Related papers: Algorithmic Guarantees for Inverse Imaging with Un…

Deep neural networks provide state-of-the-art performance for image denoising, where the goal is to recover a near noise-free image from a noisy observation. The underlying principle is that neural networks trained on large datasets have…

The solution of linear inverse problems arising, for example, in signal and image processing is a challenging problem since the ill-conditioning amplifies, in the solution, the noise present in the data. Recently introduced algorithms based…

Image alignment across domains has recently become one of the realistic and popular topics in the research community. In this problem, a deep learning-based image alignment method is usually trained on an available largescale database.…

Single image super-resolution (SR) via deep learning has recently gained significant attention in the literature. Convolutional neural networks (CNNs) are typically learned to represent the mapping between low-resolution (LR) and…

In the recent years, there has been a significant improvement in the quality of samples produced by (deep) generative models such as variational auto-encoders and generative adversarial networks. However, the representation capabilities of…

Model-based optimization methods and discriminative learning methods have been the two dominant strategies for solving various inverse problems in low-level vision. Typically, those two kinds of methods have their respective merits and…

We examine the theoretical properties of enforcing priors provided by generative deep neural networks via empirical risk minimization. In particular we consider two models, one in which the task is to invert a generative neural network…

Inverse scattering problems, such as those in electromagnetic imaging using phaseless data (PD-ISPs), involve imaging objects using phaseless measurements of wave scattering. Such inverse problems can be highly non-linear and ill-posed…

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…

In inverse problems, it is widely recognized that the incorporation of a sparsity prior yields a regularization effect on the solution. This approach is grounded on the a priori assumption that the unknown can be appropriately represented…

Learning a good image prior is a long-term goal for image restoration and manipulation. While existing methods like deep image prior (DIP) capture low-level image statistics, there are still gaps toward an image prior that captures rich…

Deep generative models (e.g. GANs and VAEs) have been developed quite extensively in recent years. Lately, there has been an increased interest in the inversion of such a model, i.e. given a (possibly corrupted) signal, we wish to recover…

Different rain models and novel network structures have been proposed to remove rain streaks from single rainy images. In this work, we bring attention to the intrinsic priors and multi-scale features of the rainy images, and develop…

Incorporating prior knowledge on model unknowns of interest is essential when dealing with ill-posed inverse problems due to the nonuniqueness of the solution and data noise. Unfortunately, it is not trivial to fully describe our priors in…

The ability of deep image prior (DIP) to recover high-quality images from incomplete or corrupted measurements has made it popular in inverse problems in image restoration and medical imaging including magnetic resonance imaging (MRI).…

Training neural networks is a challenging non-convex optimization problem, and backpropagation or gradient descent can get stuck in spurious local optima. We propose a novel algorithm based on tensor decomposition for guaranteed training of…

We mainly analyze and solve the overfitting problem of deep image prior (DIP). Deep image prior can solve inverse problems such as super-resolution, inpainting and denoising. The main advantage of DIP over other deep learning approaches is…

We present the first framework to solve linear inverse problems leveraging pre-trained latent diffusion models. Previously proposed algorithms (such as DPS and DDRM) only apply to pixel-space diffusion models. We theoretically analyze our…

Inverse problems are ubiquitous in nature, arising in almost all areas of science and engineering ranging from geophysics and climate science to astrophysics and biomechanics. One of the central challenges in solving inverse problems is…

Advances in compressive sensing provided reconstruction algorithms of sparse signals from linear measurements with optimal sample complexity, but natural extensions of this methodology to nonlinear inverse problems have been met with…