random inhomogeneous illuminations (speckles). In a blind context, where the illuminations are unknown, we study the intrinsic capacity of speckle-based imagers to recover spatial frequencies outside the frequency support of the data, with minimal assumptions about the sample. We demonstrate that, under physically realistic conditions, the covariance of the data has a super-resolution power corresponding to the squared magnitude of the imager point spread function. This theoretical result is important for many practical imaging systems such as acoustic and electromagnetic tomographs, fluorescence and photoacoustic microscopes, or synthetic aperture radar imaging. A numerical validation is presented in the case of fluorescence microscopy.
Regularized estimation of mixed spectra using a circular Gibbs-Markov model

Formulated as a linear inverse problem, spectral estimation is particularly underdetermined when only short data sets are available. Regularization by penalization is an appealing nonparametric approach to solve such ill-posed problems. Following Sacchi et al. (see ibid., vol.46, no.1, p.32-38, 1998), we first address line spectra recovering in this framework. Then, we extend the methodology to situations of increasing difficulty: the case of smooth spectra and the case of mixed spectra, i.e., peaks embedded in smooth spectral contributions. The practical stake of the latter case is very high since it encompasses many problems of target detection and localization from remote sensing. The stress is put on adequate choices of penalty functions: following Sacchi et al., separable functions are retained to retrieve peaks, whereas Gibbs-Markov potential functions are introduced to encode spectral smoothness. Finally, mixed spectra are obtained from the conjunction of contributions, each one bringing its own penalty function. Spectral estimates are defined as minimizers of strictly convex criteria. In the cases of smooth and mixed spectra, we obtain nondifferentable criteria. We adopt a graduated nondifferentiability approach to compute an estimate. The performance of the proposed techniques is tested on the well-known Kay and Marple (1982) example.
Semi-blind deconvolution of neural impulse response in fMRI using a Gibbs sampling method

In functional magnetic resonance imaging (fMRI), the hemodynamic response function (HRF) represents the impulse response of the neurovascular system. Its identification is essential for a better understanding of cerebral activity since it provides a typical time course of the response to a stimulus in a given region of interest (ROI). The authors have developed an HRF estimation method based on a single time course (Ciuciu, P. et al., , no.10, p.1235-51, 2003). We now propose an extension that takes the spatial homogeneity of the HRF into account. Our hypothesis, based on biological results, is that a ROI can be characterized by a single HRF but varying magnitude in space. Our goal is to estimate those magnitudes that could then be interpreted as a correlate of the neural response. We are thus faced with a semi-blind deconvolution inverse problem since the time arrivals of the neural response are known - they correspond to stimuli timing. To cope with this issue, we introduce specific prior information about the HRF and the neural response. Finally, we develop an MCMC approach to approximate the posterior mean estimates of unknown quantities. Simulation results show the improvement brought by our formulation compared to our earlier approach.
Primal-dual interior-point optimization based on majorization-minimization for edge-preserving spectral unmixing

Primal-dual interior-point methods are used in image processing to solve inversion problems that can be reduced to constrained convex minimization. Such iterative methods require the solution of a sequence of linear systems which are used to derive descent directions. This approach is very consuming in terms of computing time and memory usage for large-scale problems, unless the involved matrices have a specific structure. This is the case in the spectral unmixing problem where these matrices are block-diagonal when no spatial regularization is considered. Here, we consider the edge-preserving regularized case and we propose to tackle the linear system solving using a majorization-minimization (MM) approach based on separable quadratic majorant functions. The resulting systems have the same structure as in the non-regularized case and can thereby be solved efficiently. The interior-point algorithm is speeded-up while remaining convergent. An example of spectral unmixing is proposed to illustrate the efficiency of this approach.
Markovian modeling for Bayesian multi-channel deconvolution

Two dimensional (2D) Bayesian restoration of layered media and its application to seismic deconvolution are addressed. The Bernoulli-Gaussian (B-G) approach is suboptimal in a 2D setting, since it does not account for spatial continuity. To compensate for this deficiency, a class of Markov random fields which suitably extends 1D Bernoulli processes to two dimensions is built. It provides a manageable model for 2D stratified structures. A maximum a posteriori detection-estimation algorithm is proposed. Compared to standard B-G algorithms, it performs much better, without an increase in computational load.<<ETX>>
Regularized estimation of flow patterns in MR velocimetry

