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The expressive power of deep neural networks is manifested by their remarkable ability to approximate multivariate functions in a way that appears to overcome the curse of dimensionality. This ability is exemplified by their success in solving high-dimensional problems where traditional numerical solvers fail due to their limitations in accurately representing high-dimensional structures. To provide a theoretical framework for explaining this phenomenon, we analyze the approximation of Hölder functions defined on a d -dimensional smooth manifold M embedded in R D , with d ≪ D , using deep neural networks. We prove that the uniform convergence estimates of the approximation and generalization errors by deep neural networks with ReLU activation functions do not depend on the ambient dimension D of the function but only on its lower manifold dimension d , in a precise sense. Our result improves existing results from the literature where approximation and generalization errors were shown to depend weakly on D. • Deep ReLU neural networks exhibit remarkable approximation properties for multivariate functions. • We prove that the approximation error of manifold-embedded data depends only on the manifold dimension. • Argument relies on preservation of pairwise ambient distances on the manifold. • Our result improves existing results where the approximation error depends weakly on the ambient dimension. • Our result implies an improved estimate of the generalization error. [ABSTRACT FROM AUTHOR]

Several strategies have been applied for the recovery of the missing parts in an image, with recovery performance depending significantly on the image type and the geometry of missing data. To provide a deeper understanding of such image restoration problem, King et al. recently introduced a rigorous multiscale analysis framework and proved that a shearlet based inpainting approach outperforms methods based on more conventional multiscale representations when missing data are line singularities. In this paper, we extend and improve the analysis of the inpainting problem to the more realistic and more challenging setting of images containing curvilinear singularities. We derive inpainting performance guarantees showing that exact image recovery is achieved if the size of the missing singularity is smaller than the size of the structure elements of appropriate functional representations of the image. Our proof relies critically on the microlocal and sparsity properties of the shearlet representation. [ABSTRACT FROM AUTHOR]

Smooth orthogonal projections with good localization properties were originally studied in the wavelet literature as a way to both understand and generalize the construction of smooth wavelet bases on L 2 (ℝ) . Smoothness plays a critical role in the construction of wavelet bases and their generalizations as it is instrumental to achieve excellent approximation properties. In this paper, we extend the construction of smooth orthogonal projections to higher dimensions, a challenging problem in general for which relatively few results are found in the literature. Our investigation is motivated by the study of multidimensional nonseparable multiscale systems such as shearlets. Using our new class of smooth orthogonal projections, we construct new smooth Parseval frames of shearlets in L 2 (ℝ 2) and L 2 (ℝ 3) . [ABSTRACT FROM AUTHOR]

Hyperspectral imagery has emerged as a popular sensing modality for a variety of applications, and sparsity-based methods were shown to be very effective to deal with challenges coming from high dimensionality in most hyperspectral classification problems. In this paper, we challenge the conventional approach to hyperspectral classification that typically builds sparsity-based classifiers directly on spectral reflectance features or features derived directly from the data. We assert that hyperspectral image (HSI) processing can benefit very significantly by decoupling data into geometrically distinct components since the resulting decoupled components are much more suitable for sparse representation-based classifiers. Specifically, we apply morphological separation to decouple data into texture and cartoon-like components, which are sparsely represented using local discrete cosine bases and multiscale shearlets, respectively. In addition to providing a structured sparse representation, this approach allows us to build classifiers with invariance properties specific to each geometrically distinct component of the data. The experimental results using real-world HSI data sets demonstrate the efficacy of the proposed framework for classifying multichannel imagery under a variety of adverse conditions—in particular, small training sample size, additive noise, and rotational variabilities between training and test samples. [ABSTRACT FROM PUBLISHER]

Edges and surface boundaries are often the most relevant features in images and multidimensional data. It is well known that multiscale methods including wavelets and their more sophisticated multidimensional siblings offer a powerful tool for the analysis and detection of such sets. Among such methods, the continuous shearlet transform has been especially successful. This method combines anisotropic scaling and directional sensitivity controlled by shear transformations in order to precisely identify not only the location of edges and boundary points but also edge orientation and corner points. In this paper, we show that this framework can be made even more flexible by controlling the scaling parameter of the anisotropic dilation matrix and considering non-parabolic scaling. We prove that, using 'higher-than-parabolic' scaling, the modified shearlet transform is also able to estimate the degree of local flatness of an edge or surface boundary, providing more detailed information about the geometry of edge and boundary points. [ABSTRACT FROM AUTHOR]

