A New Implementation for Neural Networks in Fourier-Space

2009 ◽  
pp. 307-330 ◽  
Author(s):  
Hazem M. El-Bakry ◽  
Mohamed Hamada
Keyword(s):  
Neural Networks ◽  
Fourier Space

scholarly journals Advancing Fourier: space–time concepts in ultrafast optics, imaging, and photonic neural networks

2019 ◽  
Vol 36 (11) ◽  
pp. C69 ◽  
Author(s):  
Luc Froehly ◽  
François Courvoisier ◽  
Daniel Brunner ◽  
Laurent Larger ◽  
Fabrice Devaux ◽  
...  
Keyword(s):  
Neural Networks ◽  
Ultrafast Optics ◽  
Space Time ◽  
Fourier Space ◽  
Time Concepts

Saliency Segmentation with Fourier-space Diffractive Deep Neural Networks

2020 ◽  
Author(s):  
Tao Yan ◽  
Jiamin Wu ◽  
Tiankuang Zhou ◽  
Hao Xie ◽  
Feng Xu ◽  
...  
Keyword(s):  
Neural Networks ◽  
Deep Neural Networks ◽  
Fourier Space

3-D reconstruction of molecular shape from microcrystal thin sections

1983 ◽  
Vol 41 ◽  
pp. 748-749
Author(s):  
S. Cusack ◽  
J.-C. Jésior
Keyword(s):  
Three Dimensional ◽  
Molecular Shape ◽  
Biological Molecules ◽  
Fourier Space ◽  
Single Particles ◽  
Thin Sections ◽  
Standard Methods ◽  
X Ray ◽  
X Ray Crystallography ◽  
Dimensional Reconstruction

Three-dimensional reconstruction techniques using electron microscopy have been principally developed for application to 2-D arrays (i.e. monolayers) of biological molecules and symmetrical single particles (e.g. helical viruses). However many biological molecules that crystallise form multilayered microcrystals which are unsuitable for study by either the standard methods of 3-D reconstruction or, because of their size, by X-ray crystallography. The grid sectioning technique enables a number of different projections of such microcrystals to be obtained in well defined directions (e.g. parallel to crystal axes) and poses the problem of how best these projections can be used to reconstruct the packing and shape of the molecules forming the microcrystal.Given sufficient projections there may be enough information to do a crystallographic reconstruction in Fourier space. We however have considered the situation where only a limited number of projections are available, as for example in the case of catalase platelets where three orthogonal and two diagonal projections have been obtained (Fig. 1).

The extended Fourier algorithm: Application in discrete optics and electron holography

1994 ◽  
Vol 52 ◽  
pp. 918-919
Author(s):  
E. Voelkl ◽  
L. F. Allard
Keyword(s):  
Fourier Transform ◽  
Fourier Transforms ◽  
Sampling Rate ◽  
Electron Holography ◽  
Optical Bench ◽  
Fourier Space ◽  
Ccd Cameras ◽  
Simulated Image ◽  
Initial Sampling ◽  
Fourier Algorithm

The conventional discrete Fourier transform can be extended to a discrete Extended Fourier transform (EFT). The EFT allows to work with discrete data in close analogy to the optical bench, where continuous data are processed. The EFT includes a capability to increase or decrease the resolution in Fourier space (thus the argument that CCD cameras with a higher number of pixels to increase the resolution in Fourier space is no longer valid). Fourier transforms may also be shifted with arbitrary increments, which is important in electron holography. Still, the analogy between the optical bench and discrete optics on a computer is limited by the Nyquist limit. In this abstract we discuss the capability with the EFT to change the initial sampling rate si of a recorded or simulated image to any other(final) sampling rate sf.

On the Use of POCS for Restoring the “Missing Wedge” in Electron Tomography

1990 ◽  
Vol 48 (1) ◽  
pp. 520-521
Author(s):  
Neng-Yu Zhang ◽  
Bruce F. McEwen ◽  
Joachim Frank
Keyword(s):  
Function Space ◽  
Convex Sets ◽  
Electron Tomography ◽  
Spinal Ganglion ◽  
Fourier Space ◽  
Missing Information ◽  
Voltage Electron ◽  
High Voltage Electron Microscope ◽  
Energy Bound ◽  
Spatial Boundedness

Reconstructions of asymmetric objects computed by electron tomography are distorted due to the absence of information, usually in an angular range from 60 to 90°, which produces a “missing wedge” in Fourier space. These distortions often interfere with the interpretation of results and thus limit biological ultrastructural information which can be obtained. We have attempted to use the Method of Projections Onto Convex Sets (POCS) for restoring the missing information. In POCS, use is made of the fact that known constraints such as positivity, spatial boundedness or an upper energy bound define convex sets in function space. Enforcement of such constraints takes place by iterating a sequence of function-space projections, starting from the original reconstruction, onto the convex sets, until a function in the intersection of all sets is found. First applications of this technique in the field of electron microscopy have been promising.To test POCS on experimental data, we have artificially reduced the range of an existing projection set of a selectively stained Golgi apparatus from ±60° to ±50°, and computed the reconstruction from the reduced set (51 projections). The specimen was prepared from a bull frog spinal ganglion as described by Lindsey and Ellisman and imaged in the high-voltage electron microscope.

Determination of S-N curves with the application of artificial neural networks

1999 ◽  
Vol 22 (8) ◽  
pp. 723-728 ◽  
Author(s):  
Artymiak ◽  
Bukowski ◽  
Feliks ◽  
Narberhaus ◽  
Zenner
Keyword(s):  
Neural Networks ◽  
Artificial Neural Networks ◽  
Artificial Neural

Review of Pattern Recognition by Self-Organizing Neural Networks.

1995 ◽  
Vol 40 (11) ◽  
pp. 1110-1110
Author(s):  
Stephen James Thomas
Keyword(s):  
Neural Networks ◽  
Pattern Recognition ◽  
Self Organizing
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