Related papers: A primal-dual algorithm for image reconstruction w…
We consider the variational reconstruction framework for inverse problems and propose to learn a data-adaptive input-convex neural network (ICNN) as the regularization functional. The ICNN-based convex regularizer is trained adversarially…
While variational methods have been among the most powerful tools for solving linear inverse problems in imaging, deep (convolutional) neural networks have recently taken the lead in many challenging benchmarks. A remaining drawback of deep…
We propose a new image restoration model based on the minimized surface regularization. The proposed model closely relates to the classical smoothing ROF model \cite{4}. We can reformulate the proposed model as a min-max problem and solve…
Our work considers the optimization of the sum of a non-smooth convex function and a finite family of composite convex functions, each one of which is composed of a convex function and a bounded linear operator. This type of problem is…
We propose an extended primal-dual algorithm framework for solving a general nonconvex optimization model. This work is motivated by image reconstruction problems in a class of nonlinear imaging, where the forward operator can be formulated…
Neural networks have shown tremendous potential for reconstructing high-resolution images in inverse problems. The non-convex and opaque nature of neural networks, however, hinders their utility in sensitive applications such as medical…
We propose a new randomized algorithm for solving convex optimization problems that have a large number of constraints (with high probability). Existing methods like interior-point or Newton-type algorithms are hard to apply to such…
In this paper, we develop unrolled neural networks to solve constrained optimization problems, offering accelerated, learnable counterparts to dual ascent (DA) algorithms. Our framework, termed constrained dual unrolling (CDU), comprises…
Data assisted reconstruction algorithms, incorporating trained neural networks, are a novel paradigm for solving inverse problems. One approach is to first apply a classical reconstruction method and then apply a neural network to improve…
Variational regularisation is the primary method for solving inverse problems, and recently there has been considerable work leveraging deeply learned regularisation for enhanced performance. However, few results exist addressing the…
The emergence of deep-learning-based methods to solve image-reconstruction problems has enabled a significant increase in reconstruction quality. Unfortunately, these new methods often lack reliability and explainability, and there is a…
We present a primal-dual algorithmic framework to obtain approximate solutions to a prototypical constrained convex optimization problem, and rigorously characterize how common structural assumptions affect the numerical efficiency. Our…
Recovering high-resolution images from limited sensory data typically leads to a serious ill-posed inverse problem, demanding inversion algorithms that effectively capture the prior information. Learning a good inverse mapping from training…
Image restoration remains a challenging task in image processing. Numerous methods tackle this problem, often solved by minimizing a non-smooth penalized co-log-likelihood function. Although the solution is easily interpretable with…
The work seeks to develop an algorithm for image reconstruction by directly inverting the non-linear data model in spectral CT. Using the non-linear data model, we formulate the image-reconstruction problem as a non-convex optimization…
Magnetic resonance imaging (MRI) is known to be a slow imaging modality and undersampling in k-space has been used to increase the imaging speed. However, image reconstruction from undersampled k-space data is an ill-posed inverse problem.…
Using an optimization algorithm to solve a machine learning problem is one of mainstreams in the field of science. In this work, we demonstrate a comprehensive comparison of some state-of-the-art first-order optimization algorithms for…
We study iterative regularization for linear models, when the bias is convex but not necessarily strongly convex. We characterize the stability properties of a primal-dual gradient based approach, analyzing its convergence in the presence…
We introduce a method for fast estimation of data-adapted, spatio-temporally dependent regularization parameter-maps for variational image reconstruction, focusing on total variation (TV)-minimization. Our approach is inspired by recent…
We consider structured minimization problems subject to smooth inequality constraints and present a flexible algorithm that combines interior point (IP) and proximal gradient schemes. While traditional IP methods cannot cope with nonsmooth…