We consider the problem of restoring images impaired by noise that is simultaneaously structured and multiplicative. Our primary motivation for this setting is the Selective Plane Illumination Microscope (SPIM) which often suffers from severe inhomogeneities due to light absorption and scattering. This type of degradation arises in other imaging devices such as ultrasonic imaging. We model the multiplicative noise as a stationary process with known distribution. This leads to a novel convex image restoration model based on a maximum a posteriori estimator. After establishing some analytical properties of the minimizers, we finally propose a fast optimization method on GPU. Numerical experiments on 2D fluorescence microscopy images demonstrate the usefulness of the proposed models in practical applications.