Abstract

We implemented the graphics processing unit (GPU) accelerated compressive sensing (CS) non-uniform in k-space spectral domain optical coherence tomography (SD OCT). Kaiser-Bessel (KB) function and Gaussian function are used independently as the convolution kernel in the gridding-based non-uniform fast Fourier transform (NUFFT) algorithm with different oversampling ratios and kernel widths. Our implementation is compared with the GPU-accelerated modified non-uniform discrete Fourier transform (MNUDFT) matrix-based CS SD OCT and the GPU-accelerated fast Fourier transform (FFT)-based CS SD OCT. It was found that our implementation has comparable performance to the GPU-accelerated MNUDFT-based CS SD OCT in terms of image quality while providing more than 5 times speed enhancement. When compared to the GPU-accelerated FFT based-CS SD OCT, it shows smaller background noise and less side lobes while eliminating the need for the cumbersome k-space grid filling and the k-linear calibration procedure. Finally, we demonstrated that by using a conventional desktop computer architecture having three GPUs, real-time B-mode imaging can be obtained in excess of 30 fps for the GPU-accelerated NUFFT based CS SD OCT with frame size 2048(axial)×1000(lateral).

© 2014 Optical Society of America

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References

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    [Crossref]
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    [Crossref]
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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    [Crossref]
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    [Crossref]
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    [Crossref] [PubMed]
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    [Crossref]
  16. K. Zhang and J. U. Kang, “Real-time 4D signal processing and visualization using graphics processing unit on a regular nonlinear-k-Fourier-domain OCT system,” Opt. Express 18(11), 11772–11784 (2010).
    [Crossref] [PubMed]
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    [Crossref]
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    [Crossref] [PubMed]
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    [Crossref]
  22. D. Xu, Y. Hunag, and J. U. Kang, “Real-time compressive sensing spectral domain optical coherence tomography,” Opt. Lett. 39(1), 76–79 (2014).
    [Crossref]
  23. S. Vergnole, D. Levesque, and G. Lamouche, “Experimental validation of an optimized signal processing method to handle non-linearity in swept-source optical coherence tomography,” Opt. Express 18(10) 10446–10461 (2010).
    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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    [Crossref]
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    [Crossref]
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  30. “NVIDIA Visual Profiler version 5.5,” (2013).
  31. “NVIDIA CUDA CUFFT library version 5.5,” (2013).
  32. T. Schmoll, C. Kollbitsch, and R. A. Leitgerb, “Ultra-high-speed volumetric tomography of human retinal blood flow,” Opt. Express 17(5), 4166–4176 (2009).
    [Crossref] [PubMed]
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    [Crossref]

2014 (1)

2013 (2)

2012 (6)

2011 (1)

2010 (6)

2009 (5)

T. Schmoll, C. Kollbitsch, and R. A. Leitgerb, “Ultra-high-speed volumetric tomography of human retinal blood flow,” Opt. Express 17(5), 4166–4176 (2009).
[Crossref] [PubMed]

S. J. Wright, R. Nowak, and M. Figueiredo, “Sparse reconstruction by separable approximation,” IEEE Trans. Signal Processing 572479–2493 (2009).
[Crossref]

D. Hillmann, G. Huttmann, and P Koch, “Using nonequispaced fast Fourier transformation to process optical coherence tomography signals,” Proc. SPIE 737273720R (2009).
[Crossref]

Y. Watanabe and T. Itagaki, “Real-time display on Fourier domain optical coherence tomography system using a graphics processing unit,” J. Biomed. Opt. 14(6), 060506 (2009).
[Crossref]

K. Wang, Z. Ding, T. Wu, C. Wang, J. Meng, M. Chen, and L. Xu, “Development of a non-uniform discrete Fourier transform based high speed spectral domain optical coherence tomography system,” Opt. Express 17(4) 12121–12131 (2009).
[Crossref] [PubMed]

2007 (1)

M. Lustig, D. Donoho, and J. M. Pauly, “Saprse MRI: the application of compressed sensing for rapid MR imaging,” Magn. Reson, Med. 58(6), 1182–1195 (2007).
[Crossref]