A Bayesian estimator of the magnetic resonance (MR) velocity image is proposed. It is based on a Markov model accounting for the spatial structure of the flow velocity. On the other hand, low MR signal intensity yields high uncertainty on the velocity. Such an important property is taken into account through the observation model. The resulting posterior likelihood is optimized using an iterative coordinate descent (ICD) algorithm. Compared to the usual least squares solution, simulation results on flows with parabolic and flat profiles demonstrate a significant gain of in the mean square error.
Spatial Mixture Modelling for the Joint Detection-Estimation of Brain Activity in fMRI

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. Recently, we have proposed a Bayesian detection-estimation approach that jointly addresses (i)-(ii). This approach provides both a spatial activity map and an estimate of brain dynamics. Here, we consider an extension that accounts for spatial correlation using a spatial mixture model (SMM) based on a binary Markov random field. It allows us to avoid any spatial smoothing of the data prior to the statistical analysis. Our simulation results support that SMM gives a better control of false positive (specificity) and false negative (sensitivity) rates than independent mixtures.
Multichannel seismic deconvolution

Deals with Bayesian estimation of 2D stratified structures from echosounding signals. This problem is of interest in seismic exploration, but also for nondestructive testing or medical imaging. The proposed approach consists of a multichannel Bayesian deconvolution method of the 2D reflectivity based upon a theoretically sound prior stochastic model. The Markov-Bernoulli random field representation introduced by Idier et al. (1993) is used to model the geometric properties of the reflectivity, and emphasis is placed on representation of the amplitudes and on deconvolution algorithms. It is shown that the algorithmic structure and computational complexity of the proposed multichannel methods are similar to those of single-channel B-G deconvolution procedures, but that explicit modeling of the stratified structure results in significantly better performances. Simulation results and examples of real-data processing illustrate the performances and the practicality of the multichannel approach.
Efficient Gaussian Sampling for Solving Large-Scale Inverse Problems Using MCMC

The resolution of many large-scale inverse problems using MCMC methods requires a step of drawing samples from a high dimensional Gaussian distribution. While direct Gaussian sampling techniques, such as those based on Cholesky factorization, induce an excessive numerical complexity and memory requirement, sequential coordinate sampling methods present a low rate of convergence. Based on the reversible jump Markov chain framework, this paper proposes an efficient Gaussian sampling algorithm having a reduced computation cost and memory usage, while maintaining the theoretical convergence of the sampler. The main feature of the algorithm is to perform an approximate resolution of a linear system with a truncation level adjusted using a self-tuning adaptive scheme allowing to achieve the minimal computation cost per effective sample. The connection between this algorithm and some existing strategies is given and its performance is illustrated on a linear inverse problem of image resolution enhancement.
Markov modeling for Bayesian restoration of two-dimensional layered structures

Bayesian estimation of two-dimensional stratified structures is described. The major point addressed is the derivation of a statistical prior model that adequately describes such layered media. This problem is of interest in applications in which the data are generally processed in one dimension only. In order to take local interactions into account, a Markovian description is used. The model is derived so as to fulfill a set of constraints that summarize physical and geometrical characteristics of the problem as well as practical requirements. The resulting class of Markov random fields presents a unilateral structure on a nonrectangular lattice and a hierarchical organization which involves a line process. In addition, it is shown to be an extension of one-dimensional models already in use. The properties of the model are investigated, and its practicality is demonstrated by an application to seismic deconvolution. Simulation results show significant improvements with respect to the usual one-dimensional methods.
Fast bilinear extrapolation of 3D ising field partition function. application to fMRI image analysis.

Symmetric ising models define the simplest discrete Markov random fields that can be used for segmentation purpose. Unsupervised segmentation requires an automatic setting of the temperature parameter of ising fields. To this end, partition function (PF) estimation becomes a key issue. In this paper, we present a bilinear extrapolation technique for a fast PF estimation of 3D ising field. The proposed method is a two-step procedure that applies to the context where multiple 3D ising fields are involved over different objects (eg, brain regions) of different size and topology. First, a small set of reference PFs is accurately estimated using path sampling. Second, the large remaining set of PFs is computed using a temperature-dependent bilinear extrapolation technique. It is shown that our approach is accurate and computationally efficient to account for topological fluctuations of ising fields on regular and irregular graphs. A convincing application to joint detection-estimation of brain activity in functional MRI is also presented.
Inversion of large-support ill-posed linear operators using a piecewise Gaussian MRF

