Single-pixel imaging with deterministic complex-valued sensing matrices

M. Zhao; J. Liu; S. Chen; C. Kang; W. Xu

doi:10.2971/jeos.2015.15041

Journal of the European Optical Society - Rapid publications, Vol 10 (2015)

Single-pixel imaging with deterministic complex-valued sensing matrices

M. Zhao, J. Liu, S. Chen, C. Kang, W. Xu

Abstract

In this paper, complex deterministic sensing matrices are explored to sample the signals in the single pixel imaging (SPI). A new analysissynthesis scheme is proposed to realize the complex deterministic sensing matrix for the DMD-based SPI. The analysis process divides the complex sensing matrix into real sensing matrix and imaginary sensing matrix, and multiple imaging is performed with these sensing matrices. After synthesizing the real and imaginary measurements, the final image of complex deterministic sensing matrix is reconstructed. The performance of deterministic sensing matrix is investigated through simulation and experiment. Compared with the random sensing matrix, the deterministic sensing matrix gives more favorable reconstructed images.

Full Text: PDF

Citation Details

Cite this article

References

B. Sun, S. S. Welsh, M. P. Edgar, J. H. Shapiro, and M. J. Padgett, ”Normalized ghost imaging,” Opt. Express 20(15), 16892–16901 (2012).

B. Sun, M. P. Edgar, R. Bowman, L. E. Vittert, S. Welsh, A. Bowman, and M. J. Padgett, ”3D Computational Imaging with Single-Pixel Detectors,” Science 340, 844–847 (2013).

M. F. Duarte, M. A. Dav M. F. Duarte, M. A. Davenport, D. Takhar, J. N. Laska, T. Sun, et al., ”Single-pixel imaging via compressive sampling,” IEEE Signal Proc. Mag. 25(2), 83–91 (2008).

D. Takhar, J.N. Laska, M. B. Wakin, M. F. Duarte, D. Baron, S. Sarvotham, K. F. Kelly, R. G. Baraniuk, ”A New Compressive Imaging Camera Architecture using Optical-Domain Compression,” Proc. SPIE 6065, 606509 (2006).

M. M. Mohades, A. Mohades, and A. Tadaion, ”A Reed-Solomon Code Based Measurement Matrix with Small Coherence,” IEEE Signal Proc. Let. 21(7), 839–843 (2014).

S. Li, and G. Ge, ”Deterministic Sensing Matrices Arising from Near Orthogonal Systems,” IEEE T. Inform. Theory 60(4), 2291–2302 (2014).

R. Calderbank, S. Howard, and S. Jafarpour, ”Construction of a large class of deterministic sensing matrices that satisfy a statistical isometry property,” IEEE J. Sel. Top. Signa. 4(2), 358–374 (2010).

Y. C. Elar, and G. Kutyniok, Compressed Sensing Theory and Applications (Cambridge Press, Cambridge, 2012).

R. Coifman, F. Geshwind, and Y. Meyer, ”Noiselets,” Appl. Comput. Harmon. A. 10, 27–44 (2001).

T. Tuma, and P. Hurley, ”On the incoherence of noiselet and Haar bases,” http://dsp.rice.edu/sites/dsp.rice.edu/files/cs/ noiselets.pdf).

E. Candes,and J. Romberg, ”Sparsity and Incoherence in Compressive Sampling,” Inverse Probl. 23, 969–985 (2007).

S. J. Wright, R. D. Nowak, and M. A. T. Figueiredo, ”Sparse Reconstruction by Separable Approximation,” IEEE T. Signal Proces. 57(7), 2479–2493 (2009).