Constrained and unconstrained deep image prior optimization models with automatic regularization

Pasquale Cascarano, Giorgia Franchini (), Erich Kobler, Federica Porta () and Andrea Sebastiani
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Pasquale Cascarano: University of Bologna
Giorgia Franchini: University of Modena and Reggio Emilia
Erich Kobler: University of Linz
Federica Porta: University of Modena and Reggio Emilia
Andrea Sebastiani: University of Bologna

Computational Optimization and Applications, 2023, vol. 84, issue 1, No 6, 125-149

Abstract: Abstract Deep Image Prior (DIP) is currently among the most efficient unsupervised deep learning based methods for ill-posed inverse problems in imaging. This novel framework relies on the implicit regularization provided by representing images as the output of generative Convolutional Neural Network (CNN) architectures. So far, DIP has been shown to be an effective approach when combined with classical and novel regularizers. Unfortunately, to obtain appropriate solutions, all the models proposed up to now require an accurate estimate of the regularization parameter. To overcome this difficulty, we consider a locally adapted regularized unconstrained model whose local regularization parameters are automatically estimated for additively separable regularizers. Moreover, we propose a novel constrained formulation in analogy to Morozov’s discrepancy principle which enables the application of a broader range of regularizers. Both the unconstrained and the constrained models are solved via the proximal gradient descent-ascent method. Numerical results demonstrate the robustness with respect to image content, noise levels and hyperparameters of the proposed models on both denoising and deblurring of simulated as well as real natural and medical images.

Keywords: Deep image prior; Convolutional neural networks; Automatic regularization; Regularization by denoising; Gradient descent-ascent methods; Image denoising; Image deblurring; 65K10; 68U10; 90C06 (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1007/s10589-022-00392-w

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