Compressive sensing spectroscopy with a single pixel camera.

Spectrometry requires high spectral resolution and high photometric precision while also balancing cost and complexity. We address these requirements by employing a compressive-sensing camera capable of improving signal acquisition speed and sensitivity in limited signal scenarios. In particular, we implement a fast single pixel spectrophotometer with no moving parts and measure absorption and emission spectra comparable with commercial products. Our method utilizes Hadamard matrices to sample the spectra and then minimizes the total variation of the signal. The experimental setup includes standard optics and a grating, a low-cost digital micromirror device, and an intensity detector. The resulting spectrometer produces a 512 pixel spectrum with low mean-squared error and up to a 90% reduction in data acquisition time when compared with a standard spectrophotometer.

[1]  E.J. Candes,et al.  An Introduction To Compressive Sampling , 2008, IEEE Signal Processing Magazine.

[3]  Lina Xu,et al.  Compressive Echelle spectroscopy , 2011, Optical Engineering + Applications.

[4]  Daria K. Graff,et al.  Fourier and Hadamard: Transforms in spectroscopy , 1995 .

[5]  Richard G. Baraniuk,et al.  From Denoising to Compressed Sensing , 2014, IEEE Transactions on Information Theory.

[6]  Adrian Stern,et al.  Compressive hyperspectral imaging by random separable projections in both the spatial and the spectral domains. , 2013, Applied optics.

[7]  Serge L. Shishkin,et al.  Fast and Robust Compressive Sensing Method Using Mixed Hadamard Sensing Matrix , 2012, IEEE Journal on Emerging and Selected Topics in Circuits and Systems.

[8]  Yin Zhang,et al.  User’s Guide for TVAL3: TV Minimization by Augmented Lagrangian and Alternating Direction Algorithms , 2010 .

[9]  H. Landau.  Sampling, data transmission, and the Nyquist rate , 1967 .

[10]  Y. Rivenson,et al.  Practical compressive sensing of large images , 2009, 2009 16th International Conference on Digital Signal Processing.

[11]  Michael J. Cree,et al.  Optical full Hadamard matrix multiplexing and noise effects. , 2009 .

[12]  Jonathan Leach,et al.  Reconstructing high-dimensional two-photon entangled states via compressive sensing , 2014, Scientific Reports.

[13]  Elad Harel,et al.  Mapping multidimensional electronic structure and ultrafast dynamics with single-element detection and compressive sensing , 2016, Nature Communications.

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

[15]  M J Cree,et al.  Optical full Hadamard matrix multiplexing and noise effects. , 2009, Applied optics.

[16]  H. Günthard,et al.  Infared diode laser double-beam spectrometer. , 1978, Applied Optics.

[17]  Richard G. Baraniuk,et al.  Kronecker Compressive Sensing , 2012, IEEE Transactions on Image Processing.

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

[19]  Daniel J. Lum,et al.  Fast Hadamard transforms for compressive sensing of joint systems: measurement of a 3.2 million-dimensional bi-photon probability distribution. , 2015, Optics express.

[20]  K. Kelly,et al.  Compressive Sensing Hyperspectral Imager , 2009 .

[21]  Elsa D. Angelini,et al.  Compressed sensing in biological microscopy , 2009, Optical Engineering + Applications.

[22]  David L Donoho,et al.  Compressed sensing , 2006, IEEE Transactions on Information Theory.

[23]  Hengyong Yu,et al.  Compressed sensing based interior tomography , 2009, Physics in medicine and biology.

[24]  John C. Howell,et al.  Efficient high-dimensional entanglement imaging with a compressive sensing, double-pixel camera , 2012, 1212.5530.

[25]  W. Schmidt.  A computerized single-beam spectrophotometer: an easy setup. , 1982, Analytical biochemistry.

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

[27]  Reduction of polarization-induced artifacts in grating-based spectrometers. , 2005, Applied optics.

[28]  Alexander Wong,et al.  Compressive fluorescence microscopy using saliency-guided sparse reconstruction ensemble fusion. , 2012, Optics express.

[29]  N J Sloane,et al.  Masks for Hadamard transform optics, and weighing designs. , 1976, Applied optics.