Adaptive compressive ghost imaging based on wavelet trees and sparse representation.

Compressed sensing is a theory which can reconstruct an image almost perfectly with only a few measurements by finding its sparsest representation. However, the computation time consumed for large images may be a few hours or more. In this work, we both theoretically and experimentally demonstrate a method that combines the advantages of both adaptive computational ghost imaging and compressed sensing, which we call adaptive compressive ghost imaging, whereby both the reconstruction time and measurements required for any image size can be significantly reduced. The technique can be used to improve the performance of all computational ghost imaging protocols, especially when measuring ultra-weak or noisy signals, and can be extended to imaging applications at any wavelength.

[1]  Soheil Darabi,et al.  Compressive Dual Photography , 2009, Comput. Graph. Forum.

[2]  Manfred Bayer,et al.  Compressive adaptive computational ghost imaging , 2013, Scientific Reports.

[3]  Shen Li,et al.  High-speed secure key distribution over an optical network based on computational correlation imaging. , 2013, Optics letters.

[4]  Emmanuel J. Candès,et al.  Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information , 2004, IEEE Transactions on Information Theory.

[5]  Ling-An Wu,et al.  Correlated two-photon imaging with true thermal light. , 2005, Optics letters.

[6]  M. Fornasier,et al.  Iterative thresholding algorithms , 2008 .

[7]  Jeffrey H. Shapiro,et al.  Computational ghost imaging , 2008, 2009 Conference on Lasers and Electro-Optics and 2009 Conference on Quantum electronics and Laser Science Conference.

[8]  Ting Sun,et al.  Single-pixel imaging via compressive sampling , 2008, IEEE Signal Process. Mag..

[9]  Ling-An Wu,et al.  A double-threshold technique for fast time-correspondence imaging , 2013, 1311.3012.

[10]  Jerome M. Shapiro,et al.  Embedded image coding using zerotrees of wavelet coefficients , 1993, IEEE Trans. Signal Process..

[11]  H. J. Pain.  Interference and Diffraction , 2005 .

[12]  William A. Pearlman,et al.  A new, fast, and efficient image codec based on set partitioning in hierarchical trees , 1996, IEEE Trans. Circuits Syst. Video Technol..

[13]  D. L. Donoho,et al.  Compressed sensing , 2006, IEEE Trans. Inf. Theory.

[14]  Shen Li,et al.  Protocol based on compressed sensing for high-speed authentication and cryptographic key distribution over a multiparty optical network. , 2013, Applied optics.

[15]  Junfeng Yang,et al.  A Fast Alternating Direction Method for TVL1-L2 Signal Reconstruction From Partial Fourier Data , 2010, IEEE Journal of Selected Topics in Signal Processing.

[16]  Amir Averbuch,et al.  Adaptive Compressed Image Sensing Using Dictionaries , 2012, SIAM J. Imaging Sci..

[17]  Shih,et al.  Observation of two-photon "ghost" interference and diffraction. , 1995, Physical review letters.

[18]  Wai Lam Chan,et al.  A single-pixel terahertz imaging system based on compressed sensing , 2008 .

[19]  Michael A. Saunders,et al.  Atomic Decomposition by Basis Pursuit , 1998, SIAM J. Sci. Comput..

[20]  Jarvis Haupt,et al.  Adaptive Sensing for Sparse Signal Recovery , 2009, 2009 IEEE 13th Digital Signal Processing Workshop and 5th IEEE Signal Processing Education Workshop.

[21]  O. Katz,et al.  Compressive ghost imaging , 2009, 0905.0321.

[22]  Stéphane Mallat,et al.  A Theory for Multiresolution Signal Decomposition: The Wavelet Representation , 1989, IEEE Trans. Pattern Anal. Mach. Intell..

[23]  Chengbo Li.  An efficient algorithm for total variation regularization with applications to the single pixel camera and compressive sensing , 2010 .

[24]  Hakan Erdogan,et al.  A* orthogonal matching pursuit: Best-first search for compressed sensing signal recovery , 2010, Digit. Signal Process..

[25]  Jeffrey H. Shapiro,et al.  Unified theory of ghost imaging with Gaussian-state light , 2007, 0712.3554.

[26]  Wenlin Gong,et al.  Experimental investigation of the quality of lensless super-resolution ghost imaging via sparsity constraints , 2012 .

[27]  A. Gatti,et al.  Ghost imaging with thermal light: comparing entanglement and classical correlation. , 2004, Physical review letters.

[28]  E. Candès,et al.  Compressive fluorescence microscopy for biological and hyperspectral imaging , 2012, Proceedings of the National Academy of Sciences.

[29]  Piotr Indyk,et al.  Sequential Sparse Matching Pursuit , 2009, 2009 47th Annual Allerton Conference on Communication, Control, and Computing (Allerton).

[30]  O. Katz,et al.  Ghost imaging with a single detector , 2008, 0812.2633.

[31]  Martin Vetterli,et al.  Adaptive wavelet thresholding for image denoising and compression , 2000, IEEE Trans. Image Process..