Background Automated detection and segmentation of somas in fluorescent images of neurons is a major goal in quantitative studies of neuronal networks, including applications of high-content-screenings where it is required to quantify multiple morphological properties of neurons. Despite recent advances in image processing targeted to neurobiological applications, existing algorithms of soma detection are often unreliable, especially when processing fluorescence image stacks of neuronal cultures. New method In this paper, we introduce an innovative algorithm for the detection and extraction of somas in fluorescent images of networks of cultured neurons where somas and other structures exist in the same fluorescent channel. Our method relies on a new geometrical descriptor called Directional Ratio and a collection of multiscale orientable filters to quantify the level of local isotropy in an image. To optimize the application of this approach, we introduce a new construction of multiscale anisotropic filters that is implemented by separable convolution. Results Extensive numerical experiments using 2D and 3D confocal images show that our automated algorithm reliably detects somas, accurately segments them, and separates contiguous ones. Comparison with existing methods We include a detailed comparison with state-of-the-art existing methods to demonstrate that our algorithm is extremely competitive in terms of accuracy, reliability and computational efficiency. Conclusions Our algorithm will facilitate the development of automated platforms for high content neuron image processing. A Matlab code is released open-source and freely available to the scientific community. [ABSTRACT FROM AUTHOR]

The analysis and detection of edges is a central problem in applied mathematics and image processing. A number of results in recent years have shown that directional multiscale methods such as continuous curvelet and shearlet transforms offer a powerful theoretical framework to capture the geometry of edge singularities, going far beyond the capabilities of the conventional wavelet transform. The continuous shearlet transform, in particular, provides a precise geometric characterization of edges in piecewise constant functions in R 2 and R 3 , including corner points. However, a question has been raised frequently: What happens if the function is piecewise smooth and not just piecewise constant? Clearly, a piecewise smooth function is a much more realistic model of images with edges. In this paper, we extend the characterization results previously known and show that, also in the case of piecewise smooth functions, the continuous shearlet transform can detect the location and orientation of edge points, including corner points, through its asymptotic decay at fine scales. The new proof introduces innovative technical constructions to deal with the more challenging problem. The new results set the theoretical groundwork for the application of the shearlet framework to a wider class of problems from image processing. [ABSTRACT FROM AUTHOR]

Accurate segmentation of 3D vessel-like structures is a major challenge in medical imaging. In this paper, we introduce a novel approach for the detection of 3D tubular structures that is particularly suited to capture the geometry of vessel-like networks, such as dendritic trees and vascular systems. Even though our approach relies on a system of isotropic multiscale analyzing atoms, we prove that their interaction via convolution with a tubular structure is equivalent to a set of directional atoms at various scales, automatically oriented along any possible direction and with cylindrical symmetry. This result sets the theoretical groundwork for the design of efficient discrete algorithms aiming at extracting the geometry of vessel-like structures in 3D medical images. [ABSTRACT FROM AUTHOR]

Suppose that Ω is a three-dimensional solid with boundary surface S = S 1 ∪ ⋯ ∪ S q , where each S r is a smooth surface with boundary curve Γ r . Multiscale directional representation systems (e.g., shearlets) are able to capture the essential geometry of Ω by precisely identifying the boundary set N = { ( p , n r ( p ) ) : p ∈ S r , r = 1 , … , q } , where n r ( p ) denotes the normal vector to the surface S r at p . This property has resulted in the successful application of multiscale directional methods in a variety of image processing problems, since edges and boundary sets are usually the most informative features in many types of multidimensional data. However, existing methods are ill-suited to capture those edge-type singularities in the three-dimensional setting resulting from the intersection of piecewise smooth boundary surfaces. In this paper, we introduce a new multiscale directional system based on a modification of the shearlet framework and prove that the associated continuous transform has the ability to precisely identify both the location and orientation of the boundary curves Γ r from the solid Ω . This paper extends a number of results appeared in the literature in recent years to the challenging problem of extracting curvilinear singularities in three-dimensional objects and is motivated by image analysis problems arising from areas including biomedical and seismic imaging and astronomy. [ABSTRACT FROM AUTHOR]