2006 (2)

D. L. Donoho, “Compressed sensing,” IEEE Trans. Inf. Theory 52(4), 1289–1306 (2006).
[Crossref]

E. J. Candes, J. Romberg, and T. Tao, “Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information,” Inf. Theory 52(2), 489–509 (2006).
[Crossref]

2005 (1)

P. J. Beatty, D. G. Nishimura, and J. M. Pauly, “Rapid gridding reconstruction with a minimal over-sampling ratio,” IEEE Trans. Med. Imaging 24(6), 799–808 (2005).
[Crossref] [PubMed]

2004 (1)

L. Greengard and J. Lee, “Accelerating the nonuniform fast Fourier transform,” SIAM Rev. 46(3), 443–454 (2004).
[Crossref]

1988 (1)

J. Barzilai and J. M. Borwein, “Two-point step size gradient methods,” IMA J. Numer. Anal. 8, 141–148 (1988).
[Crossref]

Alley, M.

M. Murphy, M. Alley, J. Demmel, K. Keutzer, S. Vasanawala, and M. Lustig, “Fast l1-SPIRiT compressed sensing parallel imaging MRI: scalable parallel implementation and clinically feasible runtime,” IEEE Trans. Med. Imaging 31(6), 1250–1262 (2012).
[Crossref] [PubMed]

Barzilai, J.

J. Barzilai and J. M. Borwein, “Two-point step size gradient methods,” IMA J. Numer. Anal. 8, 141–148 (1988).
[Crossref]

Beatty, P. J.

P. J. Beatty, D. G. Nishimura, and J. M. Pauly, “Rapid gridding reconstruction with a minimal over-sampling ratio,” IEEE Trans. Med. Imaging 24(6), 799–808 (2005).
[Crossref] [PubMed]

Bie, H.

Bizheva, K.

Borwein, J. M.

J. Barzilai and J. M. Borwein, “Two-point step size gradient methods,” IMA J. Numer. Anal. 8, 141–148 (1988).
[Crossref]

Bradu, A.

S. Van der Jeught, A. Bradu, and A. G. Podoleanu, “Real-time resampling in Fourier domain optical coherence tomography using a graphics processing unit,” J. Biomed. Opt. 15(3), 030511 (2010).
[Crossref] [PubMed]

Candes, E. J.

E. J. Candes, J. Romberg, and T. Tao, “Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information,” Inf. Theory 52(2), 489–509 (2006).
[Crossref]

Chan, K. K. H.

K. K. H. Chan and S. Tang, “Selection of convolution kernel in non-uniform fast Fourier transform for Fourier domain optical coherence tomography,” Opt. Express 19(27), 26891–26904 (2011).
[Crossref]

K. K. H. Chan and S. Tang, “High-speed spectral domain optical coherence tomography using non-uniform fast Fourier transform,” Biomed. Opt. Express 1(5), 1308–1319 (2010).
[Crossref]

Chen, M.

Chen, T.

Clausi, D. A.

Demmel, J.

M. Murphy, M. Alley, J. Demmel, K. Keutzer, S. Vasanawala, and M. Lustig, “Fast l1-SPIRiT compressed sensing parallel imaging MRI: scalable parallel implementation and clinically feasible runtime,” IEEE Trans. Med. Imaging 31(6), 1250–1262 (2012).
[Crossref] [PubMed]

Ding, Z.

Donoho, D.

M. Lustig, D. Donoho, and J. M. Pauly, “Saprse MRI: the application of compressed sensing for rapid MR imaging,” Magn. Reson, Med. 58(6), 1182–1195 (2007).
[Crossref]

Donoho, D. L.

D. L. Donoho, “Compressed sensing,” IEEE Trans. Inf. Theory 52(4), 1289–1306 (2006).
[Crossref]

Fang, L.

Farsiu, S.

Fieguth, P.

Figueiredo, M.

S. J. Wright, R. Nowak, and M. Figueiredo, “Sparse reconstruction by separable approximation,” IEEE Trans. Signal Processing 572479–2493 (2009).
[Crossref]

Greengard, L.

