Journal of Digital Contents Society (디지털콘텐츠학회 논문지)

Digital Contents Society (한국디지털콘텐츠학회)
권호 표지
DOI QR코드

DOI QR Code

Random Partial Haar Wavelet Transformation for Single Instruction Multiple Threads

단일 명령 다중 스레드 병렬 플랫폼을 위한 무작위 부분적 Haar 웨이블릿 변환

  • Park, Taejung (Dept. of Digital Media, Duksung Women's University)
  • Received : 2015.09.01
  • Accepted : 2015.10.31
  • Published : 2015.10.31
Download PDF
⟨ Previous Next ⟩

Abstract

Many researchers expect the compressive sensing and sparse recovery problem can overcome the limitation of conventional digital techniques. However, these new approaches require to solve the l1 norm optimization problems when it comes to signal reconstruction. In the signal reconstruction process, the transform computation by multiplication of a random matrix and a vector consumes considerable computing power. To address this issue, parallel processing is applied to the optimization problems. In particular, due to huge size of original signal, it is hard to store the random matrix directly in memory, which makes one need to design a procedural approach in handling the random matrix. This paper presents a new parallel algorithm to calculate random partial Haar wavelet transform based on Single Instruction Multiple Threads (SIMT) platform.

Compressive sensing 및 희소 복원 문제(sparse recovery problem)는 기존 디지털 기술의 한계를 극복할 수 있는 새로운 이론으로 많은 관심을 받고 있다. 그러나 신호 재구성에서 l1 norm 최적화 문제 해결에 많은 연산이 수행되며 따라서 병렬 처리 기법이 필요하다. 이 과정에서 무작위 행렬과 벡터 연산을 통한 변환 연산이 전체 과정 중에서 많은 부분을 차지하는데, 특히 원본 신호의 크기로 인해 이 과정에서 필요한 무작위 행렬을 메모리에 저장하기 곤란하며 계산 시 무작위 행렬의 절차적(procedural) 처리 방식이 필수적이다. 본 논문에서는 이 문제에 대한 해결책으로 단일 명령 다중 스레드(SIMT) 병렬 플랫폼 상에서 무작위 부분적 Haar 웨이블릿 변환을 절차적으로 계산할 수 있는 새로운 병렬 알고리듬을 제안한다.

Keywords

References

  1. D.L. Donoho, "Compressed sensing," IEEE Transactions on Information Theory, Vol.52, No.4, pp.1289-1306, April 2006. https://doi.org/10.1109/TIT.2006.871582
  2. Yonina C. Eldar and Gitta Kutyniok, "Compressed Sensing: Theory and Applications", 1st edition, Cambridge University Press, 2012
  3. https://developer.nvidia.com/cuda-zone
  4. T. Park, "CUDA-based Object Oriented Programming Techniques for Efficient Parallel Visualization of 3D Content", Journal of Digital Contents Society, Vol.13, No.2, pp. 169-176, 2012. https://doi.org/10.9728/dcs.2012.13.2.169
  5. P. Sen and S. Darabi, "Compressive Rendering: A Rendering Application of Compressed Sensing, " IEEE Transactions on Visualization and Computer Graphics, Vol.17, No.4, pp.487-499, April 2011. https://doi.org/10.1109/TVCG.2010.46
  6. M. Andrecut, "Fast GPU Implementation of Sparse Signal Recovery from Random Projections", http://arxiv.org/abs/0809.1833?context=q-bio
  7. E.J. Candes and M.B. Wakin, "An Introduction To Compressive Sampling," IEEE Signal Processing Magazine, Vol.25, No.2, pp.21-30, March 2008. https://doi.org/10.1109/MSP.2007.914731
  8. J. Cheng, M. Grossman, and T. McKercher, "Professional CUDA C Programming", 1st Edition, Wrox, September 2014.
  9. G. Strang, "Computational Science and Engineering", 1st Edition, Wellesley-Cambridge Press, November, 2007.
  10. C. Tenllado, J. Setoain, M. Prieto, L. Pinuel, F. Tirado, "Parallel Implementation of the 2D Discrete Wavelet Transform on Graphics Processing Units: Filter Bank versus Lifting," IEEE Transactions on Parallel and Distributed Systems, Vol.19, No.3, pp.299-310, March 2008. https://doi.org/10.1109/TPDS.2007.70716
  11. http://developer.download.nvidia.com/compute/cuda/1.1-Beta/x86_website/projects/reduction/doc/reduction.pdf
  12. https://www.jasondavies.com/poisson-disc/
  13. http://www.mathworks.com/matlabcentral/fileexchange/4619-haarmtx