We propose a method for the reconstruction of signals and images observed partially through a linear operator with a large support (e.g., a Fourier transform on a sparse set). This inverse problem is ill-posed and we resolve it by incorporating the prior information that the reconstructed objects are composed of smooth regions separated by sharp transitions. This feature is modeled by a piecewise Gaussian (PG) Markov random field (MRF), known also as the weak-string in one dimension and the weak-membrane in two dimensions. The reconstruction is defined as the maximum a posteriori estimate. The prerequisite for the use of such a prior is the success of the optimization stage. The posterior energy corresponding to a PG MRF is generally multimodal and its minimization is particularly problematic. In this context, general forms of simulated annealing rapidly become intractable when the observation operator extends over a large support. In this paper, global optimization is dealt with by extending the graduated nonconvexity (GNC) algorithm to ill-posed linear inverse problems. GNC has been pioneered by Blake and Zisserman in the field of image segmentation. The resulting algorithm is mathematically suboptimal but it is seen to be very efficient in practice. We show that the original GNC does not correctly apply to ill-posed problems. Our extension is based on a proper theoretical analysis, which provides further insight into the GNC. The performance of the proposed algorithm is corroborated by a synthetic example in the area of diffraction tomography.
Maximum likelihood and maximum a posteriori estimation of Gaussian spectra. Application to attenuation measurements and color Doppler velocimetry

We address the problem of tracking slowly varying mean frequency and spectral width from a series of data vectors yp (p=1, 2, ... P). When the yp are small-sized, usual methods (periodogram, correlation lags...) suffer from strong variability. Moreover, the discrete nature of observed signals results in ambiguity in spectral domain. First in a Gaussian setting both for the shape of the spectra and for the statistics of observed signals, a maximum likelihood (ML) technique is provided for spectral moments estimation. Second, we propose a maximum a posteriori (MAP) method in order to account also for the slowly varying character of the spectral moments. Noticeable improvement are obtained with respect to usual methods: strong variance reduction in the field of ultrasound attenuation measurement (AM), and correct estimation beyond the Shannon limit in the field of color flow mapping (CFM)
Inversion of large-support ill-conditioned linear operators using a Markov model with a line process

We propose a method for the reconstruction of an image, only partially observed through a linear integral operator. As such an inverse problem is ill-posed, prior information must be introduced. We consider the case of a compound Markov random field with a non-interacting line process. In order to maximise the posterior likelihood function, we propose an extension of the graduated non convexity principle pioneered by Blake and Zisserman (1987) which allows its use for ill-posed linear inverse problems. We discuss the role of the observation scale and some aspects of the implemented algorithm. Finally, we present an application of the method to a diffraction tomography imaging problem.<<ETX>>
Homotopy Based Algorithms for $\ell _{\scriptscriptstyle 0}$-Regularized Least-Squares

Sparse signal restoration is usually formulated as the minimization of a quadratic cost function |y-Ax ||2<sup>2</sup> where \mbi A is a dictionary and \mbi x is an unknown sparse vector. It is well-known that imposing an ℓ<sub>0</sub> constraint leads to an NP-hard minimization problem. The convex relaxation approach has received considerable attention, where the ℓ<sub>0</sub>-norm is replaced by the ℓ<sub>1</sub>-norm. Among the many effective ℓ<sub>1</sub> solvers, the homotopy algorithm minimizes ||y-Ax ||2<sup>2</sup>+λ||x||<sub>1</sub> with respect to x for a continuum of λ's. It is inspired by the piecewise regularity of the ℓ<sub>1</sub>-regularization path, also referred to as the homotopy path. In this paper, we address the minimization problem ||y-Ax||2<sup>2</sup>+λ||x||<sub>0</sub> for a continuum of λ's and propose two heuristic search algorithms for ℓ<sub>0</sub>-homotopy.  Best Replacement is a forward-backward greedy strategy extending the Single Best Replacement algorithm, previously proposed for ℓ<sub>0</sub>-minimization at a given λ. The adaptive search of the λ-values is inspired by ℓ<sub>1</sub>-homotopy. ℓ<sub>0</sub> Regularization Path Descent is a more complex algorithm exploiting the structural properties of the ℓ<sub>0</sub>-regularization path, which is piecewise constant with respect to λ. Both algorithms are empirically evaluated for difficult inverse problems involving ill-conditioned dictionaries. Finally, we show that they can be easily coupled with usual methods of model order selection.
Correction of RF inhomogeneities for high throughput water and fat quantification by MRI

The object of this study is to assess the relevance of MRI water/fat separation to quantify fat and water in fish in a view of high throughput measurements. The major issue for this purpose is the spatial inhomogeneities of the signal. They are inherent to MRI and they may induce a position dependent bias in the quantification. We have combined water/fat separation methods from the literature and extended them in order to estimate these inhomogeneities. Experimental results show the efficiency of our method and validate the possibility to use MRI for water and fat quantification at a rate higher than one minute per fish cutlet.
Bayesian interpretation of periodograms