The major limitation in current facial recognition systems is that they do not perform very well in uncontrolled environments, that is, when faces present variations in pose, illumination, facial expressions and environment. This is a serious obstacle in applications such as law enforcement and surveillance systems. To address this limitation, in this paper we introduce an improved approach to ensure robust face recognition, that relies on two innovative ideas. First, we apply a new multiscale directional framework, called Shearlet Network (SN), to extract facial features. The advantage of this approach comes from the highly sparse representation properties of the shearlet framework that is especially designed to robustly extract the fundamental geometric content of an image. Second, we apply a refinement of the Multi-Task Sparse Learning (MTSL) framework to exploit the relationships among multiple shared tasks generated by changing the regularization parameter during the recognition stage. We provide extensive numerical tests to show that our Sparse Multi-Regularized Shearlet Network (SMRSN) algorithm performs very competitively when compared against different state-of-the-art methods on different experimental protocols, including face recognition in uncontrolled conditions and single-sample-per-person. [ABSTRACT FROM AUTHOR]

This paper introduces a new decomposition of the 3D X-ray transform based on the shearlet representation, a multiscale directional representation which is optimally efficient in handling 3D data containing edge singularities. Using this decomposition, we derive a highly effective reconstruction algorithm yielding a near-optimal rate of convergence in estimating piecewise smooth objects from 3D X-ray tomographic data which are corrupted by white Gaussian noise. This algorithm is achieved by applying a thresholding scheme on the 3D shearlet transform coefficients of the noisy data which, for a given noise level ε, can be tuned so that the estimator attains the essentially optimal mean square error rate O(log( ε) ε), as ε→0. This is the first published result to achieve this type of error estimate, outperforming methods based on Wavelet-Vaguelettes decomposition and on SVD, which can only achieve MSE rates of O( ε) and O( ε), respectively. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a digital implementation of the 3-D shearlet transform and illustrate its application to problems of video denoising and enhancement. The shearlet representation is a multiscale pyramid of well-localized waveforms defined at various locations and orientations, which was introduced to overcome the limitations of traditional multiscale systems in dealing with multidimensional data. While the shearlet approach shares the general philosophy of curvelets and surfacelets, it is based on a very different mathematical framework, which is derived from the theory of affine systems and uses shearing matrices rather than rotations. This allows a natural transition from the continuous setting to the digital setting and a more flexible mathematical structure. The 3-D digital shearlet transform algorithm presented in this paper consists in a cascade of a multiscale decomposition and a directional filtering stage. The filters employed in this decomposition are implemented as finite-length filters, and this ensures that the transform is local and numerically efficient. To illustrate its performance, the 3-D discrete shearlet transform is applied to problems of video denoising and enhancement, and compared against other state-of-the-art multiscale techniques, including curvelets and surfacelets. [ABSTRACT FROM AUTHOR]

This paper introduces a Parseval frame of shearlets for the representation of three-dimensional (3D) data, which is especially designed to handle geometric features such as discontinuous boundaries with very high efficiency. This system of 3D shearlets forms a multiscale pyramid of well-localized waveforms at various locations and orientations, which become increasingly thin and elongated at fine scales. We prove that this 3D shearlet construction provides essentially optimal sparse representations for functions on R3 which are C²-regular away from discontinuities along C²2 surfaces. As a consequence, we show that, within this class of functions, the N-term approximation fNS obtained by selecting the N largest coefficients of the shearlet expansion of f satisfies the asymptotic estimate ... This asymptotic behavior significantly outperforms wavelet and Fourier series approximations, which yield an approximation rate of only O(N-1/2) and O(N-1/3), respectively. This result extends to the 3D setting the (essentially) optimally sparse approximation results obtained by the authors using 2D shearlets and by Candes and Donoho using curvelets and is the first nonadaptive construction to provide provably (nearly) optimal representations for a large class of 3D data. [ABSTRACT FROM AUTHOR]