L. Greengard and J. Lee, “Accelerating the nonuniform fast Fourier transform,” SIAM Rev. 46(3), 443–454 (2004).
[Crossref]

Harris, M.

M. Harris, “Optimizing parallel reduction in CUDA,” NVIDIA Dev. Tech (2007).

Hillmann, D.

D. Hillmann, G. Huttmann, and P Koch, “Using nonequispaced fast Fourier transformation to process optical coherence tomography signals,” Proc. SPIE 737273720R (2009).
[Crossref]

Huang, Y.

Hunag, Y.

Huo, T.

Huttmann, G.

D. Hillmann, G. Huttmann, and P Koch, “Using nonequispaced fast Fourier transformation to process optical coherence tomography signals,” Proc. SPIE 737273720R (2009).
[Crossref]

Itagaki, T.

Y. Watanabe and T. Itagaki, “Real-time display on Fourier domain optical coherence tomography system using a graphics processing unit,” J. Biomed. Opt. 14(6), 060506 (2009).
[Crossref]

Izatt, J. A.

Kang, J. U.

Keutzer, K.

M. Murphy, M. Alley, J. Demmel, K. Keutzer, S. Vasanawala, and M. Lustig, “Fast l1-SPIRiT compressed sensing parallel imaging MRI: scalable parallel implementation and clinically feasible runtime,” IEEE Trans. Med. Imaging 31(6), 1250–1262 (2012).
[Crossref] [PubMed]

Koch, P

D. Hillmann, G. Huttmann, and P Koch, “Using nonequispaced fast Fourier transformation to process optical coherence tomography signals,” Proc. SPIE 737273720R (2009).
[Crossref]

Kollbitsch, C.

Lamouche, G.

Lee, J.

L. Greengard and J. Lee, “Accelerating the nonuniform fast Fourier transform,” SIAM Rev. 46(3), 443–454 (2004).
[Crossref]

Lee, S.

S. Lee and S. J. Wright, “Implementing algorithms for signal and image reconstruction on graphical processing units,” Technical Report, University of Wisconsin-Madison (2008).

Leitgerb, R. A.

Levesque, D.

Li, H.

D. Yang, G. D. Peterson, and H. Li, “Compressed sensing and Cholesky decomposition on FPGAs and GPUs,” Parallel Comput. 38(8), 421–437 (2012).
[Crossref]

Li, S.

Liu, C.

Liu, X.

Lustig, M.

M. Murphy, M. Alley, J. Demmel, K. Keutzer, S. Vasanawala, and M. Lustig, “Fast l1-SPIRiT compressed sensing parallel imaging MRI: scalable parallel implementation and clinically feasible runtime,” IEEE Trans. Med. Imaging 31(6), 1250–1262 (2012).
[Crossref] [PubMed]

M. Lustig, D. Donoho, and J. M. Pauly, “Saprse MRI: the application of compressed sensing for rapid MR imaging,” Magn. Reson, Med. 58(6), 1182–1195 (2007).
[Crossref]

Meng, J.

Murphy, M.

M. Murphy, M. Alley, J. Demmel, K. Keutzer, S. Vasanawala, and M. Lustig, “Fast l1-SPIRiT compressed sensing parallel imaging MRI: scalable parallel implementation and clinically feasible runtime,” IEEE Trans. Med. Imaging 31(6), 1250–1262 (2012).
[Crossref] [PubMed]

Nie, Q.

Nishimura, D. G.

P. J. Beatty, D. G. Nishimura, and J. M. Pauly, “Rapid gridding reconstruction with a minimal over-sampling ratio,” IEEE Trans. Med. Imaging 24(6), 799–808 (2005).
[Crossref] [PubMed]

Nowak, R.

S. J. Wright, R. Nowak, and M. Figueiredo, “Sparse reconstruction by separable approximation,” IEEE Trans. Signal Processing 572479–2493 (2009).
[Crossref]

Pauly, J. M.

