nils-herrmann/clean_scirepeval huggingface dataset:
Phaseless diffraction tomography with regularized beam propagation

In recent years, researchers have obtained impressive reconstructions of the refractive index (RI) of biological objects through the combined use of advanced physics (nonlinear forward model) and regularization. Here, we propose an adaptation of these techniques for the more challenging problem of intensity-only measurements. It involves a difficult nonconvex optimization problem where phase and distribution of the RI must be jointly estimated. Using an adequate splitting, we leverage recent achievements in phase retrieval and RI reconstruction to perform this task. This yields an efficient reconstruction method with sparsity constraints.
VOW: Variance-optimal wavelets for the steerable pyramid

We study the issue of localization in the context of isotropic wavelet frames. We define a variance-type measure of localization and propose an algorithm based on calculus of variations to minimize this criterion under the constraint of a tight wavelet frame. Based on these calculations, we design the variance-optimal wavelet (VOW). Finally, we demonstrate the advantage of better localization in a practical image-processing task.
General surface energy for spinal cord and aorta segmentation

We present a new surface energy potential for the segmentation of cylindrical objects in 3D medical imaging using parametric spline active contours (a.k.a. spline-snakes). Our energy formulation is based on an optimal steerable surface detector. Thus, we combine the concept of steerability with spline-snakes that have open topology for semi-automatic segmentation. We show that the proposed energy yields segmentation results that are more robust to noise compared to classical gradient-based surface energies. We finally validate our model by segmenting the aorta on a cohort of 14 real 3D MRI images, and also provide an example of spinal cord segmentation using the same tool.
Template-Free Wavelet-Based Detection of Local Symmetries

Our goal is to detect and group different kinds of local symmetries in images in a scale- and rotation-invariant way. We propose an efficient wavelet-based method to determine the order of local symmetry at each location. Our algorithm relies on circular harmonic wavelets which are used to generate steerable wavelet channels corresponding to different symmetry orders. To give a measure of local symmetry, we use the F-test to examine the distribution of the energy across different channels. We provide experimental results on synthetic images, biological micrographs, and electron-microscopy images to demonstrate the performance of the algorithm.
WAVELET-BASED STATISTICAL ANALYSIS FOR OPTICAL IMAGING IN MOUSE OLFACTORY BULB

Optical imaging is a powerful technique to map brain function in animals. In this study, we consider in vivo optical imaging of the murine olfactory bulb, using an intrinsic signal and a genetically expressed activity reporter fluorescent protein (synaptopHfluorin). The aim is to detect odor-evoked activations that occur in small spherical structures of the olfactory bulb called glomeruli. We propose a new way of analyzing this kind of data that combines a linear model (LM) fitting along the temporal dimension, together with a discrete wavelet transform (DWT) along the spatial dimensions. We show that relevant regressors for the LM are available for both types of optical signals. In addition, the spatial wavelet transform allows us to exploit spatial correlation at different scales, and in particular to extract activation patterns at the expected size of glomeruli. Our framework also provides a statistical significance for every pixel in the activation maps and it has strong type I error control.
Hessian-Based Norm Regularization for Image Restoration With Biomedical Applications

We present nonquadratic Hessian-based regularization methods that can be effectively used for image restoration problems in a variational framework. Motivated by the great success of the total-variation (TV) functional, we extend it to also include second-order differential operators. Specifically, we derive second-order regularizers that involve matrix norms of the Hessian operator. The definition of these functionals is based on an alternative interpretation of TV that relies on mixed norms of directional derivatives. We show that the resulting regularizers retain some of the most favorable properties of TV, i.e., convexity, homogeneity, rotation, and translation invariance, while dealing effectively with the staircase effect. We further develop an efficient minimization scheme for the corresponding objective functions. The proposed algorithm is of the iteratively reweighted least-square type and results from a majorization-minimization approach. It relies on a problem-specific preconditioned conjugate gradient method, which makes the overall minimization scheme very attractive since it can be applied effectively to large images in a reasonable computational time. We validate the overall proposed regularization framework through deblurring experiments under additive Gaussian noise on standard and biomedical images.
Locally refinable parametric snakes

Shape segmentation is an active field of research in biomedical imaging. In this context, we present a new parameterization of a snake that is locally refinable. We introduce the possibility of locally increasing the approximation power of the parametric model by inserting basis functions at a specific location. This is controlled by a user-interface that permits the refinement of an initial segmentation around an anchor position selected by a user. Our approach relies on scaling functions that satisfy the refinement relation and are related to wavelets. We also derive explicit formulas for the energy functions associated to our new parameterization. We demonstrate the accuracy of our snake and its robustness under noisy conditions on phantom data. We also present segmentation results on real cell images, which are our main target. The algorithm is made freely available as a plugin for the open source platform Icy.
Fast implementation of the continuous wavelet transform with integer scales