Wavelets with composite dilations provide a general framework for the construction of waveforms defined not only at various scales and locations, as traditional wavelets, but also at various orientations and with different scaling factors in each coordinate. As a result, they are useful to analyze the geometric information that often dominate multidimensional data much more efficiently than traditional wavelets. The shearlet system, for example, is a particular well-known realization of this framework, which provides optimally sparse representations of images with edges. In this paper, we further investigate the constructions derived from this approach to develop critically sampled wavelets with composite dilations for the purpose of image coding. Not only do we show that many nonredundant directional constructions recently introduced in the literature can be derived within this setting, but we also introduce new critically sampled discrete transforms that achieve much better nonlinear approximation rates than traditional discrete wavelet transforms and outperform the other critically sampled multiscale transforms recently proposed. [ABSTRACT FROM AUTHOR]

Abstract: Directional multiscale transforms such as the shearlet transform have emerged in recent years for their ability to capture the geometrical information associated with the singularity sets of bivariate functions and distributions. One of the most striking features of the continuous shearlet transform is that it provides a very simple and precise geometrical characterization for the boundary curves of general planar regions. However, no specific results were known so far in higher dimensions, since the arguments used in dimension do not directly carry over to the higher dimensional setting. In this paper, we extend this framework for the analysis of singularities to the 3-dimensional setting, and show that the 3-dimensional continuous shearlet transform precisely characterizes the boundary set of solid regions in by identifying both its location and local orientation. [ABSTRACT FROM AUTHOR]

Abstract: PRISMA (PRecursore IperSpettrale della Missione Applicativa) hyperspectral instrument is an advanced hyperspectral sensor including a panchromatic camera at medium resolution. The instrument is the focus of the new Earth observation mission that a consortium of Italian companies has started developing under contract of Italian Space Agency. Key features of the instrument are the very high requirement for signal-to-noise and the high quality of data that have to be provided. To meet these demanding figures the optical system has been based on a high transmittance optical system, including a single mirror telescope and two prism spectrometers based on an innovative concept to minimize number of optical elements, while high performance detectors have been chosen for the photon detection. To provide the required data quality for the entire mission lifetime an accurate calibration unit (radiometric and spectral) will be included in the instrument optomechanical assembly. The thermo-mechanical design of the instrument is based on innovative concepts, considering that the use of prism spectrometers implies a tight control of temperature variations to guarantee the stability of all instrument features once in orbit. The presented paper describes the concepts and design principle of the optomechanical assembly of the instrument, at the present status of development. [Copyright &y& Elsevier]

Abstract: It is well known that the continuous wavelet transform has the ability to identify the set of singularities of a function or distribution f. It was recently shown that certain multidimensional generalizations of the wavelet transform are useful to capture additional information about the geometry of the singularities of f. In this paper, we consider the continuous shearlet transform, which is the mapping , where the analyzing elements form an affine system of well localized functions at continuous scales , locations , and oriented along lines of slope in the frequency domain. We show that the continuous shearlet transform allows one to exactly identify the location and orientation of the edges of planar objects. In particular, if where the functions are smooth and the sets have smooth boundaries, then one can use the asymptotic decay of , as (fine scales), to exactly characterize the location and orientation of the boundaries . This improves similar results recently obtained in the literature and provides the theoretical background for the development of improved algorithms for edge detection and analysis. [Copyright &y& Elsevier]

It is well known that the wavelet transform provides a very effective framework for analysis of multiscale edges. In this paper, we propose a novel approach based on the shearlet transform: a multiscale directional transform with a greater ability to localize distributed discontinuities such as edges. Indeed, unlike traditional wavelets, shearlets are theoretically optimal in representing images with edges and, in particular, have the ability to fully capture directional and other geometrical features. Numerical examples demonstrate that the shearlet approach is highly effective at detecting both the location and orientation of edges, and outperforms methods based on wavelets as well as other standard methods. Furthermore, the shearlet approach is useful to design simple and effective algorithms for the detection of corners and junctions. [ABSTRACT FROM AUTHOR]

