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Composite minimization is a powerful framework in large-scale convex optimization, based on decoupling of the objective function into terms with structurally different properties and allowing for more flexible algorithmic design. We…

Compression of hyperspectral images onboard of spacecrafts is a tradeoff between the limited computational resources and the ever-growing spatial and spectral resolution of the optical instruments. As such, it requires low-complexity…

In this paper we present an efficient active-set method for the solution of convex quadratic programming problems with general piecewise-linear terms in the objective, with applications to sparse approximations and risk-minimization. The…

Markov Chain Monte Carlo (MCMC) algorithms are standard approaches to solve imaging inverse problems and quantify estimation uncertainties, a key requirement in absence of ground-truth data. To improve estimation quality, Plug-and-Play MCMC…

The orthogonalization process is an essential building block in Krylov space methods, which takes up a large portion of the computational time. Commonly used methods, like the Gram-Schmidt method, consider the projection and normalization…

Magnetic resonance imaging (MRI) is a powerful noninvasive diagnostic imaging tool that provides unparalleled soft tissue contrast and anatomical detail. Noise contamination, especially in accelerated and/or low-field acquisitions, can…

Compressed Sensing (CS) significantly speeds up Magnetic Resonance Image (MRI) processing and achieves accurate MRI reconstruction from under-sampled k-space data. According to the current research, there are still several problems with…

The restoration of images affected by blur and noise has been widely studied and has broad potential for applications including in medical imaging modalities like computed tomography (CT). Although the blur and noise in CT images can be…

Incoherent k-space undersampling and deep learning-based reconstruction methods have shown great success in accelerating MRI. However, the performance of most previous methods will degrade dramatically under high acceleration factors, e.g.,…

Plug-and-Play (PnP) methods are efficient iterative algorithms for solving ill-posed image inverse problems. PnP methods are obtained by using deep Gaussian denoisers instead of the proximal operator or the gradient-descent step within…

Since its discovery over the last decade, Compressed Sensing (CS) has been successfully applied to Magnetic Reso- nance Imaging (MRI). It has been shown to be a powerful way to reduce scanning time without sacrificing image quality. MR…

Inspired by the remarkable success of large neural networks, there has been significant interest in understanding the generalization performance of over-parameterized models. Substantial efforts have been invested in characterizing how…

Deep learning models are often successfully trained using gradient descent, despite the worst case hardness of the underlying non-convex optimization problem. The key question is then under what conditions can one prove that optimization…

Accelerating magnetic resonance image (MRI) reconstruction process is a challenging ill-posed inverse problem due to the excessive under-sampling operation in k-space. In this paper, we propose a recurrent transformer model, namely…

Gradient compression is of growing interests for solving constrained optimization problems including compressed sensing, noisy recovery and matrix completion under limited communication resources and storage costs. Convergence analysis of…

Markov random fields (MRFs) have been widely used as prior models in various inverse problems such as tomographic reconstruction. While MRFs provide a simple and often effective way to model the spatial dependencies in images, they suffer…

The application of compressed sensing (CS)-enabled data reconstruction for accelerating magnetic resonance imaging (MRI) remains a challenging problem. This is due to the fact that the information lost in k-space from the acceleration mask…

Following the success of deep learning in a wide range of applications, neural network-based machine-learning techniques have received significant interest for accelerating magnetic resonance imaging (MRI) acquisition and reconstruction…

Discretization of continuous stochastic processes is needed to numerically simulate them or to infer models from experimental time series. However, depending on the nature of the process, the same discretization scheme, if not accurate…

Dynamic imaging addresses the recovery of a time-varying 2D or 3D object at each time instant using its undersampled measurements. In particular, in the case of dynamic tomography, only a single projection at a single view angle may be…