52 citations · 385 across the 25 of their papers we have counts for
25 papers
Stochastic mirror descent method for linear ill-posed problems in Banach spaces
Qinian Jin, Xiliang Lu, Liuying Zhang
Consider linear ill-posed problems governed by the system for , where each is a bounded linear operator from a Banach space to a Hilbert sp…
Imaging Conductivity from Current Density Magnitude using Neural Networks
Bangti Jin, Xiyao Li, Xiliang Lu
Conductivity imaging represents one of the most important tasks in medical imaging. In this work we develop a neural network based reconstruction technique for imaging the conducti…
Imaging Anisotropic Conductivities from Current Densities
Huan Liu, Bangti Jin, Xiliang Lu
In this paper, we propose and analyze a reconstruction algorithm for imaging an anisotropic conductivity tensor in a second-order elliptic PDE with a nonzero Dirichlet boundary con…
Convergence Rate Analysis of Galerkin Approximation of Inverse Potential Problem
Bangti Jin, Xiliang Lu, Qimeng Quan +1
In this work we analyze the inverse problem of recovering the space-dependent potential coefficient in an elliptic / parabolic problem from distributed observation. We establish no…
Convergence Rate Analysis for Deep Ritz Method
Chenguang Duan, Yuling Jiao, Yanming Lai +2
Using deep neural networks to solve PDEs has attracted a lot of attentions recently. However, why the deep learning method works is falling far behind its empirical success. In thi…
Generative Learning With Euler Particle Transport
Yuan Gao, Jian Huang, Yuling Jiao +3
We propose an Euler particle transport (EPT) approach for generative learning. The proposed approach is motivated by the problem of finding an optimal transport map from a referenc…
Robust Decoding from Binary Measurements with Cardinality Constraint Least Squares
Zhao Ding, Junjun Huang, Yuling Jiao +2
The main goal of 1-bit compressive sampling is to decode dimensional signals with sparsity level from binary measurements. This is a challenging task due to the presenc…
Sparse Signal Recovery from Phaseless Measurements via Hard Thresholding Pursuit
Jian-Feng Cai, Jingzhi Li, Xiliang Lu +1
In this paper, we consider the sparse phase retrieval problem, recovering an -sparse signal from phaseless samples $y_i=|\langle\bm{x}^{\n…
A Support Detection and Root Finding Approach for Learning High-dimensional Generalized Linear Models
Jian Huang, Yuling Jiao, Lican Kang +3
Feature selection is important for modeling high-dimensional data, where the number of variables can be much larger than the sample size. In this paper, we develop a support detect…
On Newton Screening
Jian Huang, Yuling Jiao, Lican Kang +4
Screening and working set techniques are important approaches to reducing the size of an optimization problem. They have been widely used in accelerating first-order methods for so…
A stochastic alternating minimizing method for sparse phase retrieval
Jianfeng Cai, Yuling Jiao, Xiliang Lu +1
Sparse phase retrieval plays an important role in many fields of applied science and thus attracts lots of attention. In this paper, we propose a \underline{sto}chastic alte\underl…
SNAP: A semismooth Newton algorithm for pathwise optimization with optimal local convergence rate and oracle properties
Jian Huang, Yuling Jiao, Xiliang Lu +2
We propose a semismooth Newton algorithm for pathwise optimization (SNAP) for the LASSO and Enet in sparse, high-dimensional linear regression. SNAP is derived from a suitable form…
Oblique Stripe Removal in Remote Sensing Images via Oriented Variation
Xinxin Liu, Xiliang Lu, Huanfeng Shen +2
Destriping is a classical problem in remote sensing image processing. Although considerable effort has been made to remove stripes, few of the existing methods can eliminate stripe…
On the Regularizing Property of Stochastic Gradient Descent
Bangti Jin, Xiliang Lu
Stochastic gradient descent is one of the most successful approaches for solving large-scale problems, especially in machine learning and statistics. At each iteration, it employs…
Robust Decoding from 1-Bit Compressive Sampling with Least Squares
Jian Huang, Yuling Jiao, Xiliang Lu +1
In 1-bit compressive sensing (1-bit CS) where target signal is coded into a binary measurement, one goal is to recover the signal from noisy and quantized samples. Mathematically,…
Preasymptotic Convergence of Randomized Kaczmarz Method
Yuling Jiao, Bangti Jin, Xiliang Lu
Kaczmarz method is one popular iterative method for solving inverse problems, especially in computed tomography. Recently, it was established that a randomized version of the metho…
Iterative Soft/Hard Thresholding with Homotopy Continuation for Sparse Recovery
Yuling Jiao, Bangti Jin, Xiliang Lu
In this note, we analyze an iterative soft / hard thresholding algorithm with homotopy continuation for recovering a sparse signal from noisy data of a noise level . Under…
A Constructive Approach to High-dimensional Regression
Jian Huang, Yuling Jiao, Yanyan Liu +1
We develop a constructive approach to estimating sparse, high-dimensional linear regression models. The approach is a computational algorithm motivated from the KKT conditions for…
Alternating Direction Method of Multipliers for Linear Inverse Problems
Yuling Jiao, Qinian Jin, Xiliang Lu +1
In this paper we propose an iterative method using alternating direction method of multipliers (ADMM) strategy to solve linear inverse problems in Hilbert spaces with general conve…
Group Sparse Recovery via the Penalty: Theory and Algorithm
Yuling Jiao, Bangti Jin, Xiliang Lu
In this work we propose and analyze a novel approach for group sparse recovery. It is based on regularized least squares with an penalty, which penalizes the numbe…
A simple finite element method for the boundary value problem with a Riemann-Liouville derivative
Bangti Jin, Raytcho Lazarov, Xiliang Lu +1
We consider a boundary value problem involving a Riemann-Liouville fractional derivative of order on the unit interval . The standard Galerkin finite element…
A Primal Dual Active Set with Continuation Algorithm for the \ell^0-Regularized Optimization Problem
Yuling Jiao, Bangti Jin, Xiliang Lu
We develop a primal dual active set with continuation algorithm for solving the \ell^0-regularized least-squares problem that frequently arises in compressed sensing. The algorithm…
A fast nonstationary iterative method with convex penalty for inverse problems in Hilbert spaces
Qinian Jin, Xiliang Lu
In this paper we consider the computation of approximate solutions for inverse problems in Hilbert spaces. In order to capture the special feature of solutions, non-smooth convex f…
A Primal Dual Active Set Algorithm with Continuation for Compressed Sensing
Qibin Fan, Yuling Jiao, Xiliang Lu
The success of compressed sensing relies essentially on the ability to efficiently find an approximately sparse solution to an under-determined linear system. In this paper, we dev…