We propose a shearlet formulation of the total variation (TV) method for denoising images. Shearlets have been mathematically proven to represent distributed discontinuities such as edges better than traditional wavelets and are a suitable tool for edge characterization. Common approaches in combining wavelet-like representations such as curvelets with TV or diffusion methods aim at reducing Gibbs-type artifacts after obtaining a nearly optimal estimate. We show that it is possible to obtain much better estimates from a shearlet representation by constraining the residual coefficients using a projected adaptive total variation scheme in the shearlet domain. We also analyze the performance of a shearlet-based diffusion method. Numerical examples demonstrate that these schemes are highly effective at denoising complex images and outperform a related method based on the use of the curvelet transform. Furthermore, the shearlet-TV scheme requires far fewer iterations than similar competitors. [ABSTRACT FROM AUTHOR]

Abstract: In spite of their remarkable success in signal processing applications, it is now widely acknowledged that traditional wavelets are not very effective in dealing multidimensional signals containing distributed discontinuities such as edges. To overcome this limitation, one has to use basis elements with much higher directional sensitivity and of various shapes, to be able to capture the intrinsic geometrical features of multidimensional phenomena. This paper introduces a new discrete multiscale directional representation called the discrete shearlet transform. This approach, which is based on the shearlet transform, combines the power of multiscale methods with a unique ability to capture the geometry of multidimensional data and is optimally efficient in representing images containing edges. We describe two different methods of implementing the shearlet transform. The numerical experiments presented in this paper demonstrate that the discrete shearlet transform is very competitive in denoising applications both in terms of performance and computational efficiency. [Copyright &y& Elsevier]

In this paper we show that shearlets, an affine-like system of functions recently introduced by the authors and their collaborators, are essentially optimal in representing 2-dimensional functions ƒ which are C2 except for discontinuities along C2 curves. More specifically, if ƒSN is the N-term reconstruction of ƒ obtained by using the N largest coefficients in the shearlet representation, then the asymptotic approximation error decays as ||ƒ-ƒNS||22 ≍ N-2 (logN)3, N → ∞ which is essentially optimal, and greatly outperforms the corresponding asymptotic approximation rate N-1 associated with wavelet approximations. Unlike curvelets, which have similar sparsity properties, shearlets form an affine-like system and have a simpler mathematical structure. In fact, the elements of this system form a Parseval frame and are generated by applying dilations, shear transformations, and translations to a single well-localized window function. [ABSTRACT FROM AUTHOR]

Abstract: Affine systems are reproducing systems of the form which arise by applying lattice translation operators to one or more generators in , followed by the application of dilation operators , associated with a countable set of invertible matrices. In the wavelet literature, is usually taken to be the group consisting of all integer powers of a fixed expanding matrix. In this paper, we develop the properties of much more general systems, for which where A and B are not necessarily commuting matrix sets. need not contain a single expanding matrix. Nonetheless, for many choices of A and B, there are wavelet systems with multiresolution properties very similar to those of classical dyadic wavelets. Typically, A expands or contracts only in certain directions, while B acts by volume-preserving maps in transverse directions. Then the resulting wavelets exhibit the geometric properties, e.g., directionality, elongated shapes, scales, oscillations, recently advocated by many authors for multidimensional signal and image processing applications. Our method is a systematic approach to the theory of affine-like systems yielding these and more general features. [Copyright &y& Elsevier]

In [E. Herna´ndez, D. Labate, G. Weiss, J. Geom. Anal. 12 (4) (2002) 615–662], three of the authors obtained a characterization of certain types of reproducing systems. In this work, we apply these results and methods to various affine-like, wave packets and Gabor systems to determine their frame properties. In particular, we study how oversampled systems inherit properties (like the frame bounds) of the original systems. Moreover, our approach allows us to study the phenomenon of oversampling in much greater generality than is found in the literature. [Copyright &y& Elsevier]

