Ms. Yuri Mejia Profile

Yuri Mejia

PhD. Student

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SPIE Journal Paper | 9 November 2016

Filtered gradient reconstruction algorithm for compressive spectral imaging

Yuri Mejia, Henry Arguello

OE, Vol. 56, Issue 04, 041306, (November 2016) https://doi.org/10.1117/12.10.1117/1.OE.56.4.041306

KEYWORDS: Reconstruction algorithms, Image filtering, Optical filters, Transmittance, Imaging spectroscopy, Coded apertures, Matrices, Signal to noise ratio, Databases, Imaging systems

Read 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.

Proceedings Article | 4 May 2016 Paper

Filtered gradient compressive sensing reconstruction algorithm for sparse and structured measurement matrices

Yuri Mejia, Henry Arguello

Proceedings Volume 9857, 98570F (2016) https://doi.org/10.1117/12.2224276

KEYWORDS: Reconstruction algorithms, Matrices, Transmittance, Compressed sensing, Algorithm development, Coded apertures, Image compression, Imaging spectroscopy, Imaging systems, Image filtering

Read Abstract +

Compressive sensing state-of-the-art proposes random Gaussian and Bernoulli as measurement matrices. Nev- ertheless, often the design of the measurement matrix is subject to physical constraints, and therefore it is frequently not possible that the matrix follows a Gaussian or Bernoulli distribution. Examples of these lim- itations are the structured and sparse matrices of the compressive X-Ray, and compressive spectral imaging systems. A standard algorithm for recovering sparse signals consists in minimizing an objective function that includes a quadratic error term combined with a sparsity-inducing regularization term. This problem can be solved using the iterative algorithms for solving linear inverse problems. This class of methods, which can be viewed as an extension of the classical gradient algorithm, is attractive due to its simplicity. However, current algorithms are slow for getting a high quality image reconstruction because they do not exploit the structured and sparsity characteristics of the compressive measurement matrices. This paper proposes the development of a gradient-based algorithm for compressive sensing reconstruction by including a filtering step that yields improved quality using less iterations. This algorithm modifies the iterative solution such that it forces to converge to a filtered version of the residual A^T y, where y is the measurement vector and A is the compressive measurement matrix. We show that the algorithm including the filtering step converges faster than the unfiltered version. We design various filters that are motivated by the structure of A^T y. Extensive simulation results using various sparse and structured matrices highlight the relative performance gain over the existing iterative process.

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