M. Lustig, D. Donoho, and J. M. Pauly, “Saprse MRI: the application of compressed sensing for rapid MR imaging,” Magn. Reson, Med. 58(6), 1182–1195 (2007).
[Crossref]

P. J. Beatty, D. G. Nishimura, and J. M. Pauly, “Rapid gridding reconstruction with a minimal over-sampling ratio,” IEEE Trans. Med. Imaging 24(6), 799–808 (2005).
[Crossref] [PubMed]

Peterson, G. D.

D. Yang, G. D. Peterson, and H. Li, “Compressed sensing and Cholesky decomposition on FPGAs and GPUs,” Parallel Comput. 38(8), 421–437 (2012).
[Crossref]

Podoleanu, A. G.

S. Van der Jeught, A. Bradu, and A. G. Podoleanu, “Real-time resampling in Fourier domain optical coherence tomography using a graphics processing unit,” J. Biomed. Opt. 15(3), 030511 (2010).
[Crossref] [PubMed]

Romberg, J.

E. J. Candes, J. Romberg, and T. Tao, “Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information,” Inf. Theory 52(2), 489–509 (2006).
[Crossref]

Schmoll, T.

Schwartz, S.

Tang, S.

K. K. H. Chan and S. Tang, “Selection of convolution kernel in non-uniform fast Fourier transform for Fourier domain optical coherence tomography,” Opt. Express 19(27), 26891–26904 (2011).
[Crossref]

K. K. H. Chan and S. Tang, “High-speed spectral domain optical coherence tomography using non-uniform fast Fourier transform,” Biomed. Opt. Express 1(5), 1308–1319 (2010).
[Crossref]

Tao, T.

E. J. Candes, J. Romberg, and T. Tao, “Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information,” Inf. Theory 52(2), 489–509 (2006).
[Crossref]

Toth, C. A.

Van der Jeught, S.

S. Van der Jeught, A. Bradu, and A. G. Podoleanu, “Real-time resampling in Fourier domain optical coherence tomography using a graphics processing unit,” J. Biomed. Opt. 15(3), 030511 (2010).
[Crossref] [PubMed]

Vasanawala, S.

M. Murphy, M. Alley, J. Demmel, K. Keutzer, S. Vasanawala, and M. Lustig, “Fast l1-SPIRiT compressed sensing parallel imaging MRI: scalable parallel implementation and clinically feasible runtime,” IEEE Trans. Med. Imaging 31(6), 1250–1262 (2012).
[Crossref] [PubMed]

Vaswani, N.

Vergnole, S.

Wang, C.

Wang, K.

Watanabe, Y.

Y. Watanabe and T. Itagaki, “Real-time display on Fourier domain optical coherence tomography system using a graphics processing unit,” J. Biomed. Opt. 14(6), 060506 (2009).
[Crossref]

Wong, A.

Wright, S. J.

S. J. Wright, R. Nowak, and M. Figueiredo, “Sparse reconstruction by separable approximation,” IEEE Trans. Signal Processing 572479–2493 (2009).
[Crossref]

S. Lee and S. J. Wright, “Implementing algorithms for signal and image reconstruction on graphical processing units,” Technical Report, University of Wisconsin-Madison (2008).

Wu, T.

Xu, D.

Xu, L.

Xue, P.

Yang, D.

D. Yang, G. D. Peterson, and H. Li, “Compressed sensing and Cholesky decomposition on FPGAs and GPUs,” Parallel Comput. 38(8), 421–437 (2012).
[Crossref]

Zhang, K.

Zhang, N.

Zheng, J.

Biomed. Opt. Express (3)

IEEE Trans. Inf. Theory (1)

D. L. Donoho, “Compressed sensing,” IEEE Trans. Inf. Theory 52(4), 1289–1306 (2006).
[Crossref]

IEEE Trans. Med. Imaging (2)

M. Murphy, M. Alley, J. Demmel, K. Keutzer, S. Vasanawala, and M. Lustig, “Fast l1-SPIRiT compressed sensing parallel imaging MRI: scalable parallel implementation and clinically feasible runtime,” IEEE Trans. Med. Imaging 31(6), 1250–1262 (2012).
[Crossref] [PubMed]