We present a new method for the stable reconstruction of a class of binary images from a small number of measurements. The images we consider are characteristic functions of algebraic domains, that is, domains defined as zero loci of bivariate polynomials, and we assume to know only a finite set of uniform samples for each image. The solution to such a problem can be set up in terms of linear equations associated to a set of image moments. However, the sensitivity of the moments to noise makes the numerical solution highly unstable. To derive a robust image recovery algorithm, we represent algebraic polynomials and the corresponding image moments in terms of bivariate Bernstein polynomials and apply polynomial-generating, refinable sampling kernels. This approach is robust to noise, computationally fast and simple to implement. We illustrate the performance of our reconstruction algorithm from noisy samples through extensive numerical experiments. Our code is released open source and freely available. [ABSTRACT FROM AUTHOR]

While astrocytes have been traditionally described as passive supportive cells, studies during the last decade have shown they are active players in many aspects of CNS physiology and function both in normal and disease states. However, the precise mechanisms regulating astrocytes function and interactions within the CNS are still poorly understood. This knowledge gap is due in large part to the limitations of current image analysis tools that cannot process astrocyte images efficiently and to the lack of methods capable of quantifying their complex morphological characteristics. To provide an unbiased and accurate framework for the quantitative analysis of fluorescent images of astrocytes, we introduce a new automated image processing pipeline whose main novelties include an innovative module for cell detection based on multiscale directional filters and a segmentation routine that leverages deep learning and sparse representations to reduce the need of training data and improve performance. Extensive numerical tests show that our method performs very competitively with respect to state-of-the-art methods also in challenging images where astrocytes are clustered together. Our code is released open source and freely available to the scientific community. [ABSTRACT FROM AUTHOR]

Abstract Recent advances in the field of multiscale representations have spurred the emergence of a new generation of powerful techniques for the efficient analysis of images and other multidimensional data. These novel techniques enable the quantification of essential geometric characteristics in complex imaging data resulting in improved algorithms for image restoration, feature extraction and classification. We discuss the application of these ideas in neuroscience imaging and describe a novel method for the accurate and efficient identification of cellular bodies of neurons in multicellular images. This method is instrumental to the design of a novel algorithm for neuronal tracing. [ABSTRACT FROM AUTHOR]

Compressive sensing (CS) has been proposed as a disruptive approach to developing a novel class of optical instrumentation used in diverse application domains. Thanks to sparsity as an inherent feature of many natural signals, CS allows for the acquisition of the signal in a very compact way, merging acquisition and compression in a single step and, furthermore, offering the capability of using a limited number of detector elements to obtain a reconstructed image with a larger number of pixels. Although the CS paradigm has already been applied in several application domains, from medical diagnostics to microscopy, studies related to space applications are very limited. In this paper, we present and discuss the instrumental concept, optical design, and performances of a CS imaging spectrometer for ultraviolet-visible (UV–Vis) stellar spectroscopy. The instrument—which is pixel-limited in the entire 300 nm–650 nm spectral range—features spectral sampling that ranges from 2.2 nm@300 nm to 22 nm@650 nm, with a total of 50 samples for each spectrum. For data reconstruction quality, the results showed good performance, measured by several quality metrics chosen from those recommended by CCSDS. The designed instrument can achieve compression ratios of 20 or higher without a significant loss of information. A pros and cons analysis of the CS approach is finally carried out, highlighting main differences with respect to a traditional system. [ABSTRACT FROM AUTHOR]

