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Compressive Covariance Matrix Estimation from a Dual-Dispersive Coded Aperture Spectral Imager

Citation Author(s):
Jonathan Monsalve, Miguel Marquez, Iñaki Esnaola, Henry Arguello
Submitted by:
Jonathan Monsal...
Last updated:
23 September 2021 - 4:52pm
Document Type:
Presentation Slides
Document Year:
2021
Event:
Presenters:
Jonathan Monsalve
Paper Code:
2544
 

Compressive covariance sampling (CCS) theory aims to recover the covariance matrix (CM) of a signal, instead of the signal itself, from a reduced set of random linear projections. Although several theoretical works demonstrate the CCS theory's advantages in compressive spectral imaging tasks, a real optical implementation has not been proposed.
Therefore, this paper proposes a compressive spectral sensing protocol for the dual-dispersive coded aperture spectral snapshot imager (DD-CASSI) to directly estimate the covariance matrix of the signal. Specifically, we propose a coded aperture design that allows recasting the vector sensing problem into matrix form, which enables to exploitation of the covariance matrix structure such as positive-semidefiniteness, low-rank, or Toeplitz. Additionally, a low-rank approximation of the image is reconstructed using a Principal Components Analysis (PCA) based method. In order to test the precision of the reconstruction, some spectral signatures of the image are captured with a spectrometer and compared with those obtained in the reconstruction using the covariance matrix. Results show the reconstructed spectrum is accurate with a spectral angle mapper (SAM) of less than 14°. RGB image composites of the spectral image also provide evidence of a correct color reconstruction.

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