Compressive sensing MRI with complex sparsification

Ying Dong, Jim Ji

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


Compressive Sensing Magnetic Resonance Imaging (CS-MRI) has been rapidly developed during last several years. To reconstruct an image from incomplete data using compressive sensing, the image has to be sparse or can be transformed to sparse representation. Gradient operators associated with total variation (TV) and discrete wavelet transform (DWT) are two commonly used sparsifying transforms in CS-MRI. Since the data acquired in MRI are complex, these transforms are usually applied to the real and the imaginary parts of the image independently. In this paper, we will explore the application of the complex wavelet transform (CWT) as a more effective sparsifying transform for CS-MRI. Specifically, dual-tree complex wavelet transform (DT-CWT), a CWT previously used for real or complex image compression, is integrated with compressive sensing reconstruction algorithm. We will test the new method using both simulated and in-vivo MRI data. The results will be compared with those of DWT and TV, which show that the new method can achieve better sparsity and reduced reconstruction errors in CS-MRI.

Original languageEnglish
Title of host publicationWavelets and Sparsity XIV
Publication statusPublished - 2011
Externally publishedYes
EventWavelets and Sparsity XIV - San Diego, CA, United States
Duration: 21 Aug 201124 Aug 2011


OtherWavelets and Sparsity XIV
CountryUnited States
CitySan Diego, CA



  • complex wavelet transform
  • Compressive sensing
  • MRI
  • sparsity

ASJC Scopus subject areas

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

Cite this

Dong, Y., & Ji, J. (2011). Compressive sensing MRI with complex sparsification. In Wavelets and Sparsity XIV (Vol. 8138). [81381I]