An interior point method for nonnegative sparse signal reconstruction

Xiang Huang, Kuan He, Seunghwan Yoo, Oliver Strides Cossairt, Aggelos K Katsaggelos, Nicola Ferrier, Mark Hereld

Research output: Chapter in Book/Report/Conference proceedingConference contribution

4 Scopus citations


We present a primal-dual interior point method (IPM) with a novel preconditioner to solve the ℓ 1 -norm regularized least square problem for nonnegative sparse signal reconstruction. IPM is a second-order method that uses both gradient and Hessian information to compute effective search directions and achieve super-linear convergence rates. It therefore requires many fewer iterations than first-order methods such as iterative shrinkage/thresholding algorithms (ISTA) that only achieve sub-linear convergence rates. However, each iteration of IPM is more expensive than in ISTA because it needs to evaluate an inverse of a Hessian matrix to compute the Newton direction. We propose to approximate each Hessian matrix by a diagonal matrix plus a rank-one matrix. This approximation matrix is easily invertible using the Sherman-Morrison formula, and is used as a novel preconditioner in a preconditioned conjugate gradient method to compute a truncated Newton direction. We demonstrate the efficiency of our algorithm in compressive 3D volumetric image reconstruction. Numerical experiments show favorable results of our method in comparison with previous interior point based and iterative shrinkage/thresholding based algorithms.

Original languageEnglish (US)
Title of host publication2018 IEEE International Conference on Image Processing, ICIP 2018 - Proceedings
PublisherIEEE Computer Society
Number of pages5
ISBN (Electronic)9781479970612
StatePublished - Aug 29 2018
Event25th IEEE International Conference on Image Processing, ICIP 2018 - Athens, Greece
Duration: Oct 7 2018Oct 10 2018

Publication series

NameProceedings - International Conference on Image Processing, ICIP
ISSN (Print)1522-4880


Conference25th IEEE International Conference on Image Processing, ICIP 2018


  • 3d volumetric image reconstruction
  • Compressive sensing
  • Nonnegative sparse
  • Norm regularized optimization
  • Primal-dual preconditioned interior point method

ASJC Scopus subject areas

  • Software
  • Computer Vision and Pattern Recognition
  • Signal Processing


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