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Inverse problems in imaging are extensively studied, with a variety of strategies, tools, and theory that have been accumulated over the years. Recently, this field has been immensely influenced by the emergence of deep-learning techniques.…
We consider an inertial primal-dual fixed point algorithm (IPDFP) to compute the minimizations of the following Problem (1.1). This is a full splitting approach, in the sense that the nonsmooth functions are processed individually via their…
We propose and analyze an accelerated iterative dual diagonal descent algorithm for the solution of linear inverse problems with general regularization and data-fit functions. In particular, we develop an inertial approach of which we…
In this paper,we present an inexact primal-dual method with correction step for a saddle point problem by introducing the notations of inexact extended proximal operators with symmetric positive definite matrix $D$. Relaxing requirement on…
We present a comprehensive overview of the Deep Image Prior (DIP) framework and its applications to image reconstruction in computed tomography. Unlike conventional deep learning methods that rely on large, supervised datasets, the DIP…
Decentralized non-convex optimization is important in many problems of practical relevance. Existing decentralized methods, however, typically either lack convergence guarantees for general non-convex problems, or they suffer from a high…
Performance is a critical challenge in mobile image processing. Given a reference imaging pipeline, or even human-adjusted pairs of images, we seek to reproduce the enhancements and enable real-time evaluation. For this, we introduce a new…
PET image reconstruction is challenging due to the ill-poseness of the inverse problem and limited number of detected photons. Recently deep neural networks have been widely and successfully used in computer vision tasks and attracted…
Image restoration has seen great progress in the last years thanks to the advances in deep neural networks. Most of these existing techniques are trained using full supervision with suitable image pairs to tackle a specific degradation.…
Pansharpening is a challenging image fusion task that involves restoring images using two different modalities: low-resolution multispectral images (LRMS) and high-resolution panchromatic (PAN). Many end-to-end specialized models based on…
Estimating hyperparameters has been a long-standing problem in machine learning. We consider the case where the task at hand is modeled as the solution to an optimization problem. Here the exact gradient with respect to the hyperparameters…
In this paper, we introduce a \textit{Bi-level OPTimization} (BiOPT) framework for minimizing the sum of two convex functions, where both can be nonsmooth. The BiOPT framework involves two levels of methodologies. At the upper level of…
Due to the hierarchical structure of many machine learning problems, bilevel programming is becoming more and more important recently, however, the complicated correlation between the inner and outer problem makes it extremely challenging…
Deep image prior (DIP) is an unsupervised deep learning framework that has been successfully applied to a variety of inverse imaging problems. However, DIP-based methods are inherently prone to overfitting, which leads to performance…
Since the 1960s I proposed that we could understand and replicate the highest level of intelligence seen in the brain, by building ever more capable and general systems for adaptive dynamic programming (ADP), which is like reinforcement…
In this work, the demand Adjustment Problem (DAP) associated to urban traffic planning is studied. The framework for the formulation of the DAP is mathematical programming with equilibrium constraints. In particular, if the optimization…
Digital artists often improve the aesthetic quality of digital photographs through manual retouching. Beyond global adjustments, professional image editing programs provide local adjustment tools operating on specific parts of an image.…
In this paper, we propose and analyze an inexact version of the symmetric proximal alternating direction method of multipliers (ADMM) for solving linearly constrained optimization problems. Basically, the method allows its first subproblem…
Deep neural networks are a very powerful tool for many computer vision tasks, including image restoration, exhibiting state-of-the-art results. However, the performance of deep learning methods tends to drop once the observation model used…
The goal of this paper is to reduce the total complexity of gradient-based methods for two classes of problems: affine-constrained composite convex optimization and bilinear saddle-point structured non-smooth convex optimization. Our…