Low-Rank + Sparse (L+S) reconstruction for accelerated dynamic MRI with separation of background and dynamic components

Ricardo Otazo, Daniel K. Sodickson, Emmanuel J. Candès

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


L+S matrix decomposition finds the low-rank (L) and sparse (S) components of a matrix M by solving the following convex optimization problem: min||L||* + γ||S||1 subject to M = L + S, where ||L||* is the nuclear-norm or sum of singular values of L and ||S||1 is the l1-norm or sum of absolute values of S. This work presents the application of the L+S decomposition to reconstruct incoherently undersampled dynamic MRI data as a superposition of a slowly or coherently changing background and sparse innovations. Feasibility of the method was tested in several accelerated dynamic MRI experiments including cardiac perfusion, time-resolved peripheral angiography and liver perfusion using Cartesian and radial sampling. The high acceleration and background separation enabled by L+S reconstruction promises to enhance spatial and temporal resolution and to enable background suppression without the need of subtraction or modeling.

Original languageEnglish (US)
Title of host publicationWavelets and Sparsity XV
StatePublished - 2013
EventWavelets and Sparsity XV - San Diego, CA, United States
Duration: Aug 26 2013Aug 29 2013

Publication series

NameProceedings of SPIE - The International Society for Optical Engineering
ISSN (Print)0277-786X
ISSN (Electronic)1996-756X


OtherWavelets and Sparsity XV
Country/TerritoryUnited States
CitySan Diego, CA


  • Compressed sensing
  • Dynamic MRI
  • Low-rank matrix completion
  • Sparsity

ASJC Scopus subject areas

  • Electronic, Optical and Magnetic Materials
  • Condensed Matter Physics
  • Computer Science Applications
  • Applied Mathematics
  • Electrical and Electronic Engineering


Dive into the research topics of 'Low-Rank + Sparse (L+S) reconstruction for accelerated dynamic MRI with separation of background and dynamic components'. Together they form a unique fingerprint.

Cite this