Introduction

Image restoration refers to the problem of recovering an image, , from its blurred and noisy observation, , for the purpose of improving its quality or obtaining some type of information that is not readily available from the degraded image. Blur is frequently due to the relative motion between the subject and the camera, atmospheric turbulence, out of focus lenses, and/or the image sensor. Film grain, electronic noise, and quantization are the major sources of noise in a digital image.

In this paper we describe how the Bayesian approach to image restoration can be used to incorporate prior information, in the form of smoothness constraints, to the R-L restoration method (Lucy 1974). We also examine the noise models and study how to remove detector errors.

The work is divided as follows. In § 2 we describe briefly the Bayesian paradigm. In § 3 we study the observation process and how to remove detector errors. § 4 is devoted to the study of prior models that take into account smoothness constraints and also to the study of the prior model used in the R-L restoration method. The next step is to calculate the estimate of the real underlying image, f; the algorithm implementing this task and its relationship to the R-L restoration method are described in § 5. Finally, a test example is shown in § 6.