Optimal restoration of noisy 3D X-ray data via shearlet

decomposition

Optimally sparse shearlet approximations of 3D data

Sparse representations of multidimensional data have gained more and more prominence in recent years, in response to the need to process large and multi-dimensional data sets arising from a variety of applications in a timely and effective manner. This is especially important in applications such as remote sensing, satellite imagery, scientific simulations and electronic surveillance. Directional multiscale systems such as shearlets are able to provide sparse representations thanks to their ability to approximate anisotropic features much more efficiently than traditional multiscale representations. In this paper, we show that the shearlet approach is essentially optimal in representing a large class of 3D containing discontinuities along surfaces. This is the first nonadaptive approach to achieve provably optimal sparsity properties in the 3D setting

A directional representation for 3D tubular structures resulting from isotropic well-localized

atom

Improved Radon Based Imaging using the Shearlet Transform

Many imaging modalities, such as Synthetic Aperture Radar (SAR), can be described mathematically as collecting data in a Radon transform domain. The process of inverting the Radon transform to form an image can be unstable when the data collected contain noise so that the inversion needs to be regularized in some way. In this work, we develop a method for inverting the Radon transform using a shearlet-based decomposition, which provides a regularization that is nearly optimal for a general class of images. We then show through a variety of examples that this technique performs better than similar competitive methods based on the use of the wavelet and the curvelet transforms. 1

Multi-Composite Wavelet Estimation

In this work, we present a new approach to image denoising derived from the general framework of wavelets with composite dilations. This framework extends the traditional wavelet approach by allowing for waveforms to be defined not only at various scales and locations but also according to various orthogonal transformations such as shearing transformations. The shearlet representation is, perhaps, the most widely known example of wavelets with composite dilations. However, many other representations are obtained within this framework, where directionality properties are controlled by different types of orthogonal matrices, such as the newly defined hyperbolets. In this paper, we show how to take advantage of different wavelets with composite dilations to sparsely represent important features such as edges and texture independently, and apply these techniques to derive improved algorithms for image denoising

characterization of

and non-directional representations for th

Inhibition of AKT signaling alters beta IV spectrin distribution at the AIS and increases neuronal excitability

The axon initial segment (AIS) is a highly regulated subcellular domain required for neuronal firing. Changes in the AIS protein composition and distribution are a form of structural plasticity, which powerfully regulates neuronal activity and may underlie several neuropsychiatric and neurodegenerative disorders. Despite its physiological and pathophysiological relevance, the signaling pathways mediating AIS protein distribution are still poorly studied. Here, we used confocal imaging and whole-cell patch clamp electrophysiology in primary hippocampal neurons to study how AIS protein composition and neuronal firing varied in response to selected kinase inhibitors targeting the AKT/GSK3 pathway, which has previously been shown to phosphorylate AIS proteins. Image-based features representing the cellular pattern distribution of the voltage-gated Na+ (Nav) channel, ankyrin G, beta IV spectrin, and the cell-adhesion molecule neurofascin were analyzed, revealing beta IV spectrin as the most sensitive AIS protein to AKT/GSK3 pathway inhibition. Within this pathway, inhibition of AKT by triciribine has the greatest effect on beta IV spectrin localization to the AIS and its subcellular distribution within neurons, a phenotype that Support Vector Machine classification was able to accurately distinguish from control. Treatment with triciribine also resulted in increased excitability in primary hippocampal neurons. Thus, perturbations to signaling mechanisms within the AKT pathway contribute to changes in beta IV spectrin distribution and neuronal firing that may be associated with neuropsychiatric and neurodegenerative disorders.United States Department of Health & Human Services National Institutes of Health (NIH) - USA ; National Science Foundation (NSF

Inhibition of AKT Signaling Alters βIV Spectrin Distribution at the AIS and Increases Neuronal Excitability

The axon initial segment (AIS) is a highly regulated subcellular domain required for neuronal firing. Changes in the AIS protein composition and distribution are a form of structural plasticity, which powerfully regulates neuronal activity and may underlie several neuropsychiatric and neurodegenerative disorders. Despite its physiological and pathophysiological relevance, the signaling pathways mediating AIS protein distribution are still poorly studied. Here, we used confocal imaging and whole-cell patch clamp electrophysiology in primary hippocampal neurons to study how AIS protein composition and neuronal firing varied in response to selected kinase inhibitors targeting the AKT/GSK3 pathway, which has previously been shown to phosphorylate AIS proteins. Image-based features representing the cellular pattern distribution of the voltage-gated Na+ (Nav) channel, ankyrin G, βIV spectrin, and the cell-adhesion molecule neurofascin were analyzed, revealing βIV spectrin as the most sensitive AIS protein to AKT/GSK3 pathway inhibition. Within this pathway, inhibition of AKT by triciribine has the greatest effect on βIV spectrin localization to the AIS and its subcellular distribution within neurons, a phenotype that Support Vector Machine classification was able to accurately distinguish from control. Treatment with triciribine also resulted in increased excitability in primary hippocampal neurons. Thus, perturbations to signaling mechanisms within the AKT pathway contribute to changes in βIV spectrin distribution and neuronal firing that may be associated with neuropsychiatric and neurodegenerative disorders.</jats:p

Improved Automatic Centerline Tracing for Dendritic and Axonal Structures

Centerline tracing in dendritic structures acquired from confocal images of neurons is an essential tool for the construction of geometrical representations of a neuronal network from its coarse scale up to its fine scale structures. In this paper, we propose an algorithm for centerline extraction that is both highly accurate and computationally efficient. The main novelties of the proposed method are (1) the use of a small set of Multiscale Isotropic Laplacian filters, acting as self-steerable filters, for a quick and efficient binary segmentation of dendritic arbors and axons; (2) an automated centerline seed points detection method based on the application of a simple 3D finite-length filter. The performance of this algorithm, which is validated on data from the DIADEM set appears to be very competitive when compared with other state-of-the-art algorithms.National Science Foundation/[1320910]/NSF-DMS/Estados UnidosNational Science Foundation/[1008900]/NSF-DMS/Estados UnidosNational Science Foundation/[1005799]/NSF-DMS/Estados UnidosNorman Hackerman Advanced Research Program/[003652-0136-2009]/NHARP/Estados UnidosUCR::Vicerrectoría de Docencia::Ciencias Básicas::Facultad de Ciencias::Escuela de Matemátic