相关论文: A semi-implicit relaxed Douglas-Rachford algorithm…

Uniqueness of solution is proved for any ptychographic scheme with a random masks under a minimum overlap condition and local geometric convergence analysis is given for the alternating projection (AP) and Douglas-Rachford (DR) algorithms.…

Generalized inverses play a fundamental role in numerical linear algebra, particularly when matrices are rectangular, singular, or rank deficient. Even when the input matrix is sparse, generalized inverses such as the M-P pseudoinverse are…

Ever brighter light sources, fast parallel detectors, and advances in phase retrieval methods, have made ptychography a practical and popular imaging technique. Compared to previous techniques, ptychography provides superior robustness and…

The Douglas-Rachford algorithm (DRA) is a powerful optimization method for minimizing the sum of two convex (not necessarily smooth) functions. The vast majority of previous research dealt with the case when the sum has at least one…

Physics-driven deep learning (PD-DL) models have proven to be a powerful approach for improved reconstruction of rapid MRI scans. In order to train these models in scenarios where fully-sampled reference data is unavailable, self-supervised…

The Inertia Relief (IR) technique is widely used by industry and produces equilibrated loads allowing to analyze unconstrained systems without resorting to the more expensive full dynamic analysis. The main goal of this work is to develop a…

Supervised Deep-Learning (DL)-based reconstruction algorithms have shown state-of-the-art results for highly-undersampled dynamic Magnetic Resonance Imaging (MRI) reconstruction. However, the requirement of excessive high-quality…

Objective: To propose and validate an unsupervised MRI reconstruction method that does not require fully sampled k-space data. Materials and Methods: The proposed method, deep image prior with structured sparsity (DISCUS), extends the deep…

We expand upon previous work that examined behavior of the iterated Douglas-Rachford method for a line and a circle by considering two generalizations: that of a line and an ellipse and that of a line together with a $p$-sphere. With…

Convex optimization has become ubiquitous in most quantitative disciplines of science, including variational image processing. Proximal splitting algorithms are becoming popular to solve such structured convex optimization problems. Within…

Sufficient dimension reduction (SDR) is continuing an active research field nowadays for high dimensional data. It aims to estimate the central subspace (CS) without making distributional assumption. To overcome the large-$p$-small-$n$…

In this paper, we propose several graph-based extensions of the Douglas-Rachford splitting (DRS) method to solve monotone inclusion problems involving the sum of $N$ maximal monotone operators. Our construction is based on a two-layer…

In this paper, we study the generalized Douglas-Rachford algorithm and its cyclic variants which include many projection-type methods such as the classical Douglas-Rachford algorithm and the alternating projection algorithm. Specifically,…

Distribution Regression (DR) on stochastic processes describes the learning task of regression on collections of time series. Path signatures, a technique prevalent in stochastic analysis, have been used to solve the DR problem. Recent…

Ptychography is a data-intensive computational imaging technique that achieves high spatial resolution over large fields of view. The technique involves scanning a coherent beam across overlapping regions and recording diffraction patterns.…

The Douglas--Rachford (DR) and alternating direction method of multipliers (ADMM) are two proximal splitting algorithms designed to minimize the sum of two proper lower semi-continuous convex functions whose proximity operators are easy to…

We study the cyclic relaxed Douglas-Rachford algorithm for possibly nonconvex, and inconsistent feasibility problems. This algorithm can be viewed as a convex relaxation between the cyclic Douglas-Rachford algorithm first introduced by…

The Douglas-Rachford algorithm is a classical and very successful method for solving optimization and feasibility problems. In this paper, we provide novel conditions sufficient for finite convergence in the context of convex feasibility…

Dimensionality reduction (DR) is a popular method for preparing and analyzing high-dimensional data. Reduced data representations are less computationally intensive and easier to manage and visualize, while retaining a significant…

Ptychography is a computational method of microscopy that recovers high-resolution transmission images of samples from a series of diffraction patterns. While conventional phase retrieval algorithms can iteratively recover the images, they…