Jordan Woehr1, Michael Smith1, 2
1Electrical and Computer Engineering, University of Calgary, Calgary, Alberta, Canada; 2Radiology, University of Calgary, Calgary, Alberta, Canada
Compressed sensing (CS) applied to under-sampled <i>k</i>-space is used in magnetic resonance to decrease 2D and 3D imaging times while maintaining image resolution. We present the Gardner transform (GT) as a potential sparsifying transform for use with CS with under-sampled or truncated signals in a non-<i>k</i>-space 4th dimension, e.g. time or frequency. New classes of signals can be sparsified with the GT such as sums of exponentials, Lorentzians, etc. We discuss the practical issues associated with GT-CS reconstruction of a simulated signal assumed to have two exponential components, MTTGM and MTTWM, and an ideal GT of two Dirac delta functions.