nils-herrmann/clean_scirepeval huggingface dataset:
Fractal modelling and analysis of flow-field images

We introduce stochastic models for flow fields with parameters that dictate the scale-dependent (self-similar) character of the field and control the balance between its rotational vs compressive behaviour. The development of our models is motivated by the availability of imaging modalities that measure flow vector fields (flow-sensitive MRI and Doppler ultrasound). To study such data, we formulate estimators of the model parameters, and use them to quantify the Hurst exponent and directional properties of synthetic and real-world flow fields (measured by means of phase-contrast MRI) in 3D.
Karhunen-Loeve analysis of dynamic sequences of thermographic images for early breast cancer detection

The Karhunen-Loeve transform (KLT) is applied to the analysis of dynamic sequences of thermograms describing the temporal evolution of body surface temperature following the application of an external thermal stimulus. The KLT may be evaluated either along the spatial or temporal dimensions of the data; the duality of both representations is emphasized. An example is presented to illustrate that the KLT allows an efficient data reduction and facilities tumor detection by highlighting physiologically important abnormalities in the time behavior of thermal patterns.<<ETX>>
Wavelet-based identification and classification of local symmetries in microscopy images

We present a method for the identification and classification of local symmetries in biological images. We aim at obtaining a precise estimate of symmetric junctions in a scale and rotation invariant way. The proposed method is template-free, which allows the test of any combination of arbitrary symmetry orders in an effective way. Our measure of local symmetry is derived from a circular harmonic wavelet analysis. The basis functions exhibit different symmetry orders. We use this measure to formulate a classifier to label the different junctions into one of several symmetry classes. We present experimental results, and validate our method using both on synthetic images and biological micrographs.
Automated extraction of serial myocardial borders from M-mode echocardiograms.

A method is presented for the automated extraction of myocardial borders in M-mode echocardiograms. The successive steps of processing are: preprocessing for noise reduction, enhancement of border characteristics using a set of suitably chosen matched filters, and final extraction of border points by searching for optimal paths along the time axis. During the last step of processing, the contribution of each elementary border element is characterised by a normalized correlation coefficient. The optimal path, defined as the one that maximizes the sum of all elementary contributions, is determined efficiently using dynamic programming. An alternative approach uses a maximum tracking procedure whose performances are improved by utilizing a local model to predict the position of the next border point. Experimental examples are presented and the performance of both border extraction algorithms are compared.
Differential phase-contrast X-ray computed tomography: From model discretization to image reconstruction

Our contribution in this paper is two fold. First, we propose a novel discretization of the forward model for differential phase-contrast imaging that uses B-spline basis functions. The approach yields a fast and accurate algorithm for implementing the forward model, which is based on the first derivative of the Radon transform. Second, as an alternative to the FBP-like approaches that are currently used in practice, we present an iterative reconstruction algorithm that remains more faithful to the data when the number of projections dwindles. Since the reconstruction is an ill-posed problem, we impose a total-variation (TV) regularization constraint. We propose to solve the reconstruction problem using the alternating direction method of multipliers (ADMM). A specificity of our system is the use of a preconditioner that improves the convergence rate of the linear solver in ADMM. Our experiments on test data suggest that our method can achieve the same quality as the standard direct reconstruction, while using only one-third of the projection data. We also find that the approach is much faster than the standard algorithms (ISTA and FISTA) that are typically used for solving linear inverse problems subject to the TV regularization constraint.
Optical Tomography based on a nonlinear model that handles multiple scattering

Learning Tomography (LT) is a nonlinear optimization algorithm for computationally imaging three-dimensional (3D) distribution of the refractive index in semi-transparent samples. Since the energy function in LT is generally non-convex, the solution it obtains is not guaranteed to be globally optimal. In this paper, we describe linear and nonlinear tomographic reconstruction methods and compare them numerically. We present a review of the LT and, in addition, we investigate the influence of the initialization and exemplify the effect of regularization on the convergence of the algorithm. In particular, we show that both are essential for high-quality imaging in strongly scattering scenarios.
Analytical form of Shepp-Logan phantom for parallel MRI

We present an analytical form of ground-truth k-space data for the 2-D Shepp-Logan brain phantom in the presence of multiple and non-homogeneous receiving coils. The analytical form allows us to conduct realistic simulations and validations of reconstruction algorithms for parallel MRI. The key contribution of our work is to use a polynomial representation of the coil's sensitivity. We show that this method is particularly accurate and fast with respect to the conventional methods. The implementation is made available to the community.
Segmentation of gated SPECT images for automatic computation of myocardial volume and ejection fraction

Describes an image processing system for the automatic assessment of ejection fraction (EF) from noisy SPECT left ventricular myocardial perfusion images. A segmentation scheme consisting of an elliptical coordinate transformation, matched filtering and dynamic contour tracking detects the endo- and epicardial boundaries. Computation of EF is performed based on the epi- rather than the endocardial boundary, which proves to be more robust for images with low signal-to-noise ratios. The computation incorporates anatomical constraints of constant myocardial mass and smooth cardiac variation. The algorithm was tested on different image modalities and shows good linear agreement with EFs obtained from conventional approaches based on planar gated blood pool imaging (PET: y=8.7+1.07x, r=0.84, Technetium-99m MIBI SPECT: y=5.0+0.80x, r=0.90, Thallium-201 SPECT: y=23.5+0.82x, r=0.77, RMS error=10.0). The proposed scheme may be an alternative for EF computation without the need for additional image acquisitions.
Undecimated haar thresholding for poisson intensity estimation

We propose a novel algorithm for denoising Poisson-corrupted images, that performs a signal-adaptive thresholding of the undecimated Haar wavelet coefficients. A Poisson's unbiased MSE estimate is devised and adapted to arbitrary transform-domain pointwise processing. This prior-free quadratic measure of quality is then used to globally optimize a linearly parameterized subband-adaptive thresholding, which accounts for the signal-dependent noise variance. We demonstrate the qualitative and computational competitiveness of the resulting denoising algorithm through comprehensive comparisons with some state-of-the-art multiscale techniques specifically designed for Poisson intensity estimation. We also show promising denoising results obtained on low-count fluorescence microscopy images.
A dual algorithm for L1-regularized reconstruction of vector fields

Recent advances in vector-field imaging have brought to the forefront the need for efficient denoising and reconstruction algorithms that take the physical properties of vector fields into account and can be applied to large volumes of data. With these requirements in mind, we propose a computationally efficient algorithm for variational de-noising and reconstruction of vector fields. Our variational objective combines rotation- and scale-invariant regularization functionals that permit one to tune the algorithm to the physical characteristics of the underlying phenomenon. In addition, these regularization terms involve L1 norms in the spirit of total-variation (TV) regularization, which, as in the scalar case, leads to better preservation of discontinuities and superior SNR performance compared to its quadratic alternative. Some experimental results are provided to illustrate and verify the proposed scheme.
Detection of symmetric junctions in biological images using 2-D steerable wavelet transforms

We present a method for designing steerable wavelets that can detect local centers of symmetry in images. Based on this design, we then propose an algorithm for estimating the locations and the orientations of M-fold symmetric junctions in biological micrographs. The analysis with 2-D steerable wavelets allows us to have detections at different scales and arbitrary orientations. Owing to the steering property of our wavelets the detection is fast and accurate. We provide experimental results on both synthetic images and biological micrographs to demonstrate the performance of the algorithm.
On the Hilbert Transform of Wavelets

A wavelet is a localized function having a prescribed number of vanishing moments. In this correspondence, we provide precise arguments as to why the Hilbert transform of a wavelet is again a wavelet. In particular, we provide sharp estimates of the localization, vanishing moments, and smoothness of the transformed wavelet. We work in the general setting of non-compactly supported wavelets. Our main result is that, in the presence of some minimal smoothness and decay, the Hilbert transform of a wavelet is again as smooth and oscillating as the original wavelet, whereas its localization is controlled by the number of vanishing moments of the original wavelet. We motivate our results using concrete examples.
Sampling in practice: is the best reconstruction space bandlimited?

Shannon's sampling theory and its variants provide effective solutions to the problem of reconstructing a signal from its samples in some "shift-invariant" space, which may or may not be bandlimited. In this paper, we present some further justification for this type of representation, while addressing the issue of the specification of the best reconstruction space. We consider a realistic setting where a multidimensional signal is prefiltered prior to sampling and the samples corrupted by additive noise. We consider two formulations of the reconstruction problem. In the first deterministic approach, we determine the continuous-space function that minimizes a variational, Tikhonov-like criterion that includes a discrete data term and a suitable continuous-space regularization functional. In the second formulation, we seek the minimum mean square error (MMSE) estimation of the signal assuming that the input signal is a realization of a stationary random process. Interestingly, both approaches yield a solution included in some optimal shift-invariant space that is generally not bandlimited. The solutions can be made equivalent by choosing a regularization operator that corresponds to the whitening filter of the process. We present some practical examples that demonstrate the optimality of the approach.
Divergence-Free Wavelet Frames

We propose an efficient construction of wavelet frames in any number of dimensions that are divergence-free. Our approach is based on applying the Leray projector, which is scale-invariant, to a standard wavelet frame. We prove that the projected wavelets retain the basic characteristics (decay rate and order of vanishing moments) of the initial wavelets. Since the Leray projector is also shift-invariant, it is defined as a Fourier multiplier, and our construction is implemented efficiently using the fast Fourier transform. In order to illustrate the practicality of the method, we present vector field denoising experiments.
Spatio-temporal nonrigid registration for ultrasound cardiac motion estimation

We propose a new spatio-temporal elastic registration algorithm for motion reconstruction from a series of images. The specific application is to estimate displacement fields from two-dimensional ultrasound sequences of the heart. The basic idea is to find a spatio-temporal deformation field that effectively compensates for the motion by minimizing a difference with respect to a reference frame. The key feature of our method is the use of a semi-local spatio-temporal parametric model for the deformation using splines, and the reformulation of the registration task as a global optimization problem. The scale of the spline model controls the smoothness of the displacement field. Our algorithm uses a multiresolution optimization strategy to obtain a higher speed and robustness. We evaluated the accuracy of our algorithm using a synthetic sequence generated with an ultrasound simulation package, together with a realistic cardiac motion model. We compared our new global multiframe approach with a previous method based on pairwise registration of consecutive frames to demonstrate the benefits of introducing temporal consistency. Finally, we applied the algorithm to the regional analysis of the left ventricle. Displacement and strain parameters were evaluated showing significant differences between the normal and pathological segments, thereby illustrating the clinical applicability of our method.
Self-Similarity: Part II—Optimal Estimation of Fractal Processes

In a companion paper (see Self-Similarity: Part I-Splines and Operators), we characterized the class of scale-invariant convolution operators: the generalized fractional derivatives of order gamma. We used these operators to specify regularization functionals for a series of Tikhonov-like least-squares data fitting problems and proved that the general solution is a fractional spline of twice the order. We investigated the deterministic properties of these smoothing splines and proposed a fast Fourier transform (FFT)-based implementation. Here, we present an alternative stochastic formulation to further justify these fractional spline estimators. As suggested by the title, the relevant processes are those that are statistically self-similar; that is, fractional Brownian motion (fBm) and its higher order extensions. To overcome the technical difficulties due to the nonstationary character of fBm, we adopt a distributional formulation due to Gel'fand. This allows us to rigorously specify an innovation model for these fractal processes, which rests on the property that they can be whitened by suitable fractional differentiation. Using the characteristic form of the fBm, we then derive the conditional probability density function (PDF) p(BH(t)|Y), where Y={BH(k)+n[k]}kisinZ are the noisy samples of the fBm BH(t) with Hurst exponent H. We find that the conditional mean is a fractional spline of degree 2H, which proves that this class of functions is indeed optimal for the estimation of fractal-like processes. The result also yields the optimal [minimum mean-square error (MMSE)] parameters for the smoothing spline estimator, as well as the connection with kriging and Wiener filtering
Full flow/motion-field recovery from pulsed-wave ultrasound Doppler data

We present a new computational method for reconstructing a vector field from scattered, pulsed-wave ultrasound Doppler data. The main difficulty is that the Doppler measurements are incomplete, for they do only capture the velocity component along the beam direction. We thus propose to combine measurements from different beam directions. However, this is not yet sufficient to make the problem well posed because (i) the angle between the directions is typically small; and (ii) the data is noisy and nonuniformly sampled. We therefore introduce a vector-spline regularization that forces the solution to be well behaved while inducing some helpful coupling between the x and y components of the vector field. We discretize our vector-spline reconstruction problem in a uniform B-spline basis, obtaining a sparse system of equations that can be solved efficiently. We validate our method using real tissue Doppler data for which the ground truth is known. Finally, we present some patient results obtained with color Doppler imaging; in particular, we are able to observe bloodflow variations in the bifurcation of the carotid artery
B-spline snakes and a JAVA interface: an intuitive tool for general contour outlining

We present a novel formulation for B-spline snakes that can be used as a tool for fast and intuitive contour outlining. The theory is implemented in a platform independent JAVA interface, which allows real time computation of the snake curve. In this paper, our main focus is on two points. First, we propose a novel B-spline snake formulation, where the intrinsic scale of the spline model is adjusted a priori. It leads to a reduction of the number of parameters to be optimized and eliminates the need for internal energies. The approach solves the two main drawbacks of traditional snakes (slow convergence speed and difficult to adjust weighting factors for internal energy terms). Second, we comment on our experience using JAVA for the implementation of the snake and for the design of the graphical user interface. Our technique provides a very intuitive, user-friendly, and platform independent tool for contour outlining, generally applicable to a vast range of images. Several biomedical examples of applications are included to illustrate the versatility of the method.
Similarity-based shape priors for 2D spline snakes

We present a new formulation of a shape space containing all continuously defined 2D spline curves up to a similarity transform of a reference shape. We are able to measure a distance between an arbitrary curve and the shape space itself. Our contribution is an explicit formula for this distance measure in the continuous domain. This allows us to define efficient snake energies based on shape-dependent prior knowledge to facilitate segmentation in bioimaging. The spline-based algorithm that we propose allows us to implement continuous-domain solutions with no additional computational cost compared to the case where curves are described by a discrete set of landmarks. The proposed implementation is freely available in the public domain.
Hermite Snakes With Control of Tangents

We introduce a new model of parametric contours defined in a continuous fashion. Our curve model relies on Hermite spline interpolation and can easily generate curves with sharp discontinuities; it also grants direct access to the tangent at each location. With these two features, the Hermite snake distinguishes itself from classical spline-snake models and allows one to address certain bioimaging problems in a more efficient way. More precisely, the Hermite snake construction allows introducing sharp corners in the snake curve and designing directional energy functionals relying on local orientation information in the input image. Using the formalism of spline theory, the model is shown to meet practical requirements such as invariance to affine transformations and good approximation properties. Finally, the dependence on initial conditions and the robustness to the noise is studied on synthetic data in order to validate our Hermite snake model, and its usefulness is illustrated on real biological images acquired using brightfield, phase-contrast, differential-interference-contrast, and scanning-electron microscopy.
Approximate Message Passing With Consistent Parameter Estimation and Applications to Sparse Learning

We consider the estimation of an independent and identically distributed (i.i.d.) (possibly non-Gaussian) vector x ∈ Rn from measurements y ∈ Rm obtained by a general cascade model consisting of a known linear transform followed by a probabilistic componentwise (possibly nonlinear) measurement channel. A novel method, called adaptive generalized approximate message passing (adaptive GAMP) is presented. It enables the joint learning of the statistics of the prior and measurement channel along with estimation of the unknown vector x. We prove that, for large i.i.d. Gaussian transform matrices, the asymptotic componentwise behavior of the adaptive GAMP is predicted by a simple set of scalar state evolution equations. In addition, we show that the adaptive GAMP yields asymptotically consistent parameter estimates, when a certain maximum-likelihood estimation can be performed in each step. This implies that the algorithm achieves a reconstruction quality equivalent to the oracle algorithm that knows the correct parameter values. Remarkably, this result applies to essentially arbitrary parametrizations of the unknown distributions, including nonlinear and non-Gaussian ones. The adaptive GAMP methodology thus provides a systematic, general and computationally efficient method applicable to a large range of linear-nonlinear models with provable guarantees.
Compressibility of symmetric-α-stable processes

Within a deterministic framework, it is well known that n-term wavelet approximation rates of functions can be deduced from their Besov regularity. We use this principle to determine approximation rates for symmetric-α-stable (SαS) stochastic processes. First, we characterize the Besov regularity of SαS processes. Then the n-term approximation rates follow. To capture the local smoothness behavior, we consider sparse processes defined on the circle that are solutions of stochastic differential equations.
On the optimality of ideal filters for pyramid and wavelet signal approximation

The reconstructed lowpass component in a quadrature mirror filter (QMF) bank provides a coarser resolution approximation of the input signal. Since the outputs of the two QMF branches are orthogonal, the transformation that provides the maximum energy compaction in the lowpass channel is also the one that results in the minimum approximation error. This property is used as a common strategy for the optimization of QMF banks, orthogonal wavelet transforms, and least squares pyramids. A general solution is derived for the QMF bank that provides the optimal decomposition of an arbitrary wide sense stationary process. This approach is extended to the continuous case to obtain the minimum error approximation of a signal at a given sampling rate. In particular, it is shown that the sine-wavelet transform is optimal for the representation at all scales of signals with non-increasing spectral density.
Maximally Localized Radial Profiles for Tight Steerable Wavelet Frames.

A crucial component of steerable wavelets is the radial profile of the generating function in the frequency domain. In this paper, we present an infinite-dimensional optimization scheme that helps us find the optimal profile for a given criterion over the space of tight frames. We consider two classes of criteria that measure the localization of the wavelet. The first class specifies the spatial localization of the wavelet profile, and the second that of the resulting wavelet coefficients. From these metrics and the proposed algorithm, we construct tight wavelet frames that are optimally localized and provide their analytical expression. In particular, one of the considered criterion helps us finding back the popular Simoncelli wavelet profile. Finally, the investigation of local orientation estimation, image reconstruction from detected contours in the wavelet domain, and denoising indicate that optimizing wavelet localization improves the performance of steerable wavelets, since our new wavelets outperform the traditional ones.