Correo Electrónico
DNINFOA - SIA
Bibliotecas
Convocatorias
Identidad U.N.
Published
Probability of correct reconstruction in compressive spectral imaging
Probabilidad de reconstrucción exitosa en el sensado compreso de imágenes espectrales
Keywords:
Restricted Isometry Property, RIP, CASSI, compressive sensing, spectral imaging, coded aperture (en)Propiedad Isométrica Restrictiva, RIP, CASSI, muestreo compresivo, imágenes hiperespectrales, códigos de apertura. (es)
Coded Aperture Snapshot Spectral Imaging (CASSI) systems capture the 3-dimensional (3D) spatio-spectral information of a scene using a set of 2-dimensional (2D) random coded Focal Plane Array (FPA) measurements. A compressed sensing reconstruction algorithm is then used to recover the underlying spatio-spectral 3D data cube. The quality of the reconstructed spectral images depends exclusively on the CASSI sensing matrix, which is determined by the statistical structure of the coded apertures. The Restricted Isometry Property (RIP) of the CASSI sensing matrix is used to determine the probability of correct image reconstruction and provides guidelines for the minimum number of FPA measurement shots needed for image reconstruction. Further, the RIP can be used to determine the optimal structure of the coded projections in CASSI. This article describes the CASSI optical architecture and develops the RIP for the sensing matrix in this system. Simulations show the higher quality of spectral image reconstructions when the RIP property is satisfied. Simulations also illustrate the higher performance of the optimal structured projections in CASSI.
El sistema de adquisición de imágenes espectrales de única captura basado en apertura codificada (CASSI), capta información tridimensional (3D) espacio-espectral de una escena, usando un conjunto de medidas bidimensionales (2D) proyectadas en un FPA (Focal Plane Array). Para recuperar el cubo de datos a partir de las proyecciones en el FPA, se usa un algoritmo de reconstrucción basado en la teoría de muestreo compresivo. En CASSI la calidad de la reconstrucción de imágenes espectrales depende exclusivamente de la matriz de sensado, que es determinada por la estructura estadística del código de apertura. La propiedad restringida isométrica (RIP) de la matriz de sensado CASSI es usada para determinar la probabilidad de una correcta reconstrucción de la imagen. Este artículo describe la arquitectura óptima CASSI y desarrolla la RIP para las matrices de muestreo, para la captura de la información del cubo de datos. En efecto, la RIP provee la guía para determinar el mínimo número de capturas FPA necesarias para la reconstrucción de una imagen. Más adelante, la RIP es usada para encontrar la estructura óptima de las proyecciones de los códigos de apertura de CASSI. Las simulaciones muestran alta calidad de la reconstrucción obtenida de las imágenes espectrales cuando se satisface la condición impuesta por la RIP. También muestran el más alto rendimiento obtenido de las estructuras óptimas de las proyecciones CASSI.
Downloads
References
Arce, G. R., Brady, D. J., Carin, L., Arguello, H., & Kittle, D. S. (2014). Compressive coded aperture spectral imaging: An introduction. Signal Processing Magazine, Vol 31. IEEE 105–115. IEEE. DOI: 10.1109/MSP.2013.2278763.
Arguello, H., & Arce, G. (2012). Spectrally Selective Compressive Imaging by Matrix System Analysis, Proc. Imaging and Applied Optics Congress. Monterey, California. DOI: 10.1364/COSI.2012.CM4B.5.
Arguello, H., & Arce, G. R. (2011). Code aperture optimization for spectrally agile compressive imaging. J. Opt. Soc. Am, Vol 28. A 2400–2413. DOI: 10.1364/josaa.28.002400.
Brady, D. J., Choi, K., Marks, D. L., Horisaki, R., & Lim, S. (2009). Compressive holography. Optics express, Vol 17. 13040–13049. Optical Society of America. DOI: 10.1364/OE.17.013040.
Candes, E., & Tao, T. (2005). Decoding by linear programming, Information Theory. IEEE Transaction, Vol 51. 4203–4215.
Correa-Pugliese, C. (2013). Lapped-windowed reconstructions in compressive spectral imaging. University of Delaware.
Diaz, N., Rueda, H., & Arguello, H. (2015). High-dynamic range compressive spectral imaging by grayscale coded aperture adaptive filtering. Ingeniería E Investigación, Vol 35(3). 53–60. DOI: 10.15446/ing.investig.v35n3.49868.
