Sparse image measurement with an optical single-pixel detector using various schemes of image sampling

We present the theoretical and experimental results of computational ghost imaging using compressive sensing. Our particular interest lies in imaging medical structures in depth of the tissue, compressible in either wavelet or Fourier domain. The measurement is based on a sequence of images from a bucket detector. We establish the optimal measurement and reconstruction basis in order to obtain the best quality of the image reconstruction with possibly few measurements. We consider several schemes of image sampling based on orthonormal basis incoherent either with the Fourier basis or with Daubechies wavelet sets, such as orthonormalised Gaussian random matrices, Hadamard matrices and noiselet matrices. Eventually, the optimal sampling scheme has been introduced into the experimental single-pixel camera set-up for imaging in the visible wavelength range.

[1]  C. Bachoc,et al.  Applied and Computational Harmonic Analysis Tight P-fusion Frames , 2022 .

[2]  E. Candès,et al.  Sparsity and incoherence in compressive sampling , 2006, math/0611957.

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

[4]  Bahram Javidi,et al.  Overview of compressive sensing techniques applied in holography [Invited]. , 2013, Applied optics.

[5]  J. Shapiro,et al.  Computational ghost imaging versus imaging laser radar for three-dimensional imaging , 2012, 1212.3253.

[6]  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.

[7]  J. Shapiro,et al.  Normalized ghost imaging , 2012, 1212.5041.

[8]  David R. Smith,et al.  Terahertz compressive imaging with metamaterial spatial light modulators , 2014, Nature Photonics.

[9]  Yonina C Eldar,et al.  Super-resolution and reconstruction of sparse sub-wavelength images. , 2009, Optics express.

[10]  Mark R. Freeman,et al.  3D Computational Imaging with Single-Pixel Detectors , 2013 .

[11]  Leonid P. Yaroslavsky.  Is "Compressed Sensing" compressive? Can it beat the Nyquist Sampling Approach? , 2015, ArXiv.

[12]  Jeffrey H. Shapiro,et al.  Ghost imaging: from quantum to classical to computational , 2009 .

[13]  Vicente Durán,et al.  Compressive holography with a single-pixel detector. , 2013, Optics letters.

[14]  慧 廣瀬.  A Mathematical Introduction to Compressive Sensing , 2015 .

[15]  Bahram Javidi,et al.  An overview of compressive sensing techniques applied in holography , 2013 .

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

[17]  Holger Rauhut,et al.  A Mathematical Introduction to Compressive Sensing , 2013, Applied and Numerical Harmonic Analysis.

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

[19]  Adrian Stern,et al.  Quantization error and dynamic range considerations for compressive imaging systems design. , 2013, Journal of the Optical Society of America. A, Optics, image science, and vision.

[20]  Chi Zhang,et al.  Object reconstitution using pseudo-inverse for ghost imaging. , 2014, Optics express.

[21]  Yuan Zhao,et al.  Distance measurement by computational ghost imaging , 2013 .

[22]  R. M. Willett,et al.  Compressed sensing for practical optical imaging systems: A tutorial , 2011, IEEE Photonics Conference 2012.

[23]  Vicente Durán,et al.  Single-pixel polarimetric imaging. , 2012, Optics letters.

[24]  Myungjin Cho,et al.  3D passive integral imaging using compressive sensing. , 2012, Optics express.

[25]  Rebecca Willett,et al.  Target detection performance bounds in compressive imaging , 2011, EURASIP Journal on Advances in Signal Processing.

[26]  Wenlin Gong,et al.  Ghost imaging lidar via sparsity constraints , 2012, 1203.3835.

[27]  David R. Smith,et al.  Resolution of the Frequency Diverse Metamaterial Aperture Imager , 2015 .

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