We describe a fast noniterative algorithm for the evaluation of continuous spline wavelet transforms at any integer scale m. In this approach, the input signal and the analyzing wavelet are both represented by polynomial splines. The algorithm uses a combination of moving sum and zero-padded filters, and its complexity per scale is O(N), where N is the signal length. The computation is exact, and the implementation is noniterative across scales. We also present examples of spline wavelets exhibiting properties that are desirable for either singularity detection (first and second derivative operators) or Gabor-like time-frequency signal analysis.
Sure-Based Wavelet Thresholding Integrating Inter-Scale Dependencies

We propose here a new pointwise wavelet thresholding function that incorporates inter-scale dependencies. This non-linear function depends on a set of four linear parameters per sub-band which are set by minimizing Stein's unbiased MSE estimate (SURE). Our approach assumes additive Gaussian white noise. In order for the inter-scale dependencies to be faithfully taken into account, we also develop a rigorous feature alignment processing, that is adapted to arbitrary wavelet filters (e.g. non-symmetric filters). Finally, we demonstrate the efficiency of our denoising approach in simulations over a wide range of noise levels for a representative set of standard images.
A shape-template based two-stage corpus callosum segmentation technique for sagittal plane T1-weighted brain magnetic resonance images

We propose a semi-automatic technique to segment corpus callosum (CC) using a two-stage snake formulation: A restricted affine transform (RAT) constrained snake followed by an unconstrained snake in an iterative fashion. A statistical model is developed to capture the shape variations of CC from a training set, which restrict the unconstrained snake to lie in the shape-space of CC. The geometry of the constrained snake is optimized using a local contrast-based energy over RAT space (which allows for five degrees of freedom). On the other hand, the unconstrained snake is optimized using a unified energy (region, gradient, and curvature energy) formulation. Joint optimization resulted in increased robustness to initialization as well as fast and accurate segmentation. The technique was validated on 243 images taken from the OASIS database and performance was quantified using Jaccard's distance, sensitivity, and specificity as the metrics.
Construction of biorthogonal wavelets starting from any two multiresolutions

Starting from any two given multiresolution analyses of L/sub 2/, {V/sub  1/}/sub j/spl isin/Z/ and {V/sub j//sup 2/}/sub j/spl isin/Z/, we construct biorthogonal wavelet bases that are associated with this chosen pair of multiresolutions. Thus, our construction method takes a point of view opposite to the one of Cohen-Daubechies-Feauveau (1992), which starts from a well-choosen pair of biorthogonal discrete filters. In our construction, the necessary and sufficient condition is the nonperpendicularity of the multiresolutions.
B-spline signal processing. I. Theory

The use of continuous B-spline representations for signal processing applications such as interpolation, differentiation, filtering, noise reduction, and data compressions is considered. The B-spline coefficients are obtained through a linear transformation, which unlike other commonly used transforms is space invariant and can be implemented efficiently by linear filtering. The same property also applies for the indirect B-spline transform as well as for the evaluation of approximating representations using smoothing or least squares splines. The filters associated with these operations are fully characterized by explicitly evaluating their transfer functions for B-splines of any order. Applications to differentiation, filtering, smoothing, and least-squares approximation are examined. The extension of such operators for higher-dimensional signals such as digital images is considered.
Statistical analysis of image differences by wavelet decomposition

The wavelet transform was studied for the analysis of glucose utilization differences between subject groups shown in PET images. To strengthen statistical inference, it was of particular interest investigating the trade-off between signal localization and image decomposition into uncorrelated components. This trade-off is governed by wavelet regularity, and was found to be best for third-order orthogonal spline wavelets. Only about 1.6% of the components were statistically different (p<.05) from noise, constituting a sufficient set to synthesize local image differences by the inverse wavelet transform.<<ETX>>
An accurate PSF model with few parameters for axially shift-variant deconvolution

Accurate knowledge of an imaging system's point spread function (PSF) is crucial for successful deconvolution. For fluorescence microscopy, PSF estimations based on either theoretical models or experimental measurements are available. However, due to the axially shift-variant nature of the PSF, neither method guarantees an estimate that is valid for the entire object space. In this work, we present a reduced- parameter version of a state-of-the-art theoretical model. We give a maximum-likelihood based algorithm for the estimation of its parameters, and we show how a fit of our model to two axially isolated point source measurements in an experimental setup can be used to accurately reproduce measured PSFs within the entire specimen.
Interpolation of signals by generalized piecewise-linear multiple generators

