Related papers: Optimization for Amortized Inverse Problems
The recently introduced Gradient Methods with Memory use a subset of the past oracle information to create an accurate model of the objective function that enables them to surpass the Gradient Method in practical performance. The model…
Given a set of observations generated by an optimization process, the goal of inverse optimization is to determine likely parameters of that process. We cast inverse optimization as a form of deep learning. Our method, called deep inverse…
We propose Amortized Posterior Sampling (APS), a novel variational inference approach for efficient posterior sampling in inverse problems. Our method trains a conditional flow model to minimize the divergence between the variational…
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…
This paper proposes a novel framework to regularize the highly ill-posed and non-linear Fourier ptychography problem using generative models. We demonstrate experimentally that our proposed algorithm, Deep Ptych, outperforms the existing…
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…
Prior probability models are a fundamental component of many image processing problems, but density estimation is notoriously difficult for high-dimensional signals such as photographic images. Deep neural networks have provided…
Recently, deep generative models have been used for posterior inference in inverse problems, including high-stakes applications in medical imaging and scientific discovery, where the uncertainty of a prediction can matter as much as the…
Diffusion models have recently emerged as powerful generative priors for solving inverse problems. However, training diffusion models in the pixel space are both data-intensive and computationally demanding, which restricts their…
The reconstruction of X-rays CT images from sparse or limited-angle geometries is a highly challenging task. The lack of data typically results in artifacts in the reconstructed image and may even lead to object distortions. For this…
This paper studies a class of distributed optimization problems with coupled equality constraints in networked systems. Many existing distributed algorithms rely on solving local subproblems via the $\operatorname{argmin}$ operator in each…
We consider amortized Bayesian inference for nonlinear inverse problems in settings where only samples from the joint distribution of parameters and observations are available. Classical methods such as Markov chain Monte Carlo require…
In practice, optimization tasks have some structure that allows developing new algorithms for every problem with faster convergence rates. Using the structure of optimization tasks, we can propose algorithms with more optimistic convergence…
Conventional inverse optimization inputs a solution and finds the parameters of an optimization model that render a given solution optimal. The literature mostly focuses on inferring the objective function in linear problems when accepted…
Deep neural network approaches to inverse imaging problems have produced impressive results in the last few years. In this paper, we consider the use of generative models in a variational regularisation approach to inverse problems. The…
We study a class of algorithms for solving bilevel optimization problems in both stochastic and deterministic settings when the inner-level objective is strongly convex. Specifically, we consider algorithms based on inexact implicit…
Obtaining a useful estimate of an object from highly incomplete imaging measurements remains a holy grail of imaging science. Deep learning methods have shown promise in learning object priors or constraints to improve the conditioning of…
This paper proposes a novel approach to regularize the ill-posed blind image deconvolution (blind image deblurring) problem using deep generative networks. We employ two separate deep generative models - one trained to produce sharp images…
Gaussian processes (GPs) are Bayesian nonparametric models for function approximation with principled predictive uncertainty estimates. Deep Gaussian processes (DGPs) are multilayer generalizations of GPs that can represent complex marginal…
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…