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Abstrakt
The atomic norm provides a generalization of the ℓ _{1}norm to continuous parameter spaces. When applied as a sparse regularizer for line spectral estimation the solution can be obtained by solving a convex optimization problem. This problem is known as atomic norm soft thresholding (AST). It can be cast as a semidefinite program and solved by standard methods. In the semidefinite formulation there are O(N ^{2}) dual variables which complicates the implementation of a standard primaldual interiorpoint method based on symmetric cones. That has lead researchers to consider the alternating direction method of multipliers (ADMM) for the solution of AST, but this method is still somewhat slow for large problem sizes. To obtain a faster algorithm we reformulate AST as a nonsymmetric conic program. That has two properties of key importance to its numerical solution: the conic formulation has only O(N) dual variables and the Toeplitz structure inherent to AST is preserved. Based on it we derive FastAST which is a primaldual interiorpoint method for solving AST. Two variants are considered with the fastest one requiring only O(N ^{2}) flops per iteration. Extensive numerical experiments demonstrate that both variants of FastAST solve AST significantly faster than a stateoftheart solver based on ADMM.
Originalsprog  Engelsk 

Tidsskrift  Signal Processing 
Vol/bind  165 
Sider (fratil)  719 
Antal sider  13 
ISSN  01651684 
DOI  
Status  Udgivet  dec. 2019 
Fingeraftryk
Dyk ned i forskningsemnerne om 'A Fast InteriorPoint Method for Atomic Norm Soft Thresholding'. Sammen danner de et unikt fingeraftryk.Projekter
 1 Afsluttet

RTC: Computational Oriented Realtime Convex Optimization in Signal Processing
Jensen, T., Jensen, S. H., Larsen, T., Giacobello, D., Dahl, J. & Diehl, M.
The Danish Council for Independent Research Technology and Production Sciences, Danmarks Frie Forskningsfond  Sapere Aude
01/06/2014 → 30/06/2017
Projekter: Projekt › Forskning