Non-additive speckle wide sense multiplicative (pseudo) noise is present in a multitude of imaging modalities, involving coherent radiation such as Synthetic Aperture Radar (SAR), LASER, Optical Coherence Tomography (OCT) and Ultrasound (US). The term wide-sense multiplicative noise is used to refer to any statistical model of noise wherein its time and/or space varying variance depends on the underlying signal to be estimated. This is the case of fluorescence images of microscopy where the noise that corrupts the images, related with the photon-counting process at the detectors, is Poisson distributed with a variance that is directly related with the amount of fluorescent dyes. Common approaches to deal with this type of non additive noise are based on Variation Stabilization Transformations, such as the Anscomb or the Fisz transforms and by non-linear transformations, e.g. logarithmic compression, to convert the multiplicative noise into additive.

Estimating the image from the noisy and possibly incomplete observations is an ill-posed problem, where regularization or some assumption on the nature of the image is needed. The statistical distribution of the noise and the algebraic observation model that leads to the image formation depends on the physics of the modality. Further, depending on hardware and sensing limitations as well as trans- mission errors, the image may need to be reconstructed from a set of partial observations.

In this line of research we investigate the observation models and underlying statistical pixel intensity models based on the physics of the acquisition process in image modalities where the raw data is corrupted by non-additive types of noise with missing and non-valid data. The ultimate goal is to decompose real images in their denoised and pure noise components in to not discarded any information that may be useful for the diagnosis or detection of pathologies.

**Principal Researcher**: João Sanches