Inverse problems with nonnegative and sparse solutions: algorithms and application to the phase retrieval problem

DOI10.1088/1361-6420/aab6c9zbMath1393.78014OpenAlexW2793508829WikidataQ130122446 ScholiaQ130122446MaRDI QIDQ4569355

Pham Quy Muoi, Dinh Nho Hào, Nguyen Huu Cong, Cuong Dang, Sujit Kumar Sahoo, Dongliang Tang

Publication date: 28 June 2018

Published in: Inverse Problems (Search for Journal in Brave)

Full work available at URL: https://hdl.handle.net/10356/106501

zbMATH Keywords

inverse problemsgradient-type algorithmphase retrieval problemnonnegative sparse regularizationnonnegative and sparse solutions

Mathematics Subject Classification ID

Ill-posedness and regularization problems in numerical linear algebra (65F22) Numerical optimization and variational techniques (65K10) Newton-type methods (49M15) Nonsmooth analysis (49J52) Methods of quasi-Newton type (90C53) Technical applications of optics and electromagnetic theory (78A55) Optimization problems in optics and electromagnetic theory (78M50)

Related Items

Convergence of proximal algorithms with stepsize controls for non-linear inverse problems and application to sparse non-negative matrix factorization, \(l^1\)-weighted regularization for the problem of recovering sparse initial conditions in parabolic equations from final measurements

Uses Software

• PhaseCut

Cites Work

• Unnamed Item
• A Fast Iterative Shrinkage-Thresholding Algorithm for Linear Inverse Problems
• Phase retrieval for imaging problems
• Convergence rates for total variation regularization of coefficient identification problems in elliptic equations. II
• Convergence rates for Tikhonov regularization of a two-coefficient identification problem in an elliptic boundary value problem
• Non-convex sparse regularisation
• On the recovery of a 2-D function from the modulus of its Fourier transform
• Descent gradient methods for nonsmooth minimization problems in ill-posed problems
• Some first-order algorithms for total variation based image restoration
• Superlinear convergence of smoothing quasi-Newton methods for nonsmooth equations
• Gradient descent for Tikhonov functionals with sparsity constraints: theory and numerical comparison of step size rules
• Semismooth Newton and quasi-Newton methods in weighted ℓ¹-regularization
• Convergence rates for total variation regularization of coefficient identification problems in elliptic equations I
• Necessary and sufficient conditions for linear convergence of ℓ1-regularization
• Reconstructing conductivity coefficients based on sparsity regularization and measured data in electrical impedance tomography
• A semismooth Newton method for Tikhonov functionals with sparsity constraints
• Convergence rates and source conditions for Tikhonov regularization with sparsity constraints
• Sparse regularization with l ^q penalty term
• Efficient Schemes for Total Variation Minimization Under Constraints in Image Processing
• Semismooth Newton Methods for Operator Equations in Function Spaces
• The Primal-Dual Active Set Strategy as a Semismooth Newton Method
• An iterative thresholding algorithm for linear inverse problems with a sparsity constraint
• Learning the parts of objects by non-negative matrix factorization
• A generalized conditional gradient method for nonlinear operator equations with sparsity constraints
• Mathematical problems in image processing. Partial differential equations and the calculus of variations. Foreword by Olivier Faugeras