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Volume: 6 | Article ID: art00043

Evaluating the Noise Variance of an Image Acquisition System with Various Reconstruction Matrices

DOI : **10.2352/CGIV.2012.6.1.art00043** Published Online : **January 2012**

Abstract

Estimation of the noise variance of image acquisition systems is very important to solve the inverse problems such as the recovery of spectral reflectances through the use of image data or to get a clear image from a blurred image, etc. In the color imaging community, the acquisition of accurate spectral reflectances of objects at the resolution of pixels is important to reproduce realistic color images under a variety of viewing illuminants. The accuracy of recovered spectral reflectances is usually evaluated by the mean square errors (MSE) between the measured and the recovered reflectances. The MSE is dependent on the noise present in an image acquisition system, which is called as the system noise below, and estimating the noise level is important to increase the estimation accuracies. In the evaluation of the influence of the noise, dividing the MSE into two terms, i.e., the noise independent MSE (MSEfree) and noise dependent MSE (MSEnoise), is essential to estimate the noise variance and to analyze the influence of the noise on the MSE. A model separating the MSE into the two terms and estimating the noise variance was already proposed based on the Wiener estimation by one of the authors. Later the model was modified to a comprehensive model based on an arbitrary reflectance reconstruction matrix and was also applied to the noise estimates by two spectral estimation models such as the Wiener and the linear model.In the previous paper, it was not possible to apply the comprehensive model to the regression model or the Imai- Berns model, which are the models to estimate spectral reflectances, because their reconstruction matrices are derived from the sensor responses which include the system noise in it.In this paper, a new method is proposed to extend the comprehensive model to four reconstruction models (Wiener, linear, regression and Imai-Berns models), since it is very interesting whether the influence of the noise on the recovery performance is dependent on the model used or not. By defining the theoretical estimates of the sensor responses and by estimating the reconstruction matrices without the system noise for the regression model and the Imai-Berns model, it is shown that the increasing in the MSE by the noise present in an image acquisition system can be evaluated by a simple formulation for the four models. From the experimental results it is shown that the comprehensive model analyzes the effect of the system noise on the increase in the MSE on the reflectance recovery.

Journal Title : **Conference on Colour in Graphics, Imaging, and Vision**

Publisher Name : **Society of Imaging Science and Technology**

Publisher Location : **7003 Kilworth Lane, Springfield, VA 22151, USA**

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Cite this article

Mikiya Hironaga, Noriyuki Shimano, Takashi Toriu, "Evaluating the Noise Variance of an Image Acquisition System with Various Reconstruction Matrices" in *Proc. IS&T CGIV 2012 6th European Conf. on Colour in Graphics, Imaging, and Vision*, 2012, pp 247 - 252, https://doi.org/10.2352/CGIV.2012.6.1.art00043

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Copyright © Society for Imaging Science and Technology 2012