## Abstract

It is well known that the noise present in an image acquisition system plays important roles in solving inverse problems, such as the reconstruction of spectral reflectances of imaged objects from the sensor responses. Usually, a recovered spectral reflectance vector $\widehat{\mathbf{r}}$ by a matrix **W** is expressed by $\widehat{\mathbf{r}}=\mathbf{W}\mathbf{p}$, where **p** is a sensor response vector. In this paper, the mean square errors (MSEs) between the recovered spectral reflectances with various reconstruction matrices **W** and actual spectral reflectances are divided into the noise independent MSE (${\mathrm{MSE}}_{\text{FREE}}$) and the noise dependent MSE (${\mathrm{MSE}}_{\text{NOISE}}$). By dividing the MSE into two terms, the ${\mathrm{MSE}}_{\text{NOISE}}$ is defined as the estimated noise variance multiplied by the sum of the squared singular values of the matrix **W**. It is shown that the relation between the increase in the MSE and the ${\mathrm{MSE}}_{\text{NOISE}}$ agrees quite well with the experimental results by the multispectral camera, and that the estimated noise variances are of the same order of magnitude for various matrices **W**, but the increase in the MSE by the noise mainly results from the increase in the sum of the squared singular values for the unregularized reconstruction matrix **W**.

© 2010 Optical Society of America

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