Claudio Fantasia
Patch-based learning of space-variant hyperparameters in variational image restoration.
Rel. Salvatore Ivan Trapasso, Luca Calatroni, Xavier Descombes. Politecnico di Torino, Corso di laurea magistrale in Data Science And Engineering, 2024
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Abstract
Solving an inverse imaging problem is the task of reconstructing an unknown image from observed, often incomplete noisy data. A standard example describing a linear degradation process is the problem of image deconvolution where the operator describing the blurring process (forward operator) is a convolution matrix. These problems are typically ill-posed, where solving the inverse formulation can cause small perturbations in the observed image (input) to lead to significant perturbations in the desired image (output). A standard paradigm overcoming such instabilities consists in considering a regularised formulation of the problem in order to guarantee stable reconstruction of the solution. Regularisation is combined with a data-fitting term along with a scalar or vector of hyperparameters balancing the two.
Total Variation regularisation is a popular regulariser in the context of imaging due to its enhanced edge-preserving behaviour and noise smoothing properties in comparison to other, simpler, regularisations (e.g
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