Towards Model Independent Image Denoising and Reconstruction
In image denoising and reconstruction, it is natural that the algebraic and statistical model of the observation be taken into account to formulate the optimization problems. There has been a lot of recent literature devoted to the respective denoising, deconvolution, and reconstruction problems, focusing on specific modalities such as ultrasound, SAR, fluorescence microscopy, MRI, etc.
Our work aims at developing a framework unifying the denoising and reconstruction problems for the various models, using assumptions, for example, that the image to be estimated is always sparse and piece-wise smooth and the noise is always irregular and non-sparse.
In the first part of the talk, our work on adaptive and recursive filtering for total variation denoising and inpainting will be presented. This approach reformulates the MAP estimation for additive and Gaussian, multiplicative and Rayleigh, or Poisson noise, as a filtered version of the respective ML estimate. Only the ML estimate and a weight matrix need to be initialized depending on the model.
We then present our method for blind inpainting, again, for the Gaussian, Rayleigh, and Poisson noise models. This framework uses a TV regularizer on the image, and the l0 norm regularizer on the support set of the observed pixels, which are estimated in the same iterative process through alternating minimization.