34,397 research outputs found
Taylor series in Hermitean Clifford analysis
In this paper, we consider the Taylor decomposition for h-monogenic functions in Hermitean Clifford analysis. The latter is to be considered as a refinement of the classical orthogonal function theory, in which the structure group underlying the equations is reduced from so(2m) to the unitary Lie algebra u(m)
A Deep Learning Reconstruction Framework for Differential Phase-Contrast Computed Tomography with Incomplete Data
Differential phase-contrast computed tomography (DPC-CT) is a powerful
analysis tool for soft-tissue and low-atomic-number samples. Limited by the
implementation conditions, DPC-CT with incomplete projections happens quite
often. Conventional reconstruction algorithms are not easy to deal with
incomplete data. They are usually involved with complicated parameter selection
operations, also sensitive to noise and time-consuming. In this paper, we
reported a new deep learning reconstruction framework for incomplete data
DPC-CT. It is the tight coupling of the deep learning neural network and DPC-CT
reconstruction algorithm in the phase-contrast projection sinogram domain. The
estimated result is the complete phase-contrast projection sinogram not the
artifacts caused by the incomplete data. After training, this framework is
determined and can reconstruct the final DPC-CT images for a given incomplete
phase-contrast projection sinogram. Taking the sparse-view DPC-CT as an
example, this framework has been validated and demonstrated with synthetic and
experimental data sets. Embedded with DPC-CT reconstruction, this framework
naturally encapsulates the physical imaging model of DPC-CT systems and is easy
to be extended to deal with other challengs. This work is helpful to push the
application of the state-of-the-art deep learning theory in the field of
DPC-CT
Spectrality of Self-Similar Tiles
We call a set with positive Lebesgue measure a {\it
spectral set} if admits an exponential orthonormal basis. It was
conjectured that is a spectral set if and only if is a tile (Fuglede's
conjecture). Despite the conjecture was proved to be false on ,
([T], [KM2]), it still poses challenging questions with additional
assumptions. In this paper, our additional assumption is self-similarity. We
study the spectral properties for the class of self-similar tiles in
that has a product structure on the associated digit sets. We
show that any strict product-form tiles and the associated modulo product-form
tiles are spectral sets. As for the converse question, we give a pilot study
for the self-similar set generated by arbitrary digit sets with four
elements. We investigate the zeros of its Fourier transform due to the
orthogonality, and verify Fuglede's conjecture for this special case.Comment: 22page
The relationship of electron Fermi energy with strong magnetic fields
In order to depict the quantization of Landau levels, we introduce Dirac
function, and gain a concise expression for the electron Fermi energy,
. The high soft X-ray luminosities of magnetars may
be naturally explained by our theory.Comment: 3 pages, 1 figure, submitted to OMEG11 Proceeding (Tokyo, Japan.
Nov.14-18, 2011
Feature-Fused SSD: Fast Detection for Small Objects
Small objects detection is a challenging task in computer vision due to its
limited resolution and information. In order to solve this problem, the
majority of existing methods sacrifice speed for improvement in accuracy. In
this paper, we aim to detect small objects at a fast speed, using the best
object detector Single Shot Multibox Detector (SSD) with respect to
accuracy-vs-speed trade-off as base architecture. We propose a multi-level
feature fusion method for introducing contextual information in SSD, in order
to improve the accuracy for small objects. In detailed fusion operation, we
design two feature fusion modules, concatenation module and element-sum module,
different in the way of adding contextual information. Experimental results
show that these two fusion modules obtain higher mAP on PASCALVOC2007 than
baseline SSD by 1.6 and 1.7 points respectively, especially with 2-3 points
improvement on some smallobjects categories. The testing speed of them is 43
and 40 FPS respectively, superior to the state of the art Deconvolutional
single shot detector (DSSD) by 29.4 and 26.4 FPS. Code is available at
https://github.com/wnzhyee/Feature-Fused-SSD. Keywords: small object detection,
feature fusion, real-time, single shot multi-box detectorComment: Artificial Intelligence;8 pages,8 figure
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