Sensing Matrix Design for Compressive Spectral Imaging via Binary Principal Component Analysis

Compressive spectral imaging (CSI) is a framework that captures coded-and-multiplexed low-dimensional projections of spectral data-cubes. In general, the sensing process in many CSI architectures is described using binary matrices, so-called sensing/projection matrices, whose elements can be either...

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Veröffentlicht in:IEEE transactions on image processing : a publication of the IEEE Signal Processing Society. - 1992. - (2019) vom: 19. Dez.
1. Verfasser: Monsalve, Jonathan (VerfasserIn)
Weitere Verfasser: Rueda-Chacon, Hoover, Arguello, Henry
Format: Online-Aufsatz
Sprache:English
Veröffentlicht: 2019
Zugriff auf das übergeordnete Werk:IEEE transactions on image processing : a publication of the IEEE Signal Processing Society
Schlagworte:Journal Article
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520 |a Compressive spectral imaging (CSI) is a framework that captures coded-and-multiplexed low-dimensional projections of spectral data-cubes. In general, the sensing process in many CSI architectures is described using binary matrices, so-called sensing/projection matrices, whose elements can be either random or designed. However, some characteristics of the spectral data, such as the ℓ2-norm or the second moment statistics, can be lost when this dimensionality reduction is performed. Similarly, principal component analysis (PCA) is a data dimensionality reduction technique that minimizes the least-squared error between the spectral data and its low-dimensional projection, but preserving its structure or variance. Thus, PCA can be used to guide the CSI acquisition process by designing the binary sensing matrix. Nonetheless, PCA requires to know the spectral image a-priori, and also, its associated projection matrix is not binary, as required by CSI optical architectures. Therefore, in this paper, an algorithm to design CSI sensing matrices by exploiting the structure-preserving property of the PCA projection is proposed. First, a set of compressive measurements obtained with random sensing matrices is used to rapidly estimate the covariance matrix associated with the spectral data. Then, a new sensing matrix is designed by solving a non-convex optimization problem that finds a set of binary vectors that approximate the principal components of the covariance matrix, thus maximizing the explanation of the data variance. Experimental results show an improvement of up to 3 dB in image reconstruction quality, in terms of the peak signal to noise ratio (PSNR), when the binary PCA-based sensing matrices are used and compared with conventional random sensing matrices and state-of-art designed matrices based on PCA 
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