A Kalman filter approach for denoising and deblurring 3-D microscopy images

This paper proposes a new method for removing noise and blurring from 3D microscopy images. The main contribution is the definition of a space-variant generating model of a 3-D signal, which is capable to stochastically describe a wide class of 3-D images. Unlike other approaches, the space-variant structure allows the model to consider the information on edge locations, if available. A suitable description of the image acquisition process, including blurring and noise, is then associated to the model. A state-space realization is finally derived, which is amenable to the application of standard Kalman filter as an image restoration algorithm. The so obtained method is able to remove, at each spatial step, both blur and noise, via a linear minimum variance recursive one-shot procedure, which does not require the simultaneous processing of the whole image. Numerical results on synthetic and real microscopy images confirm the merit of the approach.