2014/12/14 by Marko Järvenpää, Järvenpää, Marko, Robert Piché +1
Computer Science · Engineering · #Advanced Image Processing Techniques #FOS: Computer and information sciences #FOS: Mathematics #Image Processing Techniques and Applications #Image and Signal Denoising Methods #Methodology (stat.ME) #Numerical Analysis (math.NA) #Sparse and Compressive Sensing Techniques
paper · pdf · doi:10.48550/arxiv.1412.4384
openalex publication_date 2014/12/14 · openalex created_date 2022/08/30 · openalex updated_date 2026/07/28
A Bayesian hierarchical model for total variation regularisation is presented\nin this paper. All the parameters of an inverse problem, including the\n"regularisation parameter", are estimated simultaneously from the data in the\nmodel. The model is based on the characterisation of the Laplace density prior\nas a scale mixture of Gaussians. With different priors on the mixture variable,\nother total variation like regularisations e.g. a prior that is related to\nt-distribution, are also obtained. An approximation of the resulting posterior\nmean is found using a variational Bayes method. In addition, an iterative\nalternating sequential algorithm for computing the maximum a posteriori\nestimate is presented. The methods are illustrated with examples of image\ndeblurring. Results show that the proposed model can be used for automatic\nedge-preserving inversion in the case of image deblurring. Despite promising\nresults, some difficulties with the model were encountered and are subject to\nfuture work.\n