scholarly journals On the Feasibility of Fast Fourier Transform Separability Property for Distributed Image Processing

2021 ◽  
Vol 2021 ◽  
pp. 1-8
Author(s):  
Arturo Téllez-Velázquez ◽  
Raúl Cruz-Barbosa
Keyword(s):  
Graphics Processing Units ◽  
Fourier Transforms ◽  
Two Dimensional ◽  
One Dimensional ◽  
Processing Times ◽  
Hardware Implementations ◽  
Separability Property ◽  
Feasible Alternative ◽  
Graphics Processing ◽  
Usage Efficiency

Given the high algorithmic complexity of applied-to-images Fast Fourier Transforms (FFT), computational-resource-usage efficiency has been a challenge in several engineering fields. Accelerator devices such as Graphics Processing Units are very attractive solutions that greatly improve processing times. However, when the number of images to be processed is large, having a limited amount of memory is a serious problem. This can be faced by using more accelerators or using higher-capability accelerators, which implies higher costs. The separability property is a resource in hardware approaches that is frequently used to divide the two-dimensional FFT work into several one-dimensional FFTs, which can be simultaneously processed by several computing units. Then, a feasible alternative to address this problem is distributed computing through an Apache Spark cluster. However, determining the separability-property feasibility in distributed systems, when migrating from hardware implementations, is not evident. For this reason, in this paper a comparative study is presented between distributed versions of two-dimensional FFTs using the separability property to determine the suitable way to process large image sets using both Spark RRDs and DataFrame APIs.

scholarly journals Integrated photonic FFT for photonic tensor operations towards efficient and high-speed neural networks

Nanophotonics ◽  
2020 ◽  
Vol 9 (13) ◽  
pp. 4097-4108 ◽  
Author(s):  
Moustafa Ahmed ◽  
Yas Al-Hadeethi ◽  
Ahmed Bakry ◽  
Hamed Dalir ◽  
Volker J. Sorger
Keyword(s):  
Neural Networks ◽  
Graphics Processing Units ◽  
High Speed ◽  
Fourier Transforms ◽  
Optoelectronic Device ◽  
Small Sample ◽  
Sample Number ◽  
Chip Area ◽  
Domain Specific ◽  
Graphics Processing

AbstractThe technologically-relevant task of feature extraction from data performed in deep-learning systems is routinely accomplished as repeated fast Fourier transforms (FFT) electronically in prevalent domain-specific architectures such as in graphics processing units (GPU). However, electronics systems are limited with respect to power dissipation and delay, due to wire-charging challenges related to interconnect capacitance. Here we present a silicon photonics-based architecture for convolutional neural networks that harnesses the phase property of light to perform FFTs efficiently by executing the convolution as a multiplication in the Fourier-domain. The algorithmic executing time is determined by the time-of-flight of the signal through this photonic reconfigurable passive FFT ‘filter’ circuit and is on the order of 10’s of picosecond short. A sensitivity analysis shows that this optical processor must be thermally phase stabilized corresponding to a few degrees. Furthermore, we find that for a small sample number, the obtainable number of convolutions per {time, power, and chip area) outperforms GPUs by about two orders of magnitude. Lastly, we show that, conceptually, the optical FFT and convolution-processing performance is indeed directly linked to optoelectronic device-level, and improvements in plasmonics, metamaterials or nanophotonics are fueling next generation densely interconnected intelligent photonic circuits with relevance for edge-computing 5G networks by processing tensor operations optically.

scholarly journals Computation of Galois field expressions for quaternary logic functions on GPUs

2014 ◽  
Vol 11 (1) ◽  
pp. 97-109
Author(s):  
Dusan Gajic
Keyword(s):  
Graphics Processing Units ◽  
Digital Signal ◽  
Galois Field ◽  
Limiting Factor ◽  
Central Processing ◽  
Processing Times ◽  
Spectral Interpretation ◽  
Problem Instances ◽  
Logic Functions ◽  
Graphics Processing

Galois field (GF) expressions are polynomials used as representations of multiple-valued logic (MVL) functions. For this purpose, MVL functions are considered as functions defined over a finite (Galois) field of order p - GF(p). The problem of computing these functional expressions has an important role in areas such as digital signal processing and logic design. Time needed for computing GF-expressions increases exponentially with the number of variables in MVL functions and, as a result, it often represents a limiting factor in applications. This paper proposes a method for an accelerated computation of GF(4)-expressions for quaternary (four-valued) logic functions using graphics processing units (GPUs). The method is based on the spectral interpretation of GF-expressions, permitting the use of fast Fourier transform (FFT)-like algorithms for their computation. These algorithms are then adapted for highly parallel processing on GPUs. The performance of the proposed solutions is compared with referent C/C++ implementations of the same algorithms processed on central processing units (CPUs). Experimental results confirm that the presented approach leads to significant reduction in processing times (up to 10.86 times when compared to CPU processing). Therefore, the proposed approach widens the set of problem instances which can be efficiently handled in practice.

Massively parallel two-dimensional TLM algorithm on graphics processing units

2008 ◽  
Author(s):  
Filippo V. Rossi ◽  
Poman P.M. So ◽  
Nikolaus Fichtner ◽  
Peter Russer
Keyword(s):  
Graphics Processing Units ◽  
Massively Parallel ◽  
Two Dimensional ◽  
Graphics Processing

One-dimensional and two-dimensional generalised discrete fourier transforms

1976 ◽  
Vol 24 (1) ◽  
pp. 97-99 ◽  
Author(s):  
G. Bongiovanni ◽  
P. Corsini ◽  
G. Frosini
Keyword(s):  
Fourier Transforms ◽  
Two Dimensional ◽  
Discrete Fourier Transforms ◽  
One Dimensional

A one-dimensional self-gravitating stellar gas

1966 ◽  
Vol 25 ◽  
pp. 46-48 ◽  
Author(s):  
M. Lecar
Keyword(s):  
Gravitational Field ◽  
Phase Space ◽  
Motion Picture ◽  
Space Distribution ◽  
Two Dimensional ◽  
One Dimensional ◽  
Phase Space Distribution ◽  
Dimensional Phase Space ◽  
The Mean

“Dynamical mixing”, i.e. relaxation of a stellar phase space distribution through interaction with the mean gravitational field, is numerically investigated for a one-dimensional self-gravitating stellar gas. Qualitative results are presented in the form of a motion picture of the flow of phase points (representing homogeneous slabs of stars) in two-dimensional phase space.

High performance computing on graphics processing units

2008 ◽  
Vol 3 (2) ◽  
pp. 27-34 ◽  
Author(s):  
Balázs Tukora ◽  
Tibor Szalay
Keyword(s):  
High Performance Computing ◽  
Graphics Processing Units ◽  
High Performance ◽  
Graphics Processing ◽  
Performance Computing

COMPARISON OF TWO-DIMENSIONAL-ONE-DIMENSIONAL COUPLING METHODS FOR TIME-HARMONIC ELASTICITY

2014 ◽  
Vol 12 (6) ◽  
pp. 485-506 ◽  
Author(s):  
Yoav Ofir ◽  
Daniel Rabinovich ◽  
Dan Givoli
Keyword(s):  
Two Dimensional ◽  
One Dimensional ◽  
Coupling Methods ◽  
Time Harmonic ◽  
Dimensional Coupling
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