A Spectral Reconstruction Algorithm of Miniature Spectrometer Based on Sparse Optimization and Dictionary Learning

The miniaturization of spectrometer can broaden the application area of spectrometry, which has huge academic and industrial value. Among various miniaturization approaches, filter-based miniaturization is a promising implementation by utilizing broadband filters with distinct transmission functions. Mathematically, filter-based spectral reconstruction can be modeled as solving a system of linear equations. In this paper, we propose an algorithm of spectral reconstruction based on sparse optimization and dictionary learning. To verify the feasibility of the reconstruction algorithm, we design and implement a simple prototype of a filter-based miniature spectrometer. The experimental results demonstrate that sparse optimization is well applicable to spectral reconstruction whether the spectra are directly sparse or not. As for the non-directly sparse spectra, their sparsity can be enhanced by dictionary learning. In conclusion, the proposed approach has a bright application prospect in fabricating a practical miniature spectrometer.

[1]  R. Tibshirani.  Regression Shrinkage and Selection via the Lasso , 1996 .

[2]  Kjersti Engan,et al.  Recursive Least Squares Dictionary Learning Algorithm , 2010, IEEE Transactions on Signal Processing.

[3]  Pascal Frossard,et al.  Dictionary Learning , 2011, IEEE Signal Processing Magazine.

[4]  Rajesh Menon,et al.  Computational spectrometer based on a broadband diffractive optic. , 2014, Optics express.

[5]  Heung-No Lee,et al.  On the estimation of target spectrum for filter-array based spectrometers. , 2008, Optics express.

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

[7]  Arvin Emadi,et al.  Design and implementation of a sub-nm resolution microspectrometer based on a Linear-Variable Optical Filter. , 2012, Optics express.

[8]  Adrian Stern,et al.  Compressive sensing spectrometry based on liquid crystal devices. , 2013, Optics letters.

[9]  S. Frick,et al.  Compressed Sensing , 2014, Computer Vision, A Reference Guide.

[10]  H. Ho,et al.  An ultra compact spectrometer based on the optical transmission through a micro interferometer array , 2013 .

[11]  H. Cao,et al.  Compact spectrometer based on a disordered photonic chip , 2013, Nature Photonics.

[12]  Joseph Sherma.  Miniature spectrometers. , 2003, Journal of AOAC International.

[13]  A. Bruckstein,et al.  K-SVD : An Algorithm for Designing of Overcomplete Dictionaries for Sparse Representation , 2005 .

[14]  Ali Adibi,et al.  Multimodal multiplex spectroscopy using photonic crystals. , 2003, Optics express.

[15]  M. Turk,et al.  Eigenfaces for Recognition , 1991, Journal of Cognitive Neuroscience.

[16]  Mário A. T. Figueiredo,et al.  Gradient Projection for Sparse Reconstruction: Application to Compressed Sensing and Other Inverse Problems , 2007, IEEE Journal of Selected Topics in Signal Processing.

[17]  Brandon Redding,et al.  All-fiber spectrometer based on speckle pattern reconstruction. , 2013, Optics express.

[18]  Hemant D. Tagare,et al.  Broadband multimode fiber spectrometer , 2016, 2016 Conference on Lasers and Electro-Optics (CLEO).

[19]  Michael Elad,et al.  Image Denoising Via Sparse and Redundant Representations Over Learned Dictionaries , 2006, IEEE Transactions on Image Processing.

[20]  Reinoud F. Wolffenbuttel,et al.  State-of-the-art in integrated optical microspectrometers , 2004, IEEE Transactions on Instrumentation and Measurement.

[21]  Wei Huang,et al.  Miniature spectrometer based on diffraction in a dispersive hole array. , 2015, Optics letters.

[22]  T. Yang,et al.  Novel high resolution miniature spectrometer using an integrated diffraction hole array , 2012, 2012 17th Opto-Electronics and Communications Conference.

[23]  Emmanuel J. Candès,et al.  Templates for convex cone problems with applications to sparse signal recovery , 2010, Math. Program. Comput..

[24]  Byung Il Choi,et al.  Filter-Based Miniature Spectrometers: Spectrum Reconstruction Using Adaptive Regularization , 2011, IEEE Sensors Journal.

[25]  Wei Lu,et al.  Integrated optical filter arrays fabricated by using the combinatorial etching technique. , 2006, Optics letters.

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

[27]  Heung-no Lee,et al.  Improving resolution of miniature spectrometers by exploiting sparse nature of signals. , 2012, Optics express.

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

[29]  Cheng-Chun Chang,et al.  Spectrum reconstruction for filter-array spectrum sensor from sparse template selection , 2011 .

[30]  Kjersti Engan,et al.  Family of iterative LS-based dictionary learning algorithms, ILS-DLA, for sparse signal representation , 2007, Digit. Signal Process..

[31]  Stephen J. Wright,et al.  Computational Methods for Sparse Solution of Linear Inverse Problems , 2010, Proceedings of the IEEE.

[32]  Wei Lu,et al.  Concept of a high-resolution miniature spectrometer using an integrated filter array. , 2007, Optics letters.

[33]  Christina P. Bacon,et al.  Miniature spectroscopic instrumentation: Applications to biology and chemistry , 2004 .

[34]  Darko Zibar,et al.  Compact silicon multimode waveguide spectrometer with enhanced bandwidth , 2017, Scientific Reports.

[35]  M. Elad,et al.  $rm K$-SVD: An Algorithm for Designing Overcomplete Dictionaries for Sparse Representation , 2006, IEEE Transactions on Signal Processing.

[36]  Michael Elad,et al.  K-SVD and its non-negative variant for dictionary design , 2005, SPIE Optics + Photonics.

[37]  Stephen P. Boyd,et al.  An Interior-Point Method for Large-Scale $\ell_1$-Regularized Least Squares , 2007, IEEE Journal of Selected Topics in Signal Processing.