The usual nonparametric approach to spectral analysis is revisited within the regularization framework. Both usual and windowed periodograms are obtained as the squared modulus of the minimizer of regularized least squares criteria. Then, particular attention is paid to their interpretation within the Bayesian statistical framework. Finally, the question of unsupervised hyperparameter and window selection is addressed. It is shown that maximum likelihood solution is both formally achievable and practically useful.
Computed tomography image restoration using convex-potential 3-D Markov random fields [for knee joint prostheses design]

In order to design and manufacture custom-fitted prostheses of the knee joint, one must perform a very accurate geometric reconstruction of the bone surface from computed tomography images. This communication deals with the image restoration used to improve the reconstructed images. In the Bayesian context of maximum a posteriori estimation, edge-preserving Markov random fields as an a priori model for the images have proven to give very good results. To avoid dealing with nonconvex optimization, we adopt the elegant method proposed by Brette and Idier [1996]. This approach leads to a very efficient single site update algorithm and an analytical formulation can be found for convex edge-preserving potentials. Moreover, we propose to define a three dimensional Markov random field to take into account the geometry of computed tomography. The resulting restoration allows good recovery of the sharp discontinuities between the bone and soft tissues and the accuracy is significantly improved by the three dimensional model.
EM parameter estimation for a piecewise AR

We design a model meant to be the equivalent of Blake's (1989) weak string but in the probabilistic framework. Independent line sites delimit piecewise stationary Gaussian autoregressives AR(1) corrupted with Gaussian white noise. Thanks to the Bayesian interpretation, we define the joint probability which in turn yields the likelihood. We demonstrate how to make its computation possible in cubic time. This calculation allows the set of parameters to be tested but not estimated due to the complex form of the criterion. Yet the computations done so far provide the materials for an iterative maximization. Indeed, the expectation maximization algorithm happens to match the features of this model and is also easily calculable. When the likelihood is known, the cost of one step of the latter algorithm is negligible in comparison with the previous calculations.
Unsupervised frequency tracking beyond the Nyquist frequency using Markov chains

This paper deals with the estimation of a sequence of frequencies from a corresponding sequence of signals. This problem arises in fields such as Doppler imaging, where its specificity is twofold. First, only short noisy data records are available (typically four sample long), and experimental constraints may cause spectral aliasing so that measurements provide unreliable, ambiguous information. Second, the frequency sequence is smooth. Here, this information is accounted for by a Markov model, and application of the Bayes rule yields the a posteriori density. The maximum a posteriori is computed by a combination of Viterbi and descent procedures. One of the major features of the method is that it is entirely unsupervised. Adjusting the hyperparameters that balance data-based and prior-based information is done automatically by maximum likelihood (ML) using an expectation-maximization (EM)-based gradient algorithm. We compared the proposed estimate to a reference one and found that it performed better: variance was greatly reduced, and tracking was correct, even beyond the Nyquist frequency.
From Bernoulli–Gaussian Deconvolution to Sparse Signal Restoration

Formulated as a least square problem under an l0 constraint, sparse signal restoration is a discrete optimization problem, known to be NP complete. Classical algorithms include, by increasing cost and efficiency, matching pursuit (MP), orthogonal matching pursuit (OMP), orthogonal least squares (OLS), stepwise regression algorithms and the exhaustive search. We revisit the single most likely replacement (SMLR) algorithm, developed in the mid-1980s for Bernoulli-Gaussian signal restoration. We show that the formulation of sparse signal restoration as a limit case of Bernoulli-Gaussian signal restoration leads to an l0-penalized least square minimization problem, to which SMLR can be straightforwardly adapted. The resulting algorithm, called single best replacement (SBR), can be interpreted as a forward-backward extension of OLS sharing similarities with stepwise regression algorithms. Some structural properties of SBR are put forward. A fast and stable implementation is proposed. The approach is illustrated on two inverse problems involving highly correlated dictionaries. We show that SBR is very competitive with popular sparse algorithms in terms of tradeoff between accuracy and computation time.
Majorization-minimization algorithms for maximum likelihood estimation of magnetic resonance images

This paper addresses maximum likelihood estimation of images corrupted by a Rician noise, with the aim to propose an efficient optimization method. The application example is the restoration of magnetic resonance images. Starting from the fact that the criterion to minimize is non-convex but unimodal, the main contribution of this work is to propose an optimization scheme based on the majorization-minimization framework after introducing a variable change allowing to get a strictly convex criterion. The resulting descent algorithm is compared to the classical MM descent algorithm and its performances are assessed using synthetic and real MR images. Finally, by combining these two MM algorithms, two optimization strategies are proposed to improve the numerical efficiency of the image restoration for any signal-to-noise ratio.