A Hybrid Interior Point - Deep Learning Approach for Poisson Image Deblurring

Abstract

In this paper we address the problem of deconvolution of an image corrupted with Poisson noise by reformulating the restoration process as a constrained minimization of a suitable regularized data fidelity function. The minimization step is performed by means of an interior-point approach, in which the constraints are incorporated within the objective function through a barrier penalty and a forward-backward algorithm is exploited to build a minimizing sequence. The key point of our proposed scheme is that the choice of the regularization, barrier and step-size parameters defining the interior point approach is automatically performed by a deep learning strategy. Numerical tests on Poisson corrupted benchmark datasets show that our method can obtain very good performance when compared to a state-of-the-art variational deblurring strategy.

Inversion of Integral Models: a Neural Network Approach

“…Conclusion of the proof. Based on the previous calculations, Condition (32) is equivalent to (26). In addition, let us note that for every n ∈ {1, .…”

“…The use of neural networks for solving inverse problems has become increasingly popular, especially in the image processing community. A rich panel of approaches have been proposed, either adapted to the sparsity of the data [18,19], or mimicking variational models [20,21], or iterating learned operators [22,23,24,25,26], or adpating Tikhonov method [27]. The successful numerical results of the aforementioned works raise two theoretical questions: when these methods are based on the iteration of a neural network, do they converge (in the sense of the algorithm)?…”

“…In iterative approaches, a regularization operator is learned, either in the form of a proximity (or denoiser) operator as [23,22,26], of a regularization term [27], of a pseudodiffential operator [28], or of its gradient [29,3]. Strong connections also exist with Plug and Play methods [30,31,24], where the regularization operator is a pre-trained neural network.…”

Stability of Unfolded Forward-Backward to Perturbations in Observed Data

“…The use of neural networks for solving inverse problems has become increasingly popular, especially in the image processing community. A rich panel of approaches have been proposed, either adapted to the sparsity of the data [5], [6], or mimicking variational models [7], [8], or iterating learned operators [9]- [13]. In iterative approaches, a regularization operator is learned, either in the form of a proximity operator as in [9], [10], [13], of a regularization term [14], of a pseudodiffential operator [15], or of its gradient [2], [16].…”

“…A rich panel of approaches have been proposed, either adapted to the sparsity of the data [5], [6], or mimicking variational models [7], [8], or iterating learned operators [9]- [13]. In iterative approaches, a regularization operator is learned, either in the form of a proximity operator as in [9], [10], [13], of a regularization term [14], of a pseudodiffential operator [15], or of its gradient [2], [16]. Strong connections also exist with Plug and Play methods [11], [17], [18], where the regularization operator is a pre-trained neural network.…”