Special Section on Optical Computational Imaging

Filtered gradient reconstruction algorithm for compressive spectral imaging

[+] Author Affiliations
Yuri Mejia

Universidad Industrial de Santander, Department of Electrical Engineering, Calle 9-Carrera 27, Bucaramanga 680002, Colombia

Henry Arguello

Universidad Industrial de Santander, Department of Computer Science, Calle 9-Carrera 27, Bucaramanga 680002, Colombia

Opt. Eng. 56(4), 041306 (Nov 09, 2016). doi:10.1117/1.OE.56.4.041306
History: Received August 13, 2016; Accepted October 13, 2016
Text Size: A A A

Abstract.  Compressive sensing matrices are traditionally based on random Gaussian and Bernoulli entries. Nevertheless, they are subject to physical constraints, and their structure unusually follows a dense matrix distribution, such as the case of the matrix related to compressive spectral imaging (CSI). The CSI matrix represents the integration of coded and shifted versions of the spectral bands. A spectral image can be recovered from CSI measurements by using iterative algorithms for linear inverse problems that minimize an objective function including a quadratic error term combined with a sparsity regularization term. However, current algorithms are slow because they do not exploit the structure and sparse characteristics of the CSI matrices. A gradient-based CSI reconstruction algorithm, which introduces a filtering step in each iteration of a conventional CSI reconstruction algorithm that yields improved image quality, is proposed. Motivated by the structure of the CSI matrix, Φ, this algorithm modifies the iterative solution such that it is forced to converge to a filtered version of the residual ΦTy, where y is the compressive measurement vector. We show that the filtered-based algorithm converges to better quality performance results than the unfiltered version. Simulation results highlight the relative performance gain over the existing iterative algorithms.

Figures in this Article
© 2016 Society of Photo-Optical Instrumentation Engineers

Citation

Yuri Mejia and Henry Arguello
"Filtered gradient reconstruction algorithm for compressive spectral imaging", Opt. Eng. 56(4), 041306 (Nov 09, 2016). ; http://dx.doi.org/10.1117/1.OE.56.4.041306


Access This Article
Sign in or Create a personal account to Buy this article ($20 for members, $25 for non-members).

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging & repositioning the boxes below.

Related Book Chapters

Topic Collections

PubMed Articles
Advertisement
  • Don't have an account?
  • Subscribe to the SPIE Digital Library
  • Create a FREE account to sign up for Digital Library content alerts and gain access to institutional subscriptions remotely.
Access This Article
Sign in or Create a personal account to Buy this article ($20 for members, $25 for non-members).
Access This Proceeding
Sign in or Create a personal account to Buy this article ($15 for members, $18 for non-members).
Access This Chapter

Access to SPIE eBooks is limited to subscribing institutions and is not available as part of a personal subscription. Print or electronic versions of individual SPIE books may be purchased via SPIE.org.