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Perceptual image restoration seeks for high-fidelity images that most likely degrade to given images. For better visual quality, previous work proposed to search for solutions within the natural image manifold, by exploiting the latent…

Learning representations of images that are invariant to sensitive or unwanted attributes is important for many tasks including bias removal and cross domain retrieval. Here, our objective is to learn representations that are invariant to…

Score-based diffusion models achieve state-of-the-art performance for inverse problems, but their practical deployment is hindered by long inference times and cumbersome hyperparameter tuning. While pretrained diffusion models can be reused…

Image denoising aims to remove noise while preserving structural details and perceptual realism, yet distortion-driven methods often produce over-smoothed reconstructions, especially under strong noise and distribution shift. This paper…

These lecture notes summarize various summer schools that I have given on the topic of solving inverse problems (state and parameter estimation) by combining optimally measurement observations and parametrized PDE models. After defining a…

The Lipschitz constant of the map between the input and output space represented by a neural network is a natural metric for assessing the robustness of the model. We present a new method to constrain the Lipschitz constant of dense deep…

Neural image compression often faces a challenging trade-off among rate, distortion and perception. While most existing methods typically focus on either achieving high pixel-level fidelity or optimizing for perceptual metrics, we propose a…

Image restoration aims to enhance low quality images, producing high quality images that exhibit natural visual characteristics and fine semantic attributes. Recently, the diffusion model has emerged as a powerful technique for image…

Deep neural networks give state-of-the-art accuracy for reconstructing images from few and noisy measurements, a problem arising for example in accelerated magnetic resonance imaging (MRI). However, recent works have raised concerns that…

When images are statistically described by a generative model we can use this information to develop optimum techniques for various image restoration problems as inpainting, super-resolution, image coloring, generative model inversion, etc.…

Learning-based methods have demonstrated remarkable performance in solving inverse problems, particularly in image reconstruction tasks. Despite their success, these approaches often lack theoretical guarantees, which are crucial in…

Despite the promise of Lipschitz-based methods for provably-robust deep learning with deterministic guarantees, current state-of-the-art results are limited to feed-forward Convolutional Networks (ConvNets) on low-dimensional data, such as…

Maximum consensus estimation plays a critically important role in robust fitting problems in computer vision. Currently, the most prevalent algorithms for consensus maximization draw from the class of randomized hypothesize-and-verify…

Diffusion models have become a successful approach for solving various image inverse problems by providing a powerful diffusion prior. Many studies tried to combine the measurement into diffusion by score function replacement, matrix…

In recent years, discriminative self-supervised methods have made significant strides in advancing various visual tasks. The central idea of learning a data encoder that is robust to data distortions/augmentations is straightforward yet…

Although remarkable progress has been made, existing methods for enhancing underexposed photos tend to produce visually unpleasing results due to the existence of visual artifacts (e.g., color distortion, loss of details and uneven…

We consider a reconstruction problem of a reduced stable positive network system with the preservation of the original interconnection structure based on an $H^2$ optimal model reduction problem with constraints. To this end, we define an…

This paper considers the decision-dependent optimization problem, where the data distributions react in response to decisions affecting both the objective function and linear constraints. We propose a new method termed repeated projected…

Learning-based image compression methods have emerged as state-of-the-art, showcasing higher performance compared to conventional compression solutions. These data-driven approaches aim to learn the parameters of a neural network model…

Diffusion models have garnered considerable interest in computer vision, owing both to their capacity to synthesize photorealistic images and to their proven effectiveness in image reconstruction tasks. However, existing approaches fail to…