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

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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.
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Document Type: Research Article

Publication date: January 1, 2012

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  • Started in 2002 and merged with the Color and Imaging Conference (CIC) in 2014, CGIV covered a wide range of topics related to colour and visual information, including color science, computational color, color in computer graphics, color reproduction, volor vision/psychophysics, color image quality, color image processing, and multispectral color science. Drawing papers from researchers, scientists, and engineers worldwide, DGIV offered attendees a unique experience to share with colleagues in industry and academic, and on national and international standards committees. Held every year in Europe, DGIV papers were more academic in their focus and had high student participation rates.

    Please note: For purposes of its Digital Library content, IS&T defines Open Access as papers that will be downloadable in their entirety for free in perpetuity. Copyright restrictions on papers vary; see individual papers for details.

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