P. J. Beatty, D. G. Nishimura, and J. M. Pauly, “Rapid gridding reconstruction with a minimal over-sampling ratio,” IEEE Trans. Med. Imaging 24(6), 799–808 (2005).
[Crossref] [PubMed]

IEEE Trans. Signal Processing (1)

S. J. Wright, R. Nowak, and M. Figueiredo, “Sparse reconstruction by separable approximation,” IEEE Trans. Signal Processing 572479–2493 (2009).
[Crossref]

IMA J. Numer. Anal. (1)

J. Barzilai and J. M. Borwein, “Two-point step size gradient methods,” IMA J. Numer. Anal. 8, 141–148 (1988).
[Crossref]

Inf. Theory (1)

E. J. Candes, J. Romberg, and T. Tao, “Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information,” Inf. Theory 52(2), 489–509 (2006).
[Crossref]

J. Biomed. Opt. (2)

Y. Watanabe and T. Itagaki, “Real-time display on Fourier domain optical coherence tomography system using a graphics processing unit,” J. Biomed. Opt. 14(6), 060506 (2009).
[Crossref]

S. Van der Jeught, A. Bradu, and A. G. Podoleanu, “Real-time resampling in Fourier domain optical coherence tomography using a graphics processing unit,” J. Biomed. Opt. 15(3), 030511 (2010).
[Crossref] [PubMed]

Magn. Reson, Med. (1)

M. Lustig, D. Donoho, and J. M. Pauly, “Saprse MRI: the application of compressed sensing for rapid MR imaging,” Magn. Reson, Med. 58(6), 1182–1195 (2007).
[Crossref]

Opt. Express (9)

T. Schmoll, C. Kollbitsch, and R. A. Leitgerb, “Ultra-high-speed volumetric tomography of human retinal blood flow,” Opt. Express 17(5), 4166–4176 (2009).
[Crossref] [PubMed]

S. Vergnole, D. Levesque, and G. Lamouche, “Experimental validation of an optimized signal processing method to handle non-linearity in swept-source optical coherence tomography,” Opt. Express 18(10) 10446–10461 (2010).
[Crossref] [PubMed]

S. Schwartz, C. Liu, A. Wong, D. A. Clausi, P. Fieguth, and K. Bizheva, “Energy-guided learning approach to compressive sensing,” Opt. Express 21(1), 329–344 (2013).
[Crossref] [PubMed]

C. Liu, A. Wong, K. Bizheva, P. Fieguth, and H. Bie, “Homotopic, non-local sparse reconstruction of optical coherence tomography imagery,” Opt. Express 20(9), 10200–10211 (2012).
[Crossref] [PubMed]

K. Zhang and J. U. Kang, “Graphics processing unit accelerated non-uniform fast Fourier transform for ultrahigh-speed, real-time Fourier-domain OCT,” Opt. Express 18(22), 23472–23487 (2010).
[Crossref] [PubMed]

K. K. H. Chan and S. Tang, “Selection of convolution kernel in non-uniform fast Fourier transform for Fourier domain optical coherence tomography,” Opt. Express 19(27), 26891–26904 (2011).
[Crossref]

K. Zhang and J. U. Kang, “Real-time 4D signal processing and visualization using graphics processing unit on a regular nonlinear-k-Fourier-domain OCT system,” Opt. Express 18(11), 11772–11784 (2010).
[Crossref] [PubMed]

X. Liu and J. U. Kang, “Compressive SD-OCT: the application of compressed sensing in spectral domain optical coherence tomography,” Opt. Express 18(21), 22010–22019 (2010).
[Crossref] [PubMed]

K. Wang, Z. Ding, T. Wu, C. Wang, J. Meng, M. Chen, and L. Xu, “Development of a non-uniform discrete Fourier transform based high speed spectral domain optical coherence tomography system,” Opt. Express 17(4) 12121–12131 (2009).
[Crossref] [PubMed]

Opt. Lett. (3)

Parallel Comput. (1)

D. Yang, G. D. Peterson, and H. Li, “Compressed sensing and Cholesky decomposition on FPGAs and GPUs,” Parallel Comput. 38(8), 421–437 (2012).
[Crossref]

Proc. SPIE (1)

D. Hillmann, G. Huttmann, and P Koch, “Using nonequispaced fast Fourier transformation to process optical coherence tomography signals,” Proc. SPIE 737273720R (2009).
[Crossref]

SIAM Rev. (1)

L. Greengard and J. Lee, “Accelerating the nonuniform fast Fourier transform,” SIAM Rev. 46(3), 443–454 (2004).
[Crossref]

Other (7)

S. Lee and S. J. Wright, “Implementing algorithms for signal and image reconstruction on graphical processing units,” Technical Report, University of Wisconsin-Madison (2008).

