High-frequency subband compressed sensing MRI using quadruplet sampling


  • Kyunghyun Sung,

    Corresponding author
    1. Department of Radiology, Stanford University, Stanford, California, USA
    2. Department of Radiological Sciences, University of California Los Angeles, Los Angeles, California, USA
    • UCLA Department of Radiological Sciences, 300 UCLA Medical Plaza, Suite B119, Los Angeles, CA 90095. E-mail: ksung@mednet.ucla.edu

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  • Brian A. Hargreaves

    1. Department of Radiology, Stanford University, Stanford, California, USA
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To present and validate a new method that formalizes a direct link between k-space and wavelet domains to apply separate undersampling and reconstruction for high- and low-spatial-frequency k-space data.

Theory and Methods

High- and low-spatial-frequency regions are defined in k-space based on the separation of wavelet subbands, and the conventional compressed sensing problem is transformed into one of localized k-space estimation. To better exploit wavelet-domain sparsity, compressed sensing can be used for high-spatial-frequency regions, whereas parallel imaging can be used for low-spatial-frequency regions. Fourier undersampling is also customized to better accommodate each reconstruction method: random undersampling for compressed sensing and regular undersampling for parallel imaging.


Examples using the proposed method demonstrate successful reconstruction of both low-spatial-frequency content and fine structures in high-resolution three-dimensional breast imaging with a net acceleration of 11–12.


The proposed method improves the reconstruction accuracy of high-spatial-frequency signal content and avoids incoherent artifacts in low-spatial-frequency regions. This new formulation also reduces the reconstruction time due to the smaller problem size. Magn Reson Med 70:1306–1318, 2013. © 2012 Wiley Periodicals, Inc.