Measurement Matrix Construction for Large-area Single Photon Compressive Imaging

We have developed a single photon compressive imaging system based on single photon counting technology and compressed sensing theory, using a photomultiplier tube (PMT) photon counting head as the bucket detector. This system can realize ultra-weak light imaging with the imaging area up to the entire digital micromirror device (DMD) working region. The measurement matrix in this system is required to be binary due to the two working states of the micromirror corresponding to two controlled elements. And it has a great impact on the performance of the imaging system, because it involves modulation of the optical signal and image reconstruction. Three kinds of binary matrix including sparse binary random matrix, m sequence matrix and true random number matrix are constructed. The properties of these matrices are analyzed theoretically with the uncertainty principle. The parameters of measurement matrix including sparsity ratio, compressive sampling ratio and reconstruction time are verified in the experimental system. The experimental results show that, the increase of sparsity ratio and compressive sampling ratio can improve the reconstruction quality. However, when the increase is up to a certain value, the reconstruction quality tends to be saturated. Compared to the other two types of measurement matrices, the m sequence matrix has better performance in image reconstruction.

[1]  Richard Obermeier,et al.  Sensing Matrix Design via Mutual Coherence Minimization for Electromagnetic Compressive Imaging Applications , 2017, IEEE Transactions on Computational Imaging.

[2]  Graham M. Gibson,et al.  Single-pixel three-dimensional imaging with time-based depth resolution , 2016, Nature Communications.

[3]  Guihua Zeng,et al.  Single-photon-counting polarization ghost imaging. , 2016, Applied optics.

[4]  J. F. Dynes,et al.  Gigacount/second photon detection with InGaAs avalanche photodiodes , 2012 .

[5]  Francescopaolo Mattioli Della Rocca,et al.  Real-time fluorescence lifetime actuation for cell sorting using a CMOS SPAD silicon photomultiplier. , 2016, Optics letters.

[6]  Xavier Intes,et al.  Compressive hyperspectral time-resolved wide-field fluorescence lifetime imaging , 2017, Nature Photonics.

[7]  Vivek K Goyal,et al.  First-Photon Imaging , 2014, Science.

[8]  M. Calvi,et al.  Characterization of the Hamamatsu H12700A-03 and R12699-03 multi-anode photomultiplier tubes , 2015, 1506.04302.

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

[10]  E. Candès,et al.  Stable signal recovery from incomplete and inaccurate measurements , 2005, math/0503066.

[11]  Hou Biao,et al.  Development and Prospect of Compressive Sensing , 2011 .

[12]  Vibha Tiwari,et al.  Designing sparse sensing matrix for compressive sensing to reconstruct high resolution medical images , 2015 .

[13]  Wen-Kai Yu,et al.  Single-photon compressive imaging with some performance benefits over raster scanning , 2014 .

[14]  Vivek K. Goyal,et al.  Compressive depth map acquisition using a single photon-counting detector: Parametric signal processing meets sparsity , 2012, 2012 IEEE Conference on Computer Vision and Pattern Recognition.

[15]  Robert W. Boyd,et al.  Imaging with a small number of photons , 2014, Nature Communications.

[16]  Daniel J. Lum,et al.  Photon counting compressive depth mapping , 2013, Optics express.

[17]  S. Tavernier,et al.  Operation of microchannel plate PMTs with TOFPET multichannel timing electronics , 2019, Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment.

[18]  Lie Wang,et al.  Stable Recovery of Sparse Signals and an Oracle Inequality , 2010, IEEE Transactions on Information Theory.

[19]  M. Chekhova,et al.  Autonomous absolute calibration of an ICCD camera in single-photon detection regime. , 2016, Optics express.

[20]  A. Pifferi,et al.  Time-resolved single-photon detection module based on silicon photomultiplier: A novel building block for time-correlated measurement systems. , 2016, The Review of scientific instruments.

[21]  Wen-Kai Yu,et al.  Measurement dimensions compressed spectral imaging with a single point detector , 2016 .

[22]  K. Taguchi,et al.  Vision 20/20: Single photon counting x-ray detectors in medical imaging. , 2013, Medical physics.

[23]  Pengpeng Zhao,et al.  An improved weak light detector used for infrared Imaging guidance system , 2016 .

[24]  A. Tosi,et al.  SPAD Figures of Merit for Photon-Counting, Photon-Timing, and Imaging Applications: A Review , 2016, IEEE Sensors Journal.

[25]  Bing Li,et al.  Large-area single photon compressive imaging based on multiple micro-mirrors combination imaging method. , 2018, Optics express.

[26]  S. Pellegrini,et al.  A SPAD-Based QVGA Image Sensor for Single-Photon Counting and Quanta Imaging , 2016, IEEE Transactions on Electron Devices.

[27]  K. König,et al.  Fluorescence lifetime imaging by time‐correlated single‐photon counting , 2004, Microscopy research and technique.

[28]  Qiurong Yan,et al.  High-speed quantum-random number generation by continuous measurement of arrival time of photons. , 2015, The Review of scientific instruments.

[29]  Amir Pourmorteza,et al.  Abdominal Imaging with Contrast-enhanced Photon-counting CT: First Human Experience. , 2016, Radiology.

[30]  Qian Chen,et al.  Adaptive compressed photon counting 3D imaging based on wavelet trees and depth map sparse representation. , 2016, Optics express.

[31]  Qiurong Yan,et al.  Multi-bit quantum random number generation by measuring positions of arrival photons. , 2014, The Review of scientific instruments.

[32]  Michael Elad,et al.  A generalized uncertainty principle and sparse representation in pairs of bases , 2002, IEEE Trans. Inf. Theory.

[33]  R. Hadfield.  Single-photon detectors for optical quantum information applications , 2009 .

[34]  J. Romberg,et al.  Imaging via Compressive Sampling , 2008, IEEE Signal Processing Magazine.

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

[36]  David J. S. Birch,et al.  A 192×128 Time Correlated Single Photon Counting Imager in 40nm CMOS Technology , 2018, ESSCIRC 2018 - IEEE 44th European Solid State Circuits Conference (ESSCIRC).

[37]  Massimo Fornasier,et al.  Compressive Sensing , 2015, Handbook of Mathematical Methods in Imaging.

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

[39]  M. Ge,et al.  Single photon counting imaging system via compressive sensing , 2012, 1202.5866.

[40]  A. Finger,et al.  Pseudo Random Signal Processing: Theory and Application , 2005 .

[41]  Dang Ku,et al.  Construction of the compressive sensing measurement matrix based on m sequences , 2015 .

[42]  R.G. Baraniuk,et al.  Compressive Sensing [Lecture Notes] , 2007, IEEE Signal Processing Magazine.

[43]  Xiaoming Huo,et al.  Uncertainty principles and ideal atomic decomposition , 2001, IEEE Trans. Inf. Theory.