“NVIDIA CUDA C programming guide version 5.5,” (2013).

American National Standards Institute, American National Standart for Safe Use of Lasers Z136.1. (2007).

“NVIDIA CUDA CUBLAS library version 5.5,” (2013).

M. Harris, “Optimizing parallel reduction in CUDA,” NVIDIA Dev. Tech (2007).

“NVIDIA Visual Profiler version 5.5,” (2013).

“NVIDIA CUDA CUFFT library version 5.5,” (2013).

Supplementary Material (2)

» Media 1: MOV (1560 KB)     
» Media 2: MOV (1883 KB)     

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Figures (3)

Fig. 1
Fig. 1 Sparsity comparison of A-scans by applying (a) NUDFT, (b) MNUDFT, (c) type-1 NUFFT to the full-length nonlinear wavenumber spectral data, and (d) FFT to the full-length linear wavenumber spectral data.
Fig. 2
Fig. 2 Sensitivity roll-off of different processing methods: (a) NUDFT on 100% data; (b) FFT-CS; (c) MNUDFT-CS; (d) NUFFT-CS with Gaussian kernel (R=2, W=5); (e) NUFFT-CS with KB kernel (R=2, W=5); (f) NUFFT-CS with KB kernel (R=1.5, W=3). (g) comparison of PSFs at a certain image depth using different processing methods; (h) maximum amplitude of PSFs using different processing methods; (i) SNR versus image depth for different processing methods.
Fig. 3
Fig. 3 B-scans of an orange: (a) original image; (b) NUFFT-CS reconstruction result (see Media 1 for real-time imaging display), and human skin: (c) original image; (d) NUFFT-CS reconstruction result (see Media 2 for real-time imaging display). The scale bars represent 100 μm. The image size is 900(axial)×950(lateral).

Tables (2)

Tables Icon

Table 1 Computation procedure of SpaRSA for a B-scan on one GPU

Tables Icon

Table 1 Computation time (μs) for an A-scan

Equations (14)

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minimize x 1 2 F u x y u 2 2 + τ Φ x 1
[ h ( 0 , 0 ) h ( 0 , N / 2 1 ) h ( 0 , N / 2 ) h ( 0 , N / 2 1 ) * h ( 0 , 1 ) * h ( N 1 , 0 ) h ( N 1 , N / 2 1 ) h ( N 1 / N / 2 ) h ( N 1 , N / 2 1 ) * h ( N 1 , 1 ) * ]
F r ( k ^ i ) = n F ( k n ) G ( k ^ i k n ) , i = 0 , , M r 1
f ˜ r ( x m ) = f r ( x m ) / g ( x m ) , m = 0 , , M r 1
F ( k n ) = i F r ( k ^ i ) G ( k n k ^ i ) , n = 0 , , N 1
G ( κ ) = exp ( κ 2 4 θ )
g ( x m ) = 2 θ exp ( x m 2 θ )
θ = 1 N 2 π R ( R 0.5 ) W 2
G ( κ ) = I 0 ( β 1 ( 2 κ / W ) 2 ) / W
g ( x m ) = sin ( ( m π W / M r ) 2 β 2 ) ( m π W / M r ) 2 β 2
β = π W 2 R 2 ( R 0.5 ) 2 0.8
x p + 1 = min z 1 2 z u p 2 2 + τ α p z 1
x i p + 1 = min z i 1 2 ( z i u i p ) 2 + τ α p | z i | = soft ( u i p , τ α p )
α p = F u s p 2 2 / s p 2 2

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