Astrocytes, a subtype of glial cells with a complex morphological structure, are active players in many aspects of the physiology of the central nervous system (CNS). However, due to their highly involved interaction with other cells in the CNS, made possible by their morphological complexity, the precise mechanisms regulating astrocyte function within the CNS are still poorly understood. This knowledge gap is also due to the current limitations of existing quantitative image analysis tools that are unable to detect and analyze images of astrocyte with sufficient accuracy and efficiency. To address this need, we introduce a new deep learning framework for the automated detection of GFAP-immunolabeled astrocytes in brightfield or fluorescent micrographs. A major novelty of our approach is the applications of YOLOv5, a sophisticated deep learning platform designed for object detection, that we customized to derive optimized classification models for the task of astrocyte detection. Extensive numerical experiments using multiple image datasets show that our method performs very competitively against both conventional and state-of-the-art methods, including the case of images where astrocytes are very dense. In the spirit of reproducible research, our numerical code and annotated data are released open source and freely available to the scientific community. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a novel two-stage denoising method for the removal of random-valued impulse noise (RVIN) in images. The first stage of our algorithm applies an impulse-noise detection routine that is a refinement of the HEIND algorithm and is very accurate in identifying the location of the noisy pixels. The second stage is an image inpainting routine that is designed to restore the missing information at those pixels that have been identified during the first stage. One of the novelties of our approach is that our inpainting routine takes advantage of the shearlet representation to efficiently recover the geometry of the original image. This method is particularly effective to eliminate jagged edges and other visual artifacts that frequently affect many RVIN denoising algorithms, especially at higher noise levels. We present extensive numerical demonstrations to show that our approach is very effective to remove random-valued impulse noise without any significant loss of fine-scale detail. Our algorithm compares very favourably against state-of-the-art methods in terms of both visual quality and quantitative measurements. [ABSTRACT FROM AUTHOR]

In COVID‐19 patients receiving enoxaparin and antiplatelets therapy, aggregometry and thromboelastography might be considered an adjunctive tool to identify the time to perform procedures at risk of bleeding, such as tracheostomy. [ABSTRACT FROM AUTHOR]

[Display omitted] Measuring single cell responses to the universe of chemicals (drugs, natural products, environmental toxicants etc.) is of paramount importance to human health as phenotypic variability in sensing stimuli is a hallmark of biology that is considered during high throughput screening. One of the ways to approach this problem is via high throughput, microscopy-based assays coupled with multi-dimensional single cell analysis methods. Here, we will summarize some of the efforts in this vast and growing field, focusing on phenotypic screens (e.g., Cell Painting), single cell analytics and quality control, with particular attention to environmental toxicology and drug screening. We will discuss advantages and limitations of high throughput assays with various end points and levels of complexity. [ABSTRACT FROM AUTHOR]

Background: Obesity and steatosis are associated with COVID-19 severe pneumonia. Elevated levels of pro-inflammatory cytokines and reduced immune response are typical of these patients. In particular, adipose tissue is the organ playing the crucial role. So, it is necessary to evaluate fat mass and not simpler body mass index (BMI), because BMI leaves a portion of the obese population unrecognized. The aim is to evaluate the relationship between Percentage of Fat Mass (FM%) and immune-inflammatory response, after 10 days in Intensive Care Unit (ICU).Methods: Prospective observational study of 22 adult patients, affected by COVID-19 pneumonia and admitted to the ICU and classified in two sets: (10) lean and (12) obese, according to FM% and age (De Lorenzo classification). Patients were analyzed at admission in ICU and at 10th day.Results: Obese have steatosis, impaired hepatic function, compromise immune response and higher inflammation. In addition, they have a reduced prognostic nutritional index (PNI), nutritional survival index for ICU patients.Conclusion: This is the first study evaluating FM% in COVID-19 patient. We underlined obese characteristic with likely poorly prognosis and an important misclassification of obesity. A not negligible number of patients with normal BMI could actually have an excess of adipose tissue and therefore have an unfavorable outcome such as an obese. Is fundamental personalized patients nutrition basing on disease phases. [ABSTRACT FROM AUTHOR]

Efficient representations of multivariate functions are critical for the design of state-of-the-art methods of data restoration and image reconstruction. In this work, we consider the representation of spatio-temporal data such as temporal sequences (videos) of 2- and 3-dimensional images, where conventional separable representations are usually very inefficient, due to their limitations in handling the geometry of the data. To address this challenge, we define a class E (A) ⊂ L 2 (R 4) of functions of 4 variables dominated by hypersurface singularities in the first three coordinates that we apply to model 4-dimensional data corresponding to temporal sequences (videos) of 3-dimensional objects. To provide an efficient representation for this type of data, we introduce a new multiscale directional system of functions based on cylindrical shearlets and prove that this new approach achieves superior approximation properties with respect to conventional multiscale representations. We illustrate the advantages of our approach by applying a discrete implementation of the new representation to a challenging problem from dynamic tomography. Numerical results confirm the potential of our novel approach with respect to conventional multiscale methods. [ABSTRACT FROM AUTHOR]