Do, T. T., Gan, L., Nguyen, N., & Tran, T. (2012). Fast an Efficient Compressive Sensing Using Structurally Random Matrices, Signal Processing. Vol 60. IEEE Transaction on 139–154.
Figueiredo, M., Nowak, R., & Wright, S. (2007). Gradient projection for sparse reconstruction: Application to compressed sensing and other inverse problems. IEEE J. of Selected Topics in Signal Processing, Vol 1. 586–597. DOI: 10.1109/jstsp.2007.910281.
Fornaiser, M. (2010). Theoretical Foundations and Numerical Methods for Sparse Recovery. (M. Fornaiser, Ed.) De Gruyter. DOI: 10.1515/9783110226157.
Foster, D. H., Amano, K., Nascimento, S. M. C., & Foster, M. (2006). J. Frequency of metamerism in natural scenes, Journal of The Optical Society of America A-optics Image Science and Vision. Vol 23. 2359–2372. DOI: 10.1364/JOSAA.23.002359.
Gehm, M. E., Kim, M. S., Fernandez, C., & Brady, D. J. (2008). High-throughput, multiplexed pushbroom hyperspectral microscopy. Optics Express, Vol 16. DOI: 10.1364/OE.16.011032.
Gupta, N. (2008). Acousto-optic tunable filter based spectropolarimetric imagers. DOI: 10.1117/12.782800.
Kittle, D., Choi, K., Wagadarikar, A. A., & Brady, D. J. (2010). Multiframe Image Estimation for Coded Aperture Snapshot Spectral Imagers. Appl. Opt, Vol 49. 6824–6833. DOI: 10.1364/AO.49.006824.
Kittle, D., Choi, K., Wagadarikar, A., & Brady, D. J. (2010). Multiframe image estimation for coded aperture snapshot spectral imagers. Applied optics, Vol 49. 6824–6833. OSA.
DOI: 10.1364/AO.49.006824.
Ledoux, M. (2001). The concentration of measure phenomenon. American Mathematical Society.
Studer, V., Bobin, J., Chahid, M., Mousavi, H. S., Candes, E., & Dahan, M. (2012). Compressive fluorescence microscopy for biological and hyperspectral imaging. Proceedings of the National Academy of Sciences, Vol 109. E1679–E1687. National Acad Sciences. DOI: 10.1073/pnas.1119511109.
Oiknine, Y., August, Y., & Stern, A. (2014). Reconstruction algorithms for compressive hyperspectral imaging systems
with separable spatial and spectral operators. In SPIE Optical Engineering Applications (p. 921703).
Wagadarikar, A. A. (2010). Compressive Spectral and Coherence Imaging.
Wagadarikar, A. A., John, R., Willett, R., & Brady, D. (2008). Single disperser design for coded aperture snapshot spectral imaging. Appl. Opt, Vol 47. B44–B51. DOI: 10.1364/AO.47.000B44.
Yu, H., & Wang, G. (2009). Compressed sensing based interior tomography. Physics in medicine and biology, Vol 54. 2791. IOP Publishing. DOI: 10.1088/0031-9155/54/9/014.
License
Copyright (c) 2016 Samuel Eduardo Pinilla, Héctor Miguel Vargas García, Henry Arguello Fuentes
This work is licensed under a Creative Commons Attribution 4.0 International License.
The authors or holders of the copyright for each article hereby confer exclusive, limited and free authorization on the Universidad Nacional de Colombia's journal Ingeniería e Investigación concerning the aforementioned article which, once it has been evaluated and approved, will be submitted for publication, in line with the following items:
1. The version which has been corrected according to the evaluators' suggestions will be remitted and it will be made clear whether the aforementioned article is an unedited document regarding which the rights to be authorized are held and total responsibility will be assumed by the authors for the content of the work being submitted to Ingeniería e Investigación, the Universidad Nacional de Colombia and third-parties;
2. The authorization conferred on the journal will come into force from the date on which it is included in the respective volume and issue of Ingeniería e Investigación in the Open Journal Systems and on the journal's main page (https://revistas.unal.edu.co/index.php/ingeinv), as well as in different databases and indices in which the publication is indexed;
3. The authors authorize the Universidad Nacional de Colombia's journal Ingeniería e Investigación to publish the document in whatever required format (printed, digital, electronic or whatsoever known or yet to be discovered form) and authorize Ingeniería e Investigación to include the work in any indices and/or search engines deemed necessary for promoting its diffusion;
4. The authors accept that such authorization is given free of charge and they, therefore, waive any right to receive remuneration from the publication, distribution, public communication and any use whatsoever referred to in the terms of this authorization.
