Lp Quasi-norm Minimization

M. E. Ashour, C. M. Lagoa, N. S. Aybat

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

2 Scopus citations


The ℓp (0 < p < 1) quasi-norm is used as a sparsity-inducing function, and has applications in diverse areas, e.g., statistics, machine learning, and signal processing. This paper proposes a heuristic based on a two-block ADMM algorithm for tackling ℓp quasi-norm minimization problems. For p = s/q < 1, s, q +, the proposed algorithm requires solving for the roots of a scalar degree 2q polynomial as opposed to applying a soft thresholding operator in the case of ℓ1. We show numerical results for two example applications, sparse signal reconstruction from few noisy measurements and spam email classification using support vector machines. Our method obtains significantly sparser solutions than those obtained by ℓ1 minimization while achieving similar level of measurement fitting in signal reconstruction, and training and test set accuracy in classification.

Original languageEnglish (US)
Title of host publicationConference Record - 53rd Asilomar Conference on Circuits, Systems and Computers, ACSSC 2019
EditorsMichael B. Matthews
PublisherIEEE Computer Society
Number of pages5
ISBN (Electronic)9781728143002
StatePublished - Nov 2019
Event53rd Asilomar Conference on Circuits, Systems and Computers, ACSSC 2019 - Pacific Grove, United States
Duration: Nov 3 2019Nov 6 2019

Publication series

NameConference Record - Asilomar Conference on Signals, Systems and Computers
ISSN (Print)1058-6393


Conference53rd Asilomar Conference on Circuits, Systems and Computers, ACSSC 2019
Country/TerritoryUnited States
CityPacific Grove

All Science Journal Classification (ASJC) codes

  • Signal Processing
  • Computer Networks and Communications


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