Compressed-sensing MRI with random encoding

Justin P. Haldar, Diego Hernando, Zhi Pei Liang

Research output: Contribution to journalArticlepeer-review


Compressed sensing (CS) has the potential to reduce magnetic resonance (MR) data acquisition time. In order for CS-based imaging schemes to be effective, the signal of interest should be sparse or compressible in a known representation, and the measurement scheme should have good mathematical properties with respect to this representation. While MR images are often compressible, the second requirement is often only weakly satisfied with respect to commonly used Fourier encoding schemes. This paper investigates the use of random encoding for CS-MRI, in an effort to emulate the universal encoding schemes suggested by the theoretical CS literature. This random encoding is achieved experimentally with tailored spatially-selective radio-frequency (RF) pulses. Both simulation and experimental studies were conducted to investigate the imaging properties of this new scheme with respect to Fourier schemes. Results indicate that random encoding has the potential to outperform conventional encoding in certain scenarios. However, our study also indicates that random encoding fails to satisfy theoretical sufficient conditions for stable and accurate CS reconstruction in many scenarios of interest. Therefore, there is still no general theoretical performance guarantee for CS-MRI, with or without random encoding, and CS-based methods should be developed and validated carefully in the context of specific applications.

Original languageEnglish (US)
Article number5599301
Pages (from-to)893-903
Number of pages11
JournalIEEE transactions on medical imaging
Issue number4
StatePublished - Apr 2011


  • Compressed sensing
  • magnetic resonance imaging (MRI)
  • radio-frequency encoding

ASJC Scopus subject areas

  • Electrical and Electronic Engineering
  • Computer Science Applications
  • Radiological and Ultrasound Technology
  • Software


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