Restoration in the presence of multiplicative noise with application to scanned photographic images

A linear minimum mean square error (LMMSE) deconvolution filter is derived in the presence of a multiplicative noise in order to incorporate the nonlinear sensor characteristics into the restoration of noisy and blurred scanned photographic images. Image restoration is proposed in the exposure domain where a linear convolutional relationship between the original and the observed images can be established at the expense of having a multiplicative observation noise. Examples of photographically blurred images are provided to demonstrate that images can be identified and restored in the exposure domain which cannot be identified or restored in the optical density domain.