Automated identification of the primary components of a neuron and extraction of its sub-cellular features are essential steps in many quantitative studies of neuronal networks. The focus of this paper is the development of an algorithm for the automated detection of the location and morphology of somas in confocal images of neuronal network cultures. This problem is motivated by applications in high-content screenings (HCS), where the extraction of multiple morphological features of neurons on large data sets is required. Existing algorithms are not very efficient when applied to the analysis of confocal image stacks of neuronal cultures. In addition to the usual difficulties associated with the processing of fluorescent images, these types of stacks contain a small number of images so that only a small number of pixels are available along the z-direction and it is challenging to apply conventional 3D filters. The algorithm we present in this paper applies a number of innovative ideas from the theory of directional multiscale representations and involves the following steps: (i) image segmentation based on support vector machines with specially designed multiscale filters; (ii) soma extraction and separation of contiguous somas, using a combination of level set method and directional multiscale filters. We also present an approach to extract the soma’s surface morphology using the 3D shearlet transform. Extensive numerical experiments show that our algorithms are computationally efficient and highly accurate in segmenting the somas and separating contiguous ones. The algorithms presented in this paper will facilitate the development of a high-throughput quantitative platform for the study of neuronal networks for HCS applications. [ABSTRACT FROM AUTHOR]

Background Phosphorylation plays an essential role in regulating voltage-gated sodium (Na v ) channels and excitability. Yet, a surprisingly limited number of kinases have been identified as regulators of Na v channels. We posited that glycogen synthase kinase 3 (GSK3), a critical kinase found associated with numerous brain disorders, might directly regulate neuronal Na v channels. Methods We used patch-clamp electrophysiology to record sodium currents from Na v 1.2 channels stably expressed in HEK-293 cells. mRNA and protein levels were quantified with RT-PCR, Western blot, or confocal microscopy, and in vitro phosphorylation and mass spectrometry to identify phosphorylated residues. Results We found that exposure of cells to GSK3 inhibitor XIII significantly potentiates the peak current density of Na v 1.2, a phenotype reproduced by silencing GSK3 with siRNA. Contrarily, overexpression of GSK3β suppressed Na v 1.2-encoded currents. Neither mRNA nor total protein expression was changed upon GSK3 inhibition. Cell surface labeling of CD4-chimeric constructs expressing intracellular domains of the Na v 1.2 channel indicates that cell surface expression of CD4-Na v 1.2 C-tail was up-regulated upon pharmacological inhibition of GSK3, resulting in an increase of surface puncta at the plasma membrane. Finally, using in vitro phosphorylation in combination with high resolution mass spectrometry, we further demonstrate that GSK3β phosphorylates T 1966 at the C-terminal tail of Na v 1.2. Conclusion These findings provide evidence for a new mechanism by which GSK3 modulates Na v channel function via its C-terminal tail. General significance These findings provide fundamental knowledge in understanding signaling dysfunction common in several neuropsychiatric disorders. [ABSTRACT FROM AUTHOR]

Abstract: The inversion of the Radon transform is a classical ill-posed inverse problem where some method of regularization must be applied in order to accurately recover the objects of interest from the observable data. A well-known consequence of the traditional regularization methods is that some important features to be recovered are lost, as evident in imaging applications where the regularized reconstructions are blurred versions of the original. In this paper, we show that the affine-like system of functions known as the shearlet system can be applied to obtain a highly effective reconstruction algorithm which provides near-optimal rate of convergence in estimating a large class of images from noisy Radon data. This is achieved by introducing a shearlet-based decomposition of the Radon operator and applying a thresholding scheme on the noisy shearlet transform coefficients. For a given noise level ε, the proposed shearlet shrinkage method can be tuned so that the estimator will attain the essentially optimal mean square error , as . Several numerical demonstrations show that its performance improves upon similar competitive strategies based on wavelets and curvelets. [Copyright &y& Elsevier]