This paper presents an interpolation method based on shifted versions of two piecewise linear generators, which provides approximation order 2 like usual piecewise-linear interpolation; i.e., this method is able to represent the constant and the ramp exactly. Our interpolation is characterized by two real parameters: /spl tau/, the location of the generators, and /spl alpha/, related to their dissymmetry. By varying these parameters, we show that it is possible to optimize the quality of the approximation, independently of the function to interpolate. We recover the optimal value of shifted-linear interpolation (/spl tau/ = 0.21 and /spl alpha/ = 1) which requires IIR prefiltering, but we also find a new configuration (/spl tau/ = 0.21 and /spl alpha/ = 0.58) which reaches almost the same quality, while requiring FIR filtering only. This new solution is able to greatly reduce the amount of Gibbs oscillations generated in the shifted-linear interpolation scheme. We validate our finding by computing the PSNR of the difference between multi-rotated images and their original version.
FAST WAVELET-REGULARIZED IMAGE DECONVOLUTION

We present a modified version of the deconvolution algorithm introduced by Figueiredo and Nowak, which leads to a substantial acceleration. The algorithm essentially consists in alternating between a Landweber-type iteration and a wavelet-domain denoising step. Our key innovations are 1) the use of a Shannon wavelet basis, which decouples the problem across subbands, and 2) the use of optimized, subband-dependent step sizes and threshold levels. At high SNR levels, where the original algorithm exhibits slow convergence, we obtain an acceleration of one order of magnitude. This result suggests that wavelet-domain l1-regularization may become tractable for the deconvolution of large datasets, e.g. in fluorescence microscopy.
Comments on 'Classification of natural textures by means of two-dimensional orthogonal masks' by P. Cohen, V. Lacasse and C.T. DeDinh

The commenter discusses a texture classification technique by Cohen et al. described in the above-titled correspondence (see ibid., vol.37, no.1,  1989) that uses features derived from a set of four orthogonal masks applied to a 2*2 local neighborhood. The technique is an extension of the sum and difference histograms method previously published by the commenter. He points out that he has published a technique that is more general and subsumes the results of Cohen et al. and of his own earlier work. He also points out a mathematical error in the work by Cohen et al., which from a practical point of view, it is likely to have only minor effects.
On the feasibility of axial tracking of a fluorescent nanoparticle using a defocusing model

The image of a subresolution nanoparticle in fluorescence microscopy corresponds to a slice of the 3D point spread function (PSF). This slice relates to the out-of-focus distance of the nanoparticle. In this paper, we investigate to which extent it is possible to estimate the out-of-focus distance of the nanoparticle from a 2D image based on the knowledge of the 3D PSF. To this end, we compute the Cramer-Rao bound (CRB) that provides a lower bound on the error of the best estimator of the axial position. The calculation of the CRB involves the specification of a 3D PSF model, the assumption of a signal-dependent Poisson noise, and some acquisition parameters. Our derivation shows that the CRB depends on the defocusing distance. Interestingly, nanometer precision can be attained over a range of defocus distances and for sufficiently high SNR levels. The theoretical results are confirmed with simulated experiments using estimators based on the least-squares (LS) and normalized cross-correlation (NCC) criterion. The results obtained are very close to the theoretical CRB.
Grid-Free Localization Algorithm Using Low-Rank Hankel Matrix for Super-Resolution Microscopy

Localization microscopy, such as STORM/PALM, can reconstruct super-resolution images with a nanometer resolution through the iterative localization of fluorescence molecules. Recent studies in this area have focused mainly on the localization of densely activated molecules to improve temporal resolutions. However, higher density imaging requires an advanced algorithm that can resolve closely spaced molecules. Accordingly, sparsity-driven methods have been studied extensively. One of the major limitations of existing sparsity-driven approaches is the need for a fine sampling grid or for Taylor series approximation which may result in some degree of localization bias toward the grid. In addition, prior knowledge of the point-spread function (PSF) is required. To address these drawbacks, here we propose a true grid-free localization algorithm with adaptive PSF estimation. Specifically, based on the observation that sparsity in the spatial domain implies a low rank in the Fourier domain, the proposed method converts source localization problems into Fourier-domain signal processing problems so that a truly grid-free localization is possible. We verify the performance of the newly proposed method with several numerical simulations and a live-cell imaging experiment.
Multiresolution Subdivision Snakes

We present a new family of snakes that satisfy the property of multiresolution by exploiting subdivision schemes. We show in a generic way how to construct such snakes based on an admissible subdivision mask. We derive the necessary energy formulations and provide the formulas for their efficient computation. Depending on the choice of the mask, such models have the ability to reproduce trigonometric or polynomial curves. They can also be designed to be interpolating, a property that is useful in user-interactive applications. We provide explicit examples of subdivision snakes and illustrate their use for the segmentation of bioimages. We show that they are robust in the presence of noise and provide a multiresolution algorithm to enlarge their basin of attraction, which decreases their dependence on initialization compared to singleresolution snakes. We show the advantages of the proposed model in terms of computation and segmentation of structures with different sizes.
Optimized Kaiser–Bessel Window Functions for Computed Tomography

Kaiser-Bessel window functions are frequently used to discretize tomographic problems because they have two desirable properties: 1) their short support leads to a low computational cost and 2) their rotational symmetry makes their imaging transform independent of the direction. In this paper, we aim at optimizing the parameters of these basis functions. We present a formalism based on the theory of approximation and point out the importance of the partition-of-unity condition. While we prove that, for compact-support functions, this condition is incompatible with isotropy, we show that minimizing the deviation from the partition of unity condition is highly beneficial. The numerical results confirm that the proposed tuning of the Kaiser-Bessel window functions yields the best performance.
Quantitative L/sup 2/ approximation error of a probability density estimate given by its samples

We present a new result characterized by an exact integral expression for the approximation error between a probability density and an integer shift invariant estimate obtained from its samples. Unlike the Parzen window estimate, this estimate avoids recomputing the complete probability density for each new sample - only a few coefficients are required, making it practical for real-time applications. We also show how to obtain the exact asymptotic behavior of the approximation error when the number of samples increases and provide the trade-off between the number of samples and the sampling step size.
Fast computation of the continuous wavelet transform through oblique projections

We introduce a fast simple method for computing the real continuous wavelet transform (CWT). The approach achieves O(N) complexity per scale and the filter coefficients can be analytically obtained by a simple integration. Our method is to use P wavelets per octave and to approximate them with their oblique projection onto a space defined by a compact scaling function. The wavelet templates are expanded to larger sizes (octaves) using the two-scale relation and zero padded filtering. Error bounds are presented to justify the use of an oblique projection over an orthogonal one.
False Discovery Rate for Wavelet-Based Statistical Parametric Mapping

Model-based statistical analysis of functional magnetic resonance imaging (fMRI) data relies on the general linear model and statistical hypothesis testing. Due to the large number of intracranial voxels, it is important to deal with the multiple comparisons problem. Many fMRI analysis tools utilize Gaussian random field theory to obtain a more sensitive thresholding; this typically involves Gaussian smoothing as a preprocessing step. Wavelet-based statistical parametric mapping (WSPM) is an alternative method to obtain parametric maps from non-smoothed data. It relies on adaptive thresholding of the parametric maps in the wavelet domain, followed by voxel-wise statistical testing. The procedure is conservative; it uses Bonferroni correction for strong type I error control. Yet, its sensitivity is close to SPM's due to the excellent denoising properties of the wavelet transform. Here, we adapt the false discovery rate (FDR) principle to the WSPM framework. Although explicit p-values cannot be obtained, we show that it is possible to retrieve the FDR threshold by a simple iterative scheme. We then validate the approach with an event-related visual stimulation task. Our results show better sensitivity with preservation of spatial resolution; i.e., activation clusters align well with the gray matter structures in the visual cortex. The spatial resolution of the activation maps is even high enough to easily identify a voxel that is very likely to be caused by the draining-vein effect.
Fast detection of cells using a continuously scalable Mexican-hat-like template

We propose a fast algorithm for the detection of cells in fluorescence images. The algorithm, which estimates the number of cells and their respective centers and radii, relies on the fast computation of intensity-based correlations between the cells and a near-isotropic Mexican-hat-like detector. The attractive features of our algorithm are its speed and accuracy. The former attribute is derived from the fact that we can compute correlations between a cell and detectors of various sizes using O(1) operations; whereas, it is our ability to continuously control the center and the radius of the detector that results in a precise estimate of the position and size of the cell. We provide experimental results on both simulated and real data to demonstrate the speed and accuracy of the algorithm.
Multidimensional elastic registration of images using splines

We present an algorithm for nonlinear multidimensional registration. The correspondence function is represented in a spline space. We also use cubic splines to interpolate the volumetric data to be registered. We use a multiresolution strategy, which gives us robustness and additional speedup. We analyze the computational complexity of the algorithm and its performance using different multidimensional optimization methods. Finally, we present an application of the algorithm for registering technetium ethylene cysteine diethylester (ECD) SPECT images for realignment of corresponding Xe inhalation SPECT images.
New parametric 3D snake for medical segmentation of structures with cylindrical topology

We propose a new parametric 3D snake with cylindrical topology. Its construction is based on interpolatory basis functions which facilitates user-interaction because the control points of the snake directly lie on the surface of the deformable cylinder. We prove that the basis functions exactly reproduce a cylinder and propose a new parametrization as a tensor-product spline surface. We provide explicit formulas for the energy function based on Green's theorem that speed up the computation of the optimization algorithm. We have implemented the proposed framework as a freely available open-source plugin for the bioimaging platform Icy. Its utility has been tested on phantom data as well as on real 3D data to segment the spinal cord and the descending aorta.