Nonlocal low-rank and sparse matrix decomposition for spectral CT reconstruction

Shanzhou Niu, Gaohang Yu, Jianhua Ma, Jing Wang

Research output: Contribution to journalArticlepeer-review

44 Scopus citations


Spectral computed tomography (CT) has been a promising technique in research and clinics because of its ability to produce improved energy resolution images with narrow energy bins. However, the narrow energy bin image is often affected by serious quantum noise because of the limited number of photons used in the corresponding energy bin. To address this problem, we present an iterative reconstruction method for spectral CT using nonlocal low-rank and sparse matrix decomposition (NLSMD), which exploits the self-similarity of patches that are collected in multi-energy images. Specifically, each set of patches can be decomposed into a low-rank component and a sparse component, and the low-rank component represents the stationary background over different energy bins, while the sparse component represents the rest of the different spectral features in individual energy bins. Subsequently, an effective alternating optimization algorithm was developed to minimize the associated objective function. To validate and evaluate the NLSMD method, qualitative and quantitative studies were conducted by using simulated and real spectral CT data. Experimental results show that the NLSMD method improves spectral CT images in terms of noise reduction, artifact suppression and resolution preservation.

Original languageEnglish (US)
Article number024003
JournalInverse Problems
Issue number2
StatePublished - Feb 2018


  • image reconstruction, nonlocal low-rank and sparse matrix decomposition (NLSMD)
  • photon counting detector (PCD)
  • spectral CT

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Signal Processing
  • Mathematical Physics
  • Computer Science Applications
  • Applied Mathematics


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