High performance non-uniform FFT on modern X86-based multi-core systems

Dhiraj D. Kalamkar, Joshua D. Trzaskoz, Srinivas Sridharan, Mikhail Smelyanskiy, Daehyun Kim, Armando Manduca, Yunhong Shu, Matthew A Bernstein, Bharat Kaul, Pradeep Dubey

Research output: Chapter in Book/Report/Conference proceedingConference contribution

5 Citations (Scopus)

Abstract

The Non-Uniform Fast Fourier Transform (NUFFT) is a generalization of FFT to non-equidistant samples. It has many applications which vary from medical imaging to radio astronomy to the numerical solution of partial differential equations. Despite recent advances in speeding up NUFFT on various platforms, its practical applications are still limited, due to its high computational cost, which is significantly dominated by the convolution of a signal between a non-uniform and uniform grids. The computational cost of the NUFFT is particularly detrimental in cases which require fast reconstruction times, such as iterative 3D non-Cartesian MRI reconstruction. We propose novel and highly scalable parallel algorithm for performing NUFFT on x86-based multi-core CPUs. The high performance of our algorithm relies on good SIMD utilization and high parallel efficiency. On convolution, we demonstrate on average 90% SIMD efficiency using SSE, as well up to linear scalability using a quad-socket 40-core Intel® Xeon® E7-4870 Processors based system. As a result, on dual socket Intel® Xeon® X5670 based server, our NUFFT implementation is more than 4x faster compared to the best available NUFFT3D implementation, when run on the same hardware. On Intel® Xeon® E5-2670 processor based server, our NUFFT implementation is 1.5X faster than any published NUFFT implementation today. Such speed improvement opens new usages for NUFFT. For example, iterative multi channel reconstruction of a 240x240x240 image could execute in just over 3 minutes, which is on the same order as contemporary non-iterative (and thus less-accurate) 3D NUFFT-based MRI reconstructions.

Original languageEnglish (US)
Title of host publicationProceedings of the 2012 IEEE 26th International Parallel and Distributed Processing Symposium, IPDPS 2012
Pages449-460
Number of pages12
DOIs
StatePublished - 2012
Event2012 IEEE 26th International Parallel and Distributed Processing Symposium, IPDPS 2012 - Shanghai, China
Duration: May 21 2012May 25 2012

Other

Other2012 IEEE 26th International Parallel and Distributed Processing Symposium, IPDPS 2012
CountryChina
CityShanghai
Period5/21/125/25/12

Fingerprint

Fast Fourier transforms
Convolution
Magnetic resonance imaging
Servers
Radio astronomy
Medical imaging
Parallel algorithms
Computer hardware
Partial differential equations
Program processors
Scalability
Costs

Keywords

  • Non-uniform FFT
  • Parallelization
  • Scalability
  • Vectorization

ASJC Scopus subject areas

  • Software

Cite this

Kalamkar, D. D., Trzaskoz, J. D., Sridharan, S., Smelyanskiy, M., Kim, D., Manduca, A., ... Dubey, P. (2012). High performance non-uniform FFT on modern X86-based multi-core systems. In Proceedings of the 2012 IEEE 26th International Parallel and Distributed Processing Symposium, IPDPS 2012 (pp. 449-460). [6267881] https://doi.org/10.1109/IPDPS.2012.49

High performance non-uniform FFT on modern X86-based multi-core systems. / Kalamkar, Dhiraj D.; Trzaskoz, Joshua D.; Sridharan, Srinivas; Smelyanskiy, Mikhail; Kim, Daehyun; Manduca, Armando; Shu, Yunhong; Bernstein, Matthew A; Kaul, Bharat; Dubey, Pradeep.

Proceedings of the 2012 IEEE 26th International Parallel and Distributed Processing Symposium, IPDPS 2012. 2012. p. 449-460 6267881.

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Kalamkar, DD, Trzaskoz, JD, Sridharan, S, Smelyanskiy, M, Kim, D, Manduca, A, Shu, Y, Bernstein, MA, Kaul, B & Dubey, P 2012, High performance non-uniform FFT on modern X86-based multi-core systems. in Proceedings of the 2012 IEEE 26th International Parallel and Distributed Processing Symposium, IPDPS 2012., 6267881, pp. 449-460, 2012 IEEE 26th International Parallel and Distributed Processing Symposium, IPDPS 2012, Shanghai, China, 5/21/12. https://doi.org/10.1109/IPDPS.2012.49
Kalamkar DD, Trzaskoz JD, Sridharan S, Smelyanskiy M, Kim D, Manduca A et al. High performance non-uniform FFT on modern X86-based multi-core systems. In Proceedings of the 2012 IEEE 26th International Parallel and Distributed Processing Symposium, IPDPS 2012. 2012. p. 449-460. 6267881 https://doi.org/10.1109/IPDPS.2012.49
Kalamkar, Dhiraj D. ; Trzaskoz, Joshua D. ; Sridharan, Srinivas ; Smelyanskiy, Mikhail ; Kim, Daehyun ; Manduca, Armando ; Shu, Yunhong ; Bernstein, Matthew A ; Kaul, Bharat ; Dubey, Pradeep. / High performance non-uniform FFT on modern X86-based multi-core systems. Proceedings of the 2012 IEEE 26th International Parallel and Distributed Processing Symposium, IPDPS 2012. 2